GiNaC Namespace Reference

Namespaces
namespace	internal

Classes
class	_numeric_digits
	This class is used to instantiate a global singleton object Digits which behaves just like Maple's Digits. More...
class	add
	Sum of expressions. More...
class	archive
	This class holds archived versions of GiNaC expressions (class ex). More...
class	archive_node
	This class stores all properties needed to record/retrieve the state of one object of class basic (or a derived class). More...
class	basic
	This class is the ABC (abstract base class) of GiNaC's class hierarchy. More...
class	basic_log_kernel
	The basic integration kernel with a logarithmic singularity at the origin. More...
class	basic_multi_iterator
	basic_multi_iterator is a base class. More...
class	basic_partition_generator
	Base class for generating all bounded combinatorial partitions of an integer n with exactly m parts in non-decreasing order. More...
class	class_info
class	clifford
	This class holds an object representing an element of the Clifford algebra (the Dirac gamma matrices). More...
class	cliffordunit
	This class represents the Clifford algebra generators (units). More...
class	color
	This class holds a generator T_a or the unity element of the Lie algebra of SU(3), as used for calculations in quantum chromodynamics. More...
class	compare_all_equal
	Comparison policy: all structures of one type are equal. More...
class	compare_bitwise
	Comparison policy: use bit-wise comparison to compare structures. More...
class	compare_std_less
	Comparison policy: use std::equal_to/std::less (defaults to operators == and <) to compare structures. More...
class	composition_generator
	Generate all compositions of a partition of an integer n, starting with the compositions which has non-decreasing order. More...
class	const_iterator
class	const_postorder_iterator
class	const_preorder_iterator
class	constant
	This class holds constants, symbols with specific numerical value. More...
class	container
	Wrapper template for making GiNaC classes out of STL containers. More...
class	container_storage
	Helper template for encapsulating the reserve() mechanics of STL containers. More...
struct	derivative_map_function
	Function object to be applied by basic::derivative(). More...
class	determinant_algo
	Switch to control algorithm for determinant computation. More...
class	diracgamma
	This class represents the Dirac gamma Lorentz vector. More...
class	diracgamma5
	This class represents the Dirac gamma5 object which anticommutates with all other gammas. More...
class	diracgammaL
	This class represents the Dirac gammaL object which behaves like 1/2 (1-gamma5). More...
class	diracgammaR
	This class represents the Dirac gammaL object which behaves like 1/2 (1+gamma5). More...
class	diracone
	This class represents the Clifford algebra unity element. More...
class	do_taylor
	Exception class thrown by classes which provide their own series expansion to signal that ordinary Taylor expansion is safe. More...
class	domain
	Domain of an object. More...
class	dunno
	Exception class thrown by functions to signal unimplemented functionality so the expression may just be .hold() More...
class	Ebar_kernel
	The Ebar-kernel. More...
class	Eisenstein_h_kernel
	The kernel corresponding to the Eisenstein series . More...
class	Eisenstein_kernel
	The kernel corresponding to the Eisenstein series . More...
class	ELi_kernel
	The ELi-kernel. More...
struct	error_and_integral
struct	error_and_integral_is_less
struct	eval_integ_map_function
	Function object to be applied by basic::eval_integ(). More...
struct	evalf_map_function
	Function object to be applied by basic::evalf(). More...
struct	evalm_map_function
	Function object to be applied by basic::evalm(). More...
class	ex
	Lightweight wrapper for GiNaC's symbolic objects. More...
struct	ex_base_is_less
struct	ex_is_equal
struct	ex_is_less
struct	ex_swap
class	expair
	A pair of expressions. More...
struct	expair_is_less
	Function object for insertion into third argument of STL's sort() etc. More...
struct	expair_rest_is_less
	Function object not caring about the numerical coefficients for insertion into third argument of STL's sort(). More...
struct	expair_swap
class	expairseq
	A sequence of class expair. More...
struct	expand_map_function
	Function object to be applied by basic::expand(). More...
class	expand_options
	Flags to control the behavior of expand(). More...
class	factor_options
	Flags to control the polynomial factorization. More...
class	fail
class	fderivative
	This class represents the (abstract) derivative of a symbolic function. More...
class	function
	The class function is used to implement builtin functions like sin, cos... and user defined functions. More...
class	function_options
class	G2_SERIAL
	Generalized multiple polylogarithm. More...
class	G3_SERIAL
	Generalized multiple polylogarithm with explicit imaginary parts. More...
struct	gcd_options
	Flags to control the behavior of gcd() and friends. More...
class	gcdheu_failed
	Exception thrown by heur_gcd() to signal failure. More...
class	has_distance
	SFINAE test for distance. More...
class	has_options
	Flags to control the behavior of has(). More...
class	idx
	This class holds one index of an indexed object. More...
struct	idx_is_equal_ignore_dim
class	indexed
	This class holds an indexed expression. More...
class	info_flags
	Possible attributes an object can have. More...
class	integral
	Symbolic integral. More...
class	integration_kernel
	The base class for integration kernels for iterated integrals. More...
struct	is_not_a_clifford
	Predicate for finding non-clifford objects. More...
struct	is_summation_idx
class	iterated_integral2_SERIAL
	Complete elliptic integral of the first kind. More...
class	iterated_integral3_SERIAL
	Iterated integral with explicit truncation. More...
class	Kronecker_dtau_kernel
	The kernel corresponding to integrating the Kronecker coefficient function in (or equivalently in ). More...
class	Kronecker_dz_kernel
	The kernel corresponding to integrating the Kronecker coefficient function in . More...
class	lanczos_coeffs
class	library_init
	Helper class to initialize the library. More...
class	make_flat_inserter
	Class to handle the renaming of dummy indices. More...
struct	map_function
	Function object for map(). More...
class	matrix
	Symbolic matrices. More...
class	minkmetric
	This class represents a Minkowski metric tensor. More...
class	modular_form_kernel
	A kernel corresponding to a polynomial in Eisenstein series. More...
class	mul
	Product of expressions. More...
class	multi_iterator_counter
	The class multi_iterator_counter defines a multi_iterator , such that. More...
class	multi_iterator_counter_indv
	The class multi_iterator_counter_indv defines a multi_iterator , such that. More...
class	multi_iterator_ordered
	The class multi_iterator_ordered defines a multi_iterator , such that. More...
class	multi_iterator_ordered_eq
	The class multi_iterator_ordered_eq defines a multi_iterator , such that. More...
class	multi_iterator_ordered_eq_indv
	The class multi_iterator_ordered_eq_indv defines a multi_iterator , such that. More...
class	multi_iterator_permutation
	The class multi_iterator_permutation defines a multi_iterator , for which. More...
class	multi_iterator_shuffle
	The class multi_iterator_shuffle defines a multi_iterator, which runs over all shuffles of a and b. More...
class	multi_iterator_shuffle_prime
	The class multi_iterator_shuffle_prime defines a multi_iterator, which runs over all shuffles of a and b, excluding the first one (a,b). More...
class	multiple_polylog_kernel
	The integration kernel for multiple polylogarithms. More...
class	ncmul
	Non-commutative product of expressions. More...
struct	normal_map_function
	Function object to be applied by basic::normal(). More...
class	numeric
	This class is a wrapper around CLN-numbers within the GiNaC class hierarchy. More...
struct	op0_is_equal
class	partition_generator
	Generate all bounded combinatorial partitions of an integer n with exactly m parts (not including zero parts) in non-decreasing order. More...
class	partition_with_zero_parts_generator
	Generate all bounded combinatorial partitions of an integer n with exactly m parts (including zero parts) in non-decreasing order. More...
class	pointer_to_map_function
class	pointer_to_map_function_1arg
class	pointer_to_map_function_2args
class	pointer_to_map_function_3args
class	pointer_to_member_to_map_function
class	pointer_to_member_to_map_function_1arg
class	pointer_to_member_to_map_function_2args
class	pointer_to_member_to_map_function_3args
class	pole_error
	Exception class thrown when a singularity is encountered. More...
class	possymbol
	Specialization of symbol to real positive domain. More...
class	power
	This class holds a two-component object, a basis and and exponent representing exponentiation. More...
class	print_context
	Base class for print_contexts. More...
class	print_context_options
	This class stores information about a registered print_context class. More...
class	print_csrc
	Base context for C source output. More...
class	print_csrc_cl_N
	Context for C source output using CLN numbers. More...
class	print_csrc_double
	Context for C source output using double precision. More...
class	print_csrc_float
	Context for C source output using float precision. More...
class	print_dflt
	Context for default (ginsh-parsable) output. More...
class	print_functor
	This class represents a print method for a certain algebraic class and print_context type. More...
class	print_functor_impl
	Base class for print_functor handlers. More...
class	print_latex
	Context for latex-parsable output. More...
class	print_memfun_handler
	print_functor handler for member functions of class T, context type C More...
class	print_options
	Flags to control the behavior of a print_context. More...
class	print_ptrfun_handler
	print_functor handler for pointer-to-functions of class T, context type C More...
class	print_python
	Context for python pretty-print output. More...
class	print_python_repr
	Context for python-parsable output. More...
class	print_tree
	Context for tree-like output for debugging. More...
class	pseries
	This class holds a extended truncated power series (positive and negative integer powers). More...
class	psi1_SERIAL
	Polylogarithm and multiple polylogarithm. More...
class	psi2_SERIAL
	Derivatives of Psi-function (aka polygamma-functions). More...
class	ptr
	Class of (intrusively) reference-counted pointers that support copy-on-write semantics. More...
class	realsymbol
	Specialization of symbol to real domain. More...
class	refcounted
	Base class for reference-counted objects. More...
class	registered_class_options
	This class stores information about a registered GiNaC class. More...
class	relational
	This class holds a relation consisting of two expressions and a logical relation between them. More...
class	remember_strategies
	Strategies how to clean up the function remember cache. More...
class	remember_table
	The remember table is organized like an n-fold associative cache in a microprocessor. More...
class	remember_table_entry
	A single entry in the remember table of a function. More...
class	remember_table_list
	A list of entries in the remember table having some least significant bits of the hashvalue in common. More...
struct	return_type_t
	To distinguish between different kinds of non-commutative objects. More...
class	return_types
class	scalar_products
	Helper class for storing information about known scalar products which are to be automatically replaced by simplify_indexed(). More...
class	series_options
	Flags to control series expansion. More...
class	solve_algo
	Switch to control algorithm for linear system solving. More...
class	spinidx
	This class holds a spinor index that can be dotted or undotted and that also has a variance. More...
class	spinmetric
	This class represents an antisymmetric spinor metric tensor which can be used to raise/lower indices of 2-component Weyl spinors. More...
class	spmapkey
class	status_flags
	Flags to store information about the state of an object. More...
class	structure
	Wrapper template for making GiNaC classes out of C++ structures. More...
class	su3d
	This class represents the tensor of symmetric su(3) structure constants. More...
class	su3f
	This class represents the tensor of antisymmetric su(3) structure constants. More...
class	su3one
	This class represents the su(3) unity element. More...
class	su3t
	This class represents an su(3) generator. More...
class	subs_options
	Flags to control the behavior of subs(). More...
class	sy_is_less
class	sy_swap
struct	sym_desc
	This structure holds information about the highest and lowest degrees in which a symbol appears in two multivariate polynomials "a" and "b". More...
class	symbol
	Basic CAS symbol. More...
class	symbolset
class	symmetry
	This class describes the symmetry of a group of indices. More...
class	symminfo
	This structure stores the individual symmetrized terms obtained during the simplification of sums. More...
class	symminfo_is_less_by_orig
class	symminfo_is_less_by_symmterm
class	tensdelta
	This class represents the delta tensor. More...
class	tensepsilon
	This class represents the totally antisymmetric epsilon tensor. More...
class	tensmetric
	This class represents a general metric tensor which can be used to raise/lower indices. More...
class	tensor
	This class holds one of GiNaC's predefined special tensors such as the delta and the metric tensors. More...
class	terminfo
	This structure stores the original and symmetrized versions of terms obtained during the simplification of sums. More...
class	terminfo_is_less
class	unarchive_table_t
class	user_defined_kernel
	A user-defined integration kernel. More...
class	varidx
	This class holds an index with a variance (co- or contravariant). More...
class	visitor
	Degenerate base class for visitors. More...
class	wildcard
	This class acts as a wildcard for subs(), match(), has() and find(). More...
class	zeta1_SERIAL
	Complex conjugate. More...
class	zeta2_SERIAL
	Alternating Euler sum or colored MZV. More...

Typedefs
typedef unsigned	archive_node_id
	Numerical ID value to refer to an archive_node.
typedef unsigned	archive_atom
	Numerical ID value to refer to a string.
typedef basic *(*	synthesize_func) ()
typedef std::map< std::string, synthesize_func >	unarchive_map_t
typedef std::vector< ex >	exvector
typedef std::set< ex, ex_is_less >	exset
typedef std::map< ex, ex, ex_is_less >	exmap
typedef ex(*	evalffunctype) ()
typedef double(*	FUNCP_1P) (double)
	Function pointer with one function parameter.
typedef double(*	FUNCP_2P) (double, double)
	Function pointer with two function parameters.
typedef void(*	FUNCP_CUBA) (const int *, const double[], const int *, double[])
	Function pointer for use with the CUBA library (http://www.feynarts.de/cuba).
typedef std::vector< expair >	epvector
	expair-vector
typedef epvector::iterator	epp
	expair-vector pointer
typedef container< std::vector >	exprseq
typedef std::multiset< unsigned >	paramset
typedef ex(*	eval_funcp) ()
typedef ex(*	evalf_funcp) ()
typedef ex(*	conjugate_funcp) ()
typedef ex(*	real_part_funcp) ()
typedef ex(*	imag_part_funcp) ()
typedef ex(*	expand_funcp) ()
typedef ex(*	derivative_funcp) ()
typedef ex(*	expl_derivative_funcp) ()
typedef ex(*	power_funcp) ()
typedef ex(*	series_funcp) ()
typedef void(*	print_funcp) ()
typedef bool(*	info_funcp) ()
typedef ex(*	eval_funcp_1) (const ex &)
typedef ex(*	evalf_funcp_1) (const ex &)
typedef ex(*	conjugate_funcp_1) (const ex &)
typedef ex(*	real_part_funcp_1) (const ex &)
typedef ex(*	imag_part_funcp_1) (const ex &)
typedef ex(*	expand_funcp_1) (const ex &, unsigned)
typedef ex(*	derivative_funcp_1) (const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_1) (const ex &, const symbol &)
typedef ex(*	power_funcp_1) (const ex &, const ex &)
typedef ex(*	series_funcp_1) (const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_1) (const ex &, const print_context &)
typedef bool(*	info_funcp_1) (const ex &, unsigned)
typedef ex(*	eval_funcp_2) (const ex &, const ex &)
typedef ex(*	evalf_funcp_2) (const ex &, const ex &)
typedef ex(*	conjugate_funcp_2) (const ex &, const ex &)
typedef ex(*	real_part_funcp_2) (const ex &, const ex &)
typedef ex(*	imag_part_funcp_2) (const ex &, const ex &)
typedef ex(*	expand_funcp_2) (const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_2) (const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_2) (const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_2) (const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_2) (const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_2) (const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_2) (const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_3) (const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_3) (const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_3) (const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_3) (const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_3) (const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_3) (const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_3) (const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_3) (const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_3) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_3) (const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_3) (const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_3) (const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_4) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_4) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_4) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_4) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_4) (const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_4) (const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_4) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_4) (const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_4) (const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	expand_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	expl_derivative_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)
typedef ex(*	power_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	series_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef void(*	print_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef bool(*	info_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)
typedef ex(*	eval_funcp_exvector) (const exvector &)
typedef ex(*	evalf_funcp_exvector) (const exvector &)
typedef ex(*	conjugate_funcp_exvector) (const exvector &)
typedef ex(*	real_part_funcp_exvector) (const exvector &)
typedef ex(*	imag_part_funcp_exvector) (const exvector &)
typedef ex(*	expand_funcp_exvector) (const exvector &, unsigned)
typedef ex(*	derivative_funcp_exvector) (const exvector &, unsigned)
typedef ex(*	expl_derivative_funcp_exvector) (const exvector &, const symbol &)
typedef ex(*	power_funcp_exvector) (const exvector &, const ex &)
typedef ex(*	series_funcp_exvector) (const exvector &, const relational &, int, unsigned)
typedef void(*	print_funcp_exvector) (const exvector &, const print_context &)
typedef bool(*	info_funcp_exvector) (const exvector &, unsigned)
template<typename T , class Hash = std::hash<ex>, class KeyEqual = std::equal_to<ex>, class Allocator = std::allocator<std::pair<const ex, T>>>
using	exhashmap = std::unordered_map< ex, T, Hash, KeyEqual, Allocator >
typedef std::map< spmapkey, ex >	spmap
typedef map< error_and_integral, ex, error_and_integral_is_less >	lookup_map
typedef container< std::list >	lst
typedef std::vector< std::size_t >	uintvector
typedef std::vector< unsigned >	unsignedvector
typedef std::vector< exvector >	exvectorvector
typedef std::vector< sym_desc >	sym_desc_vec
typedef void(*	digits_changed_callback) (long)
	Function pointer to implement callbacks in the case 'Digits' gets changed.
typedef class_info< print_context_options >	print_context_class_info
typedef class_info< registered_class_options >	registered_class_info

Enumerations
enum	{ callback_registered = 1 }

Functions
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (add, expairseq, print_func< print_context >(&add::do_print). print_func< print_latex >(&add::do_print_latex). print_func< print_csrc >(&add::do_print_csrc). print_func< print_tree >(&add::do_print_tree). print_func< print_python_repr >(&add::do_print_python_repr)) add
	GINAC_BIND_UNARCHIVER (add)
	GINAC_DECLARE_UNARCHIVER (add)
static void	write_unsigned (std::ostream &os, unsigned val)
	Write unsigned integer quantity to stream.
static unsigned	read_unsigned (std::istream &is)
	Read unsigned integer quantity from stream.
std::ostream &	operator<< (std::ostream &os, const archive_node &n)
	Write archive_node to binary data stream.
std::ostream &	operator<< (std::ostream &os, const archive &ar)
	Write archive to binary data stream.
std::istream &	operator>> (std::istream &is, archive_node &n)
	Read archive_node from binary data stream.
std::istream &	operator>> (std::istream &is, archive &ar)
	Read archive from binary data stream.
static synthesize_func	find_factory_fcn (const std::string &name)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (basic, void, print_func< print_context >(&basic::do_print). print_func< print_tree >(&basic::do_print_tree). print_func< print_python_repr >(&basic::do_print_python_repr)) basic
	basic copy constructor: implicitly assumes that the other class is of the exact same type (as it's used by duplicate()), so it can copy the tinfo_key and the hash value.
template<class T >
bool	is_a (const basic &obj)
	Check if obj is a T, including base classes.
template<class T >
bool	is_exactly_a (const basic &obj)
	Check if obj is a T, not including base classes.
template<class B , typename... Args>
B &	dynallocate (Args &&... args)
	Constructs a new (class basic or derived) B object on the heap.
template<class B >
B &	dynallocate (std::initializer_list< ex > il)
	Constructs a new (class basic or derived) B object on the heap.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (clifford, indexed, print_func< print_dflt >(&clifford::do_print_dflt). print_func< print_latex >(&clifford::do_print_latex). print_func< print_tree >(&clifford::do_print_tree)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone
	print_func< print_dflt > (&diracone::do_print). print_func< print_latex >(&diracone
	GINAC_BIND_UNARCHIVER (clifford)
	GINAC_BIND_UNARCHIVER (cliffordunit)
	GINAC_BIND_UNARCHIVER (diracone)
	GINAC_BIND_UNARCHIVER (diracgamma)
	GINAC_BIND_UNARCHIVER (diracgamma5)
	GINAC_BIND_UNARCHIVER (diracgammaL)
	GINAC_BIND_UNARCHIVER (diracgammaR)
static bool	is_dirac_slash (const ex &seq0)
static void	base_and_index (const ex &c, ex &b, ex &i)
	This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix)
ex	dirac_ONE (unsigned char rl=0)
	Create a Clifford unity object.
static unsigned	get_dim_uint (const ex &e)
ex	clifford_unit (const ex &mu, const ex &metr, unsigned char rl=0)
	Create a Clifford unit object.
ex	dirac_gamma (const ex &mu, unsigned char rl=0)
	Create a Dirac gamma object.
ex	dirac_gamma5 (unsigned char rl=0)
	Create a Dirac gamma5 object.
ex	dirac_gammaL (unsigned char rl=0)
	Create a Dirac gammaL object.
ex	dirac_gammaR (unsigned char rl=0)
	Create a Dirac gammaR object.
ex	dirac_slash (const ex &e, const ex &dim, unsigned char rl=0)
	Create a term of the form e_mu * gamma~mu with a unique index mu.
static unsigned char	get_representation_label (const return_type_t &ti)
	Extract representation label from tinfo key (as returned by return_type_tinfo()).
static ex	trace_string (exvector::const_iterator ix, size_t num)
	Take trace of a string of an even number of Dirac gammas given a vector of indices.
ex	dirac_trace (const ex &e, const std::set< unsigned char > &rls, const ex &trONE=4)
	Calculate dirac traces over the specified set of representation labels.
ex	dirac_trace (const ex &e, const lst &rll, const ex &trONE=4)
	Calculate dirac traces over the specified list of representation labels.
ex	dirac_trace (const ex &e, unsigned char rl=0, const ex &trONE=4)
	Calculate the trace of an expression containing gamma objects with a specified representation label.
ex	canonicalize_clifford (const ex &e)
	Bring all products of clifford objects in an expression into a canonical order.
ex	clifford_star_bar (const ex &e, bool do_bar, unsigned options)
	An auxillary function performing clifford_star() and clifford_bar().
ex	clifford_prime (const ex &e)
	Automorphism of the Clifford algebra, simply changes signs of all clifford units.
ex	remove_dirac_ONE (const ex &e, unsigned char rl=0, unsigned options=0)
	Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1.
int	clifford_max_label (const ex &e, bool ignore_ONE=false)
	Returns the maximal representation label of a clifford object if e contains at least one, otherwise returns -1.
ex	clifford_norm (const ex &e)
	Calculation of the norm in the Clifford algebra.
ex	clifford_inverse (const ex &e)
	Calculation of the inverse in the Clifford algebra.
ex	lst_to_clifford (const ex &v, const ex &mu, const ex &metr, unsigned char rl=0)
	List or vector conversion into the Clifford vector.
ex	lst_to_clifford (const ex &v, const ex &e)
	List or vector conversion into the Clifford vector.
static ex	get_clifford_comp (const ex &e, const ex &c, bool root=true)
	Auxiliary structure to define a function for striping one Clifford unit from vectors.
lst	clifford_to_lst (const ex &e, const ex &c, bool algebraic=true)
	An inverse function to lst_to_clifford().
ex	clifford_moebius_map (const ex &a, const ex &b, const ex &c, const ex &d, const ex &v, const ex &G, unsigned char rl=0)
	Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix (a b\c d) in linear spaces with arbitrary signature.
ex	clifford_moebius_map (const ex &M, const ex &v, const ex &G, unsigned char rl=0)
	The second form of Moebius transformations defined by a 2x2 Clifford matrix M This function takes the transformation matrix M as a single entity.
	GINAC_DECLARE_UNARCHIVER (clifford)
	GINAC_DECLARE_UNARCHIVER (diracone)
	GINAC_DECLARE_UNARCHIVER (cliffordunit)
	GINAC_DECLARE_UNARCHIVER (diracgamma)
	GINAC_DECLARE_UNARCHIVER (diracgamma5)
	GINAC_DECLARE_UNARCHIVER (diracgammaL)
	GINAC_DECLARE_UNARCHIVER (diracgammaR)
bool	is_clifford_tinfo (const return_type_t &ti)
	Check whether a given return_type_t object (as returned by return_type_tinfo() is that of a clifford object (with an arbitrary representation label).
ex	clifford_bar (const ex &e)
	Main anti-automorphism of the Clifford algebra: makes reversion and changes signs of all clifford units.
ex	clifford_star (const ex &e)
	Reversion of the Clifford algebra, reverse the order of all clifford units in ncmul.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (su3one, tensor, print_func< print_dflt >(&su3one::do_print). print_func< print_latex >(&su3one::do_print_latex)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t
	print_func< print_dflt > (&su3t::do_print). print_func< print_latex >(&su3t
	GINAC_BIND_UNARCHIVER (color)
	GINAC_BIND_UNARCHIVER (su3one)
	GINAC_BIND_UNARCHIVER (su3t)
	GINAC_BIND_UNARCHIVER (su3f)
	GINAC_BIND_UNARCHIVER (su3d)
static ex	permute_free_index_to_front (const exvector &iv3, const exvector &iv2, int &sig)
	Given a vector iv3 of three indices and a vector iv2 of two indices that is a subset of iv3, return the (free) index that is in iv3 but not in iv2 and the sign introduced by permuting that index to the front.
ex	color_ONE (unsigned char rl=0)
	Create the su(3) unity element.
ex	color_T (const ex &a, unsigned char rl=0)
	Create an su(3) generator.
ex	color_f (const ex &a, const ex &b, const ex &c)
	Create an su(3) antisymmetric structure constant.
ex	color_d (const ex &a, const ex &b, const ex &c)
	Create an su(3) symmetric structure constant.
ex	color_h (const ex &a, const ex &b, const ex &c)
	This returns the linear combination d.a.b.c+I*f.a.b.c.
static bool	is_color_tinfo (const return_type_t &ti)
	Check whether a given tinfo key (as returned by return_type_tinfo() is that of a color object (with an arbitrary representation label).
static unsigned char	get_representation_label (const return_type_t &ti)
	Extract representation label from tinfo key (as returned by return_type_tinfo()).
ex	color_trace (const ex &e, const std::set< unsigned char > &rls)
	Calculate color traces over the specified set of representation labels.
ex	color_trace (const ex &e, const lst &rll)
	Calculate color traces over the specified list of representation labels.
ex	color_trace (const ex &e, unsigned char rl=0)
	Calculate the trace of an expression containing color objects with a specified representation label.
	GINAC_DECLARE_UNARCHIVER (color)
	GINAC_DECLARE_UNARCHIVER (su3one)
	GINAC_DECLARE_UNARCHIVER (su3t)
	GINAC_DECLARE_UNARCHIVER (su3f)
	GINAC_DECLARE_UNARCHIVER (su3d)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (constant, basic, print_func< print_context >(&constant::do_print). print_func< print_latex >(&constant::do_print_latex). print_func< print_tree >(&constant::do_print_tree). print_func< print_python_repr >(&constant::do_print_python_repr)) const ant
	GINAC_BIND_UNARCHIVER (constant)
	GINAC_DECLARE_UNARCHIVER (constant)
static unsigned	crc32 (const char *c, const unsigned len, const unsigned crcinit)
bool	are_ex_trivially_equal (const ex &e1, const ex &e2)
	Compare two objects of class quickly without doing a deep tree traversal.
std::ostream &	operator<< (std::ostream &os, const exvector &e)
std::ostream &	operator<< (std::ostream &os, const exset &e)
std::ostream &	operator<< (std::ostream &os, const exmap &e)
size_t	nops (const ex &thisex)
ex	expand (const ex &thisex, unsigned options=0)
ex	conjugate (const ex &thisex)
ex	real_part (const ex &thisex)
ex	imag_part (const ex &thisex)
bool	has (const ex &thisex, const ex &pattern, unsigned options=0)
bool	find (const ex &thisex, const ex &pattern, exset &found)
bool	is_polynomial (const ex &thisex, const ex &vars)
int	degree (const ex &thisex, const ex &s)
int	ldegree (const ex &thisex, const ex &s)
ex	coeff (const ex &thisex, const ex &s, int n=1)
ex	numer (const ex &thisex)
ex	denom (const ex &thisex)
ex	numer_denom (const ex &thisex)
ex	normal (const ex &thisex)
ex	to_rational (const ex &thisex, exmap &repl)
ex	to_polynomial (const ex &thisex, exmap &repl)
ex	collect (const ex &thisex, const ex &s, bool distributed=false)
ex	eval (const ex &thisex)
ex	evalf (const ex &thisex)
ex	evalm (const ex &thisex)
ex	eval_integ (const ex &thisex)
ex	diff (const ex &thisex, const symbol &s, unsigned nth=1)
ex	series (const ex &thisex, const ex &r, int order, unsigned options=0)
bool	match (const ex &thisex, const ex &pattern, exmap &repl_lst)
ex	simplify_indexed (const ex &thisex, unsigned options=0)
ex	simplify_indexed (const ex &thisex, const scalar_products &sp, unsigned options=0)
ex	symmetrize (const ex &thisex)
ex	symmetrize (const ex &thisex, const lst &l)
ex	antisymmetrize (const ex &thisex)
ex	antisymmetrize (const ex &thisex, const lst &l)
ex	symmetrize_cyclic (const ex &thisex)
ex	symmetrize_cyclic (const ex &thisex, const lst &l)
ex	op (const ex &thisex, size_t i)
ex	lhs (const ex &thisex)
ex	rhs (const ex &thisex)
bool	is_zero (const ex &thisex)
void	swap (ex &e1, ex &e2)
ex	subs (const ex &thisex, const exmap &m, unsigned options=0)
ex	subs (const ex &thisex, const lst &ls, const lst &lr, unsigned options=0)
ex	subs (const ex &thisex, const ex &e, unsigned options=0)
template<class T >
bool	is_a (const ex &obj)
	Check if ex is a handle to a T, including base classes.
template<class T >
bool	is_exactly_a (const ex &obj)
	Check if ex is a handle to a T, not including base classes.
template<class T >
attribute_pure const T &	ex_to (const ex &e)
	Return a reference to the basic-derived class T object embedded in an expression.
void	compile_ex (const ex &expr, const symbol &sym, FUNCP_1P &fp, const std::string filename="")
	Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.
void	compile_ex (const ex &expr, const symbol &sym1, const symbol &sym2, FUNCP_2P &fp, const std::string filename="")
	Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.
void	compile_ex (const lst &exprs, const lst &syms, FUNCP_CUBA &fp, const std::string filename="")
	Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.
void	link_ex (const std::string filename, FUNCP_1P &fp)
	Opens an existing so-file and returns a function pointer of type FUNCP_1P to the contained function.
void	link_ex (const std::string filename, FUNCP_2P &fp)
	Opens an existing so-file and returns a function pointer of type FUNCP_2P to the contained function.
void	link_ex (const std::string filename, FUNCP_CUBA &fp)
	Opens an existing so-file and returns a function pointer of type FUNCP_CUBA to the contained function.
void	unlink_ex (const std::string filename)
	Closes all linked .so files that have the supplied filename.
void	swap (expair &e1, expair &e2)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (expairseq, basic, print_func< print_context >(&expairseq::do_print). print_func< print_tree >(&expairseq::do_print_tree)) class epp_is_less
epvector *	conjugateepvector (const epvector &)
	Complex conjugate every element of an epvector.
ex	factor (const ex &poly, unsigned options)
	Interface function to the outside world.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (fail, basic, print_func< print_context >(&fail::do_print). print_func< print_tree >(&fail::do_print_tree)) GINAC_BIND_UNARCHIVER(fail)
	GINAC_DECLARE_UNARCHIVER (fail)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (fderivative, function, print_func< print_context >(&fderivative::do_print). print_func< print_latex >(&fderivative::do_print_latex). print_func< print_csrc >(&fderivative::do_print_csrc). print_func< print_tree >(&fderivative::do_print_tree)) fderivative
	GINAC_BIND_UNARCHIVER (fderivative)
	GINAC_DECLARE_UNARCHIVER (fderivative)
	GINAC_BIND_UNARCHIVER (function)
	GINAC_DECLARE_UNARCHIVER (function)
template<typename T >
bool	is_the_function (const ex &x)
static unsigned	make_hash_seed (const std::type_info &tinfo)
	We need a hash function which gives different values for objects of different types.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (idx, basic, print_func< print_context >(&idx::do_print). print_func< print_latex >(&idx::do_print_latex). print_func< print_csrc >(&idx::do_print_csrc). print_func< print_tree >(&idx::do_print_tree)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx
	print_func< print_context > (&varidx::do_print). print_func< print_latex >(&varidx
	GINAC_BIND_UNARCHIVER (idx)
	GINAC_BIND_UNARCHIVER (varidx)
	GINAC_BIND_UNARCHIVER (spinidx)
bool	is_dummy_pair (const idx &i1, const idx &i2)
	Check whether two indices form a dummy pair.
bool	is_dummy_pair (const ex &e1, const ex &e2)
	Check whether two expressions form a dummy index pair.
void	find_free_and_dummy (exvector::const_iterator it, exvector::const_iterator itend, exvector &out_free, exvector &out_dummy)
	Given a vector of indices, split them into two vectors, one containing the free indices, the other containing the dummy indices (numeric indices are neither free nor dummy ones).
ex	minimal_dim (const ex &dim1, const ex &dim2)
	Return the minimum of two index dimensions.
	GINAC_DECLARE_UNARCHIVER (idx)
	GINAC_DECLARE_UNARCHIVER (varidx)
	GINAC_DECLARE_UNARCHIVER (spinidx)
void	find_free_and_dummy (const exvector &v, exvector &out_free, exvector &out_dummy)
	Given a vector of indices, split them into two vectors, one containing the free indices, the other containing the dummy indices (numeric indices are neither free nor dummy ones).
void	find_dummy_indices (const exvector &v, exvector &out_dummy)
	Given a vector of indices, find the dummy indices.
size_t	count_dummy_indices (const exvector &v)
	Count the number of dummy index pairs in an index vector.
size_t	count_free_indices (const exvector &v)
	Count the number of dummy index pairs in an index vector.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (indexed, exprseq, print_func< print_context >(&indexed::do_print). print_func< print_latex >(&indexed::do_print_latex). print_func< print_tree >(&indexed::do_print_tree)) indexed
	GINAC_BIND_UNARCHIVER (indexed)
static bool	indices_consistent (const exvector &v1, const exvector &v2)
	Check whether two sorted index vectors are consistent (i.e.
template<class T >
size_t	number_of_type (const exvector &v)
template<class T >
static ex	rename_dummy_indices (const ex &e, exvector &global_dummy_indices, exvector &local_dummy_indices)
	Rename dummy indices in an expression.
static void	find_variant_indices (const exvector &v, exvector &variant_indices)
	Given a set of indices, extract those of class varidx.
bool	reposition_dummy_indices (ex &e, exvector &variant_dummy_indices, exvector &moved_indices)
	Raise/lower dummy indices in a single indexed objects to canonicalize their variance.
static void	product_to_exvector (const ex &e, exvector &v, bool &non_commutative)
template<class T >
ex	idx_symmetrization (const ex &r, const exvector &local_dummy_indices)
ex	simplify_indexed (const ex &e, exvector &free_indices, exvector &dummy_indices, const scalar_products &sp)
	Simplify indexed expression, return list of free indices.
ex	simplify_indexed_product (const ex &e, exvector &free_indices, exvector &dummy_indices, const scalar_products &sp)
	Simplify product of indexed expressions (commutative, noncommutative and simple squares), return list of free indices.
bool	hasindex (const ex &x, const ex &sym)
exvector	get_all_dummy_indices_safely (const ex &e)
	More reliable version of the form.
exvector	get_all_dummy_indices (const ex &e)
	Returns all dummy indices from the exvector.
lst	rename_dummy_indices_uniquely (const exvector &va, const exvector &vb)
	Similar to above, where va and vb are the same and the return value is a list of two lists for substitution in b.
ex	rename_dummy_indices_uniquely (const exvector &va, const exvector &vb, const ex &b)
	Same as above, where va and vb contain the indices of a and b and are sorted.
ex	rename_dummy_indices_uniquely (const ex &a, const ex &b)
	Returns b with all dummy indices, which are common with a, renamed.
ex	rename_dummy_indices_uniquely (exvector &va, const ex &b, bool modify_va=false)
	Returns b with all dummy indices, which are listed in va, renamed if modify_va is set to TRUE all dummy indices of b will be appended to va.
ex	expand_dummy_sum (const ex &e, bool subs_idx=false)
	This function returns the given expression with expanded sums for all dummy index summations, where the dimensionality of the dummy index is a nonnegative integer.
	GINAC_DECLARE_UNARCHIVER (indexed)
static ex	conjugate_evalf (const ex &arg)
static ex	conjugate_eval (const ex &arg)
static void	conjugate_print_latex (const ex &arg, const print_context &c)
static ex	conjugate_conjugate (const ex &arg)
static ex	conjugate_expl_derivative (const ex &arg, const symbol &s)
static ex	conjugate_real_part (const ex &arg)
static ex	conjugate_imag_part (const ex &arg)
static bool	func_arg_info (const ex &arg, unsigned inf)
static bool	conjugate_info (const ex &arg, unsigned inf)
	REGISTER_FUNCTION (conjugate_function, eval_func(conjugate_eval). evalf_func(conjugate_evalf). expl_derivative_func(conjugate_expl_derivative). info_func(conjugate_info). print_func< print_latex >(conjugate_print_latex). conjugate_func(conjugate_conjugate). real_part_func(conjugate_real_part). imag_part_func(conjugate_imag_part). set_name("conjugate","conjugate"))
static ex	real_part_evalf (const ex &arg)
static ex	real_part_eval (const ex &arg)
static void	real_part_print_latex (const ex &arg, const print_context &c)
static ex	real_part_conjugate (const ex &arg)
static ex	real_part_real_part (const ex &arg)
static ex	real_part_imag_part (const ex &arg)
static ex	real_part_expl_derivative (const ex &arg, const symbol &s)
	REGISTER_FUNCTION (real_part_function, eval_func(real_part_eval). evalf_func(real_part_evalf). expl_derivative_func(real_part_expl_derivative). print_func< print_latex >(real_part_print_latex). conjugate_func(real_part_conjugate). real_part_func(real_part_real_part). imag_part_func(real_part_imag_part). set_name("real_part","real_part"))
static ex	imag_part_evalf (const ex &arg)
static ex	imag_part_eval (const ex &arg)
static void	imag_part_print_latex (const ex &arg, const print_context &c)
static ex	imag_part_conjugate (const ex &arg)
static ex	imag_part_real_part (const ex &arg)
static ex	imag_part_imag_part (const ex &arg)
static ex	imag_part_expl_derivative (const ex &arg, const symbol &s)
	REGISTER_FUNCTION (imag_part_function, eval_func(imag_part_eval). evalf_func(imag_part_evalf). expl_derivative_func(imag_part_expl_derivative). print_func< print_latex >(imag_part_print_latex). conjugate_func(imag_part_conjugate). real_part_func(imag_part_real_part). imag_part_func(imag_part_imag_part). set_name("imag_part","imag_part"))
static ex	abs_evalf (const ex &arg)
static ex	abs_eval (const ex &arg)
static ex	abs_expand (const ex &arg, unsigned options)
static ex	abs_expl_derivative (const ex &arg, const symbol &s)
static void	abs_print_latex (const ex &arg, const print_context &c)
static void	abs_print_csrc_float (const ex &arg, const print_context &c)
static ex	abs_conjugate (const ex &arg)
static ex	abs_real_part (const ex &arg)
static ex	abs_imag_part (const ex &arg)
static ex	abs_power (const ex &arg, const ex &exp)
bool	abs_info (const ex &arg, unsigned inf)
	REGISTER_FUNCTION (abs, eval_func(abs_eval). evalf_func(abs_evalf). expand_func(abs_expand). expl_derivative_func(abs_expl_derivative). info_func(abs_info). print_func< print_latex >(abs_print_latex). print_func< print_csrc_float >(abs_print_csrc_float). print_func< print_csrc_double >(abs_print_csrc_float). conjugate_func(abs_conjugate). real_part_func(abs_real_part). imag_part_func(abs_imag_part). power_func(abs_power))
static ex	step_evalf (const ex &arg)
static ex	step_eval (const ex &arg)
static ex	step_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	step_conjugate (const ex &arg)
static ex	step_real_part (const ex &arg)
static ex	step_imag_part (const ex &arg)
	REGISTER_FUNCTION (step, eval_func(step_eval). evalf_func(step_evalf). series_func(step_series). conjugate_func(step_conjugate). real_part_func(step_real_part). imag_part_func(step_imag_part))
static ex	csgn_evalf (const ex &arg)
static ex	csgn_eval (const ex &arg)
static ex	csgn_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	csgn_conjugate (const ex &arg)
static ex	csgn_real_part (const ex &arg)
static ex	csgn_imag_part (const ex &arg)
static ex	csgn_power (const ex &arg, const ex &exp)
	REGISTER_FUNCTION (csgn, eval_func(csgn_eval). evalf_func(csgn_evalf). series_func(csgn_series). conjugate_func(csgn_conjugate). real_part_func(csgn_real_part). imag_part_func(csgn_imag_part). power_func(csgn_power))
static ex	eta_evalf (const ex &x, const ex &y)
static ex	eta_eval (const ex &x, const ex &y)
static ex	eta_series (const ex &x, const ex &y, const relational &rel, int order, unsigned options)
static ex	eta_conjugate (const ex &x, const ex &y)
static ex	eta_real_part (const ex &x, const ex &y)
static ex	eta_imag_part (const ex &x, const ex &y)
	REGISTER_FUNCTION (eta, eval_func(eta_eval). evalf_func(eta_evalf). series_func(eta_series). latex_name("\\eta"). set_symmetry(sy_symm(0, 1)). conjugate_func(eta_conjugate). real_part_func(eta_real_part). imag_part_func(eta_imag_part))
static ex	Li2_evalf (const ex &x)
static ex	Li2_eval (const ex &x)
static ex	Li2_deriv (const ex &x, unsigned deriv_param)
static ex	Li2_series (const ex &x, const relational &rel, int order, unsigned options)
static ex	Li2_conjugate (const ex &x)
	REGISTER_FUNCTION (Li2, eval_func(Li2_eval). evalf_func(Li2_evalf). derivative_func(Li2_deriv). series_func(Li2_series). conjugate_func(Li2_conjugate). latex_name("\\mathrm{Li}_2"))
static ex	Li3_eval (const ex &x)
	REGISTER_FUNCTION (Li3, eval_func(Li3_eval). latex_name("\\mathrm{Li}_3"))
static ex	zetaderiv_eval (const ex &n, const ex &x)
static ex	zetaderiv_deriv (const ex &n, const ex &x, unsigned deriv_param)
	REGISTER_FUNCTION (zetaderiv, eval_func(zetaderiv_eval). derivative_func(zetaderiv_deriv). latex_name("\\zeta^\\prime"))
static ex	factorial_evalf (const ex &x)
static ex	factorial_eval (const ex &x)
static void	factorial_print_dflt_latex (const ex &x, const print_context &c)
static ex	factorial_conjugate (const ex &x)
static ex	factorial_real_part (const ex &x)
static ex	factorial_imag_part (const ex &x)
	REGISTER_FUNCTION (factorial, eval_func(factorial_eval). evalf_func(factorial_evalf). print_func< print_dflt >(factorial_print_dflt_latex). print_func< print_latex >(factorial_print_dflt_latex). conjugate_func(factorial_conjugate). real_part_func(factorial_real_part). imag_part_func(factorial_imag_part))
static ex	binomial_evalf (const ex &x, const ex &y)
static ex	binomial_sym (const ex &x, const numeric &y)
static ex	binomial_eval (const ex &x, const ex &y)
static ex	binomial_conjugate (const ex &x, const ex &y)
static ex	binomial_real_part (const ex &x, const ex &y)
static ex	binomial_imag_part (const ex &x, const ex &y)
	REGISTER_FUNCTION (binomial, eval_func(binomial_eval). evalf_func(binomial_evalf). conjugate_func(binomial_conjugate). real_part_func(binomial_real_part). imag_part_func(binomial_imag_part))
static ex	Order_eval (const ex &x)
static ex	Order_series (const ex &x, const relational &r, int order, unsigned options)
static ex	Order_conjugate (const ex &x)
static ex	Order_real_part (const ex &x)
static ex	Order_imag_part (const ex &x)
static ex	Order_power (const ex &x, const ex &e)
static ex	Order_expl_derivative (const ex &arg, const symbol &s)
	REGISTER_FUNCTION (Order, eval_func(Order_eval). series_func(Order_series). latex_name("\\mathcal{O}"). expl_derivative_func(Order_expl_derivative). conjugate_func(Order_conjugate). real_part_func(Order_real_part). imag_part_func(Order_imag_part). power_func(Order_power))
ex	lsolve (const ex &eqns, const ex &symbols, unsigned options=solve_algo::automatic)
	Factorial function.
const numeric	fsolve (const ex &f, const symbol &x, const numeric &x1, const numeric &x2)
	Find a real root of real-valued function f(x) numerically within a given interval.
template<typename T1 >
function	zeta (const T1 &p1)
template<typename T1 , typename T2 >
function	zeta (const T1 &p1, const T2 &p2)
template<>
bool	is_the_function< zeta_SERIAL > (const ex &x)
template<typename T1 , typename T2 >
function	G (const T1 &x, const T2 &y)
template<typename T1 , typename T2 , typename T3 >
function	G (const T1 &x, const T2 &s, const T3 &y)
template<>
bool	is_the_function< G_SERIAL > (const ex &x)
template<typename T1 >
function	psi (const T1 &p1)
template<typename T1 , typename T2 >
function	psi (const T1 &p1, const T2 &p2)
template<>
bool	is_the_function< psi_SERIAL > (const ex &x)
template<typename T1 , typename T2 >
function	iterated_integral (const T1 &kernel_lst, const T2 &lambda)
template<typename T1 , typename T2 , typename T3 >
function	iterated_integral (const T1 &kernel_lst, const T2 &lambda, const T3 &N_trunc)
template<>
bool	is_the_function< iterated_integral_SERIAL > (const ex &x)
bool	is_order_function (const ex &e)
	Check whether a function is the Order (O(n)) function.
ex	convert_H_to_Li (const ex &parameterlst, const ex &arg)
	Converts a given list containing parameters for H in Remiddi/Vermaseren notation into the corresponding GiNaC functions.
static ex	EllipticK_evalf (const ex &k)
static ex	EllipticK_eval (const ex &k)
static ex	EllipticK_deriv (const ex &k, unsigned deriv_param)
static ex	EllipticK_series (const ex &k, const relational &rel, int order, unsigned options)
static void	EllipticK_print_latex (const ex &k, const print_context &c)
	REGISTER_FUNCTION (EllipticK, evalf_func(EllipticK_evalf). eval_func(EllipticK_eval). derivative_func(EllipticK_deriv). series_func(EllipticK_series). print_func< print_latex >(EllipticK_print_latex). do_not_evalf_params())
static ex	EllipticE_evalf (const ex &k)
static ex	EllipticE_eval (const ex &k)
static ex	EllipticE_deriv (const ex &k, unsigned deriv_param)
static ex	EllipticE_series (const ex &k, const relational &rel, int order, unsigned options)
static void	EllipticE_print_latex (const ex &k, const print_context &c)
	REGISTER_FUNCTION (EllipticE, evalf_func(EllipticE_evalf). eval_func(EllipticE_eval). derivative_func(EllipticE_deriv). series_func(EllipticE_series). print_func< print_latex >(EllipticE_print_latex). do_not_evalf_params())
static ex	iterated_integral_evalf_impl (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)
static ex	iterated_integral2_evalf (const ex &kernel_lst, const ex &lambda)
static ex	iterated_integral3_evalf (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)
static ex	iterated_integral2_eval (const ex &kernel_lst, const ex &lambda)
static ex	iterated_integral3_eval (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)
static ex	lgamma_evalf (const ex &x)
static ex	lgamma_eval (const ex &x)
	Evaluation of lgamma(x), the natural logarithm of the Gamma function.
static ex	lgamma_deriv (const ex &x, unsigned deriv_param)
static ex	lgamma_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	lgamma_conjugate (const ex &x)
	REGISTER_FUNCTION (lgamma, eval_func(lgamma_eval). evalf_func(lgamma_evalf). derivative_func(lgamma_deriv). series_func(lgamma_series). conjugate_func(lgamma_conjugate). latex_name("\\log \\Gamma"))
static ex	tgamma_evalf (const ex &x)
static ex	tgamma_eval (const ex &x)
	Evaluation of tgamma(x), the true Gamma function.
static ex	tgamma_deriv (const ex &x, unsigned deriv_param)
static ex	tgamma_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	tgamma_conjugate (const ex &x)
	REGISTER_FUNCTION (tgamma, eval_func(tgamma_eval). evalf_func(tgamma_evalf). derivative_func(tgamma_deriv). series_func(tgamma_series). conjugate_func(tgamma_conjugate). latex_name("\\Gamma"))
static ex	beta_evalf (const ex &x, const ex &y)
static ex	beta_eval (const ex &x, const ex &y)
static ex	beta_deriv (const ex &x, const ex &y, unsigned deriv_param)
static ex	beta_series (const ex &arg1, const ex &arg2, const relational &rel, int order, unsigned options)
	REGISTER_FUNCTION (beta, eval_func(beta_eval). evalf_func(beta_evalf). derivative_func(beta_deriv). series_func(beta_series). latex_name("\\mathrm{B}"). set_symmetry(sy_symm(0, 1)))
static ex	psi1_evalf (const ex &x)
static ex	psi1_eval (const ex &x)
	Evaluation of digamma-function psi(x).
static ex	psi1_deriv (const ex &x, unsigned deriv_param)
static ex	psi1_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	psi2_evalf (const ex &n, const ex &x)
static ex	psi2_eval (const ex &n, const ex &x)
	Evaluation of polygamma-function psi(n,x).
static ex	psi2_deriv (const ex &n, const ex &x, unsigned deriv_param)
static ex	psi2_series (const ex &n, const ex &arg, const relational &rel, int order, unsigned options)
static ex	G2_evalf (const ex &x_, const ex &y)
static ex	G2_eval (const ex &x_, const ex &y)
static ex	G3_evalf (const ex &x_, const ex &s_, const ex &y)
static ex	G3_eval (const ex &x_, const ex &s_, const ex &y)
static ex	Li_evalf (const ex &m_, const ex &x_)
static ex	Li_eval (const ex &m_, const ex &x_)
static ex	Li_series (const ex &m, const ex &x, const relational &rel, int order, unsigned options)
static ex	Li_deriv (const ex &m_, const ex &x_, unsigned deriv_param)
static void	Li_print_latex (const ex &m_, const ex &x_, const print_context &c)
	REGISTER_FUNCTION (Li, evalf_func(Li_evalf). eval_func(Li_eval). series_func(Li_series). derivative_func(Li_deriv). print_func< print_latex >(Li_print_latex). do_not_evalf_params())
static ex	S_evalf (const ex &n, const ex &p, const ex &x)
static ex	S_eval (const ex &n, const ex &p, const ex &x)
static ex	S_series (const ex &n, const ex &p, const ex &x, const relational &rel, int order, unsigned options)
static ex	S_deriv (const ex &n, const ex &p, const ex &x, unsigned deriv_param)
static void	S_print_latex (const ex &n, const ex &p, const ex &x, const print_context &c)
	REGISTER_FUNCTION (S, evalf_func(S_evalf). eval_func(S_eval). series_func(S_series). derivative_func(S_deriv). print_func< print_latex >(S_print_latex). do_not_evalf_params())
static ex	H_evalf (const ex &x1, const ex &x2)
static ex	H_eval (const ex &m_, const ex &x)
static ex	H_series (const ex &m, const ex &x, const relational &rel, int order, unsigned options)
static ex	H_deriv (const ex &m_, const ex &x, unsigned deriv_param)
static void	H_print_latex (const ex &m_, const ex &x, const print_context &c)
	REGISTER_FUNCTION (H, evalf_func(H_evalf). eval_func(H_eval). series_func(H_series). derivative_func(H_deriv). print_func< print_latex >(H_print_latex). do_not_evalf_params())
static ex	zeta1_evalf (const ex &x)
static ex	zeta1_eval (const ex &m)
static ex	zeta1_deriv (const ex &m, unsigned deriv_param)
static void	zeta1_print_latex (const ex &m_, const print_context &c)
static ex	zeta2_evalf (const ex &x, const ex &s)
static ex	zeta2_eval (const ex &m, const ex &s_)
static ex	zeta2_deriv (const ex &m, const ex &s, unsigned deriv_param)
static void	zeta2_print_latex (const ex &m_, const ex &s_, const print_context &c)
static ex	exp_evalf (const ex &x)
static ex	exp_eval (const ex &x)
static ex	exp_expand (const ex &arg, unsigned options)
static ex	exp_deriv (const ex &x, unsigned deriv_param)
static ex	exp_real_part (const ex &x)
static ex	exp_imag_part (const ex &x)
static ex	exp_conjugate (const ex &x)
static ex	exp_power (const ex &x, const ex &a)
static bool	exp_info (const ex &x, unsigned inf)
	REGISTER_FUNCTION (exp, eval_func(exp_eval). evalf_func(exp_evalf). info_func(exp_info). expand_func(exp_expand). derivative_func(exp_deriv). real_part_func(exp_real_part). imag_part_func(exp_imag_part). conjugate_func(exp_conjugate). power_func(exp_power). latex_name("\\exp"))
static ex	log_evalf (const ex &x)
static ex	log_eval (const ex &x)
static ex	log_deriv (const ex &x, unsigned deriv_param)
static ex	log_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	log_real_part (const ex &x)
static ex	log_imag_part (const ex &x)
static ex	log_expand (const ex &arg, unsigned options)
static ex	log_conjugate (const ex &x)
static bool	log_info (const ex &x, unsigned inf)
	REGISTER_FUNCTION (log, eval_func(log_eval). evalf_func(log_evalf). info_func(log_info). expand_func(log_expand). derivative_func(log_deriv). series_func(log_series). real_part_func(log_real_part). imag_part_func(log_imag_part). conjugate_func(log_conjugate). latex_name("\\ln"))
static ex	sin_evalf (const ex &x)
static ex	sin_eval (const ex &x)
static ex	sin_deriv (const ex &x, unsigned deriv_param)
static ex	sin_real_part (const ex &x)
static ex	sin_imag_part (const ex &x)
static ex	sin_conjugate (const ex &x)
static bool	trig_info (const ex &x, unsigned inf)
	REGISTER_FUNCTION (sin, eval_func(sin_eval). evalf_func(sin_evalf). info_func(trig_info). derivative_func(sin_deriv). real_part_func(sin_real_part). imag_part_func(sin_imag_part). conjugate_func(sin_conjugate). latex_name("\\sin"))
static ex	cos_evalf (const ex &x)
static ex	cos_eval (const ex &x)
static ex	cos_deriv (const ex &x, unsigned deriv_param)
static ex	cos_real_part (const ex &x)
static ex	cos_imag_part (const ex &x)
static ex	cos_conjugate (const ex &x)
	REGISTER_FUNCTION (cos, eval_func(cos_eval). info_func(trig_info). evalf_func(cos_evalf). derivative_func(cos_deriv). real_part_func(cos_real_part). imag_part_func(cos_imag_part). conjugate_func(cos_conjugate). latex_name("\\cos"))
static ex	tan_evalf (const ex &x)
static ex	tan_eval (const ex &x)
static ex	tan_deriv (const ex &x, unsigned deriv_param)
static ex	tan_real_part (const ex &x)
static ex	tan_imag_part (const ex &x)
static ex	tan_series (const ex &x, const relational &rel, int order, unsigned options)
static ex	tan_conjugate (const ex &x)
	REGISTER_FUNCTION (tan, eval_func(tan_eval). evalf_func(tan_evalf). info_func(trig_info). derivative_func(tan_deriv). series_func(tan_series). real_part_func(tan_real_part). imag_part_func(tan_imag_part). conjugate_func(tan_conjugate). latex_name("\\tan"))
static ex	asin_evalf (const ex &x)
static ex	asin_eval (const ex &x)
static ex	asin_deriv (const ex &x, unsigned deriv_param)
static ex	asin_conjugate (const ex &x)
static bool	asin_info (const ex &x, unsigned inf)
	REGISTER_FUNCTION (asin, eval_func(asin_eval). evalf_func(asin_evalf). info_func(asin_info). derivative_func(asin_deriv). conjugate_func(asin_conjugate). latex_name("\\arcsin"))
static ex	acos_evalf (const ex &x)
static ex	acos_eval (const ex &x)
static ex	acos_deriv (const ex &x, unsigned deriv_param)
static ex	acos_conjugate (const ex &x)
	REGISTER_FUNCTION (acos, eval_func(acos_eval). evalf_func(acos_evalf). info_func(asin_info). derivative_func(acos_deriv). conjugate_func(acos_conjugate). latex_name("\\arccos"))
static ex	atan_evalf (const ex &x)
static ex	atan_eval (const ex &x)
static ex	atan_deriv (const ex &x, unsigned deriv_param)
static ex	atan_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	atan_conjugate (const ex &x)
static bool	atan_info (const ex &x, unsigned inf)
	REGISTER_FUNCTION (atan, eval_func(atan_eval). evalf_func(atan_evalf). info_func(atan_info). derivative_func(atan_deriv). series_func(atan_series). conjugate_func(atan_conjugate). latex_name("\\arctan"))
static ex	atan2_evalf (const ex &y, const ex &x)
static ex	atan2_eval (const ex &y, const ex &x)
static ex	atan2_deriv (const ex &y, const ex &x, unsigned deriv_param)
static bool	atan2_info (const ex &y, const ex &x, unsigned inf)
	REGISTER_FUNCTION (atan2, eval_func(atan2_eval). evalf_func(atan2_evalf). info_func(atan2_info). evalf_func(atan2_evalf). derivative_func(atan2_deriv))
static ex	sinh_evalf (const ex &x)
static ex	sinh_eval (const ex &x)
static ex	sinh_deriv (const ex &x, unsigned deriv_param)
static ex	sinh_real_part (const ex &x)
static ex	sinh_imag_part (const ex &x)
static ex	sinh_conjugate (const ex &x)
	REGISTER_FUNCTION (sinh, eval_func(sinh_eval). evalf_func(sinh_evalf). info_func(atan_info). derivative_func(sinh_deriv). real_part_func(sinh_real_part). imag_part_func(sinh_imag_part). conjugate_func(sinh_conjugate). latex_name("\\sinh"))
static ex	cosh_evalf (const ex &x)
static ex	cosh_eval (const ex &x)
static ex	cosh_deriv (const ex &x, unsigned deriv_param)
static ex	cosh_real_part (const ex &x)
static ex	cosh_imag_part (const ex &x)
static ex	cosh_conjugate (const ex &x)
	REGISTER_FUNCTION (cosh, eval_func(cosh_eval). evalf_func(cosh_evalf). info_func(exp_info). derivative_func(cosh_deriv). real_part_func(cosh_real_part). imag_part_func(cosh_imag_part). conjugate_func(cosh_conjugate). latex_name("\\cosh"))
static ex	tanh_evalf (const ex &x)
static ex	tanh_eval (const ex &x)
static ex	tanh_deriv (const ex &x, unsigned deriv_param)
static ex	tanh_series (const ex &x, const relational &rel, int order, unsigned options)
static ex	tanh_real_part (const ex &x)
static ex	tanh_imag_part (const ex &x)
static ex	tanh_conjugate (const ex &x)
	REGISTER_FUNCTION (tanh, eval_func(tanh_eval). evalf_func(tanh_evalf). info_func(atan_info). derivative_func(tanh_deriv). series_func(tanh_series). real_part_func(tanh_real_part). imag_part_func(tanh_imag_part). conjugate_func(tanh_conjugate). latex_name("\\tanh"))
static ex	asinh_evalf (const ex &x)
static ex	asinh_eval (const ex &x)
static ex	asinh_deriv (const ex &x, unsigned deriv_param)
static ex	asinh_conjugate (const ex &x)
	REGISTER_FUNCTION (asinh, eval_func(asinh_eval). evalf_func(asinh_evalf). info_func(atan_info). derivative_func(asinh_deriv). conjugate_func(asinh_conjugate))
static ex	acosh_evalf (const ex &x)
static ex	acosh_eval (const ex &x)
static ex	acosh_deriv (const ex &x, unsigned deriv_param)
static ex	acosh_conjugate (const ex &x)
	REGISTER_FUNCTION (acosh, eval_func(acosh_eval). evalf_func(acosh_evalf). info_func(asin_info). derivative_func(acosh_deriv). conjugate_func(acosh_conjugate))
static ex	atanh_evalf (const ex &x)
static ex	atanh_eval (const ex &x)
static ex	atanh_deriv (const ex &x, unsigned deriv_param)
static ex	atanh_series (const ex &arg, const relational &rel, int order, unsigned options)
static ex	atanh_conjugate (const ex &x)
	REGISTER_FUNCTION (atanh, eval_func(atanh_eval). evalf_func(atanh_evalf). info_func(asin_info). derivative_func(atanh_deriv). series_func(atanh_series). conjugate_func(atanh_conjugate))
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (integral, basic, print_func< print_dflt >(&integral::do_print). print_func< print_python >(&integral::do_print). print_func< print_latex >(&integral::do_print_latex)) integral
ex	subsvalue (const ex &var, const ex &value, const ex &fun)
ex	adaptivesimpson (const ex &x, const ex &a_in, const ex &b_in, const ex &f, const ex &error)
	Numeric integration routine based upon the "Adaptive Quadrature" one in "Numerical Analysis" by Burden and Faires.
	GINAC_BIND_UNARCHIVER (integral)
	GINAC_DECLARE_UNARCHIVER (integral)
ex	ifactor (const numeric &n)
	Returns the decomposition of the positive integer n into prime numbers in the form lst( lst(p1,...,pr), lst(a1,...,ar) ) such that n = p1^a1 ... pr^ar.
bool	is_discriminant_of_quadratic_number_field (const numeric &n)
	Returns true if the integer n is either one or the discriminant of a quadratic number field.
numeric	kronecker_symbol (const numeric &a, const numeric &n)
	Returns the Kronecker symbol a: integer n: integer.
numeric	primitive_dirichlet_character (const numeric &n, const numeric &a)
	Defines a primitive Dirichlet character through the Kronecker symbol.
numeric	dirichlet_character (const numeric &n, const numeric &a, const numeric &N)
	Defines a Dirichlet character through the Kronecker symbol.
numeric	generalised_Bernoulli_number (const numeric &k, const numeric &b)
	The generalised Bernoulli number.
ex	Bernoulli_polynomial (const numeric &k, const ex &x)
	The Bernoulli polynomials.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (integration_kernel, basic, print_func< print_context >(&integration_kernel::do_print)) integration_kernel
	GINAC_BIND_UNARCHIVER (integration_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (basic_log_kernel, integration_kernel, print_func< print_context >(&basic_log_kernel::do_print)) basic_log_kernel
	GINAC_BIND_UNARCHIVER (basic_log_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (multiple_polylog_kernel, integration_kernel, print_func< print_context >(&multiple_polylog_kernel::do_print)) multiple_polylog_kernel
	GINAC_BIND_UNARCHIVER (multiple_polylog_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (ELi_kernel, integration_kernel, print_func< print_context >(&ELi_kernel::do_print)) ELi_kernel
	GINAC_BIND_UNARCHIVER (ELi_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (Ebar_kernel, integration_kernel, print_func< print_context >(&Ebar_kernel::do_print)) Ebar_kernel
	GINAC_BIND_UNARCHIVER (Ebar_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (Kronecker_dtau_kernel, integration_kernel, print_func< print_context >(&Kronecker_dtau_kernel::do_print)) Kronecker_dtau_kernel
	GINAC_BIND_UNARCHIVER (Kronecker_dtau_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (Kronecker_dz_kernel, integration_kernel, print_func< print_context >(&Kronecker_dz_kernel::do_print)) Kronecker_dz_kernel
	GINAC_BIND_UNARCHIVER (Kronecker_dz_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (Eisenstein_kernel, integration_kernel, print_func< print_context >(&Eisenstein_kernel::do_print)) Eisenstein_kernel
	GINAC_BIND_UNARCHIVER (Eisenstein_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (Eisenstein_h_kernel, integration_kernel, print_func< print_context >(&Eisenstein_h_kernel::do_print)) Eisenstein_h_kernel
	GINAC_BIND_UNARCHIVER (Eisenstein_h_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (modular_form_kernel, integration_kernel, print_func< print_context >(&modular_form_kernel::do_print)) modular_form_kernel
	GINAC_BIND_UNARCHIVER (modular_form_kernel)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (user_defined_kernel, integration_kernel, print_func< print_context >(&user_defined_kernel::do_print)) user_defined_kernel
	GINAC_BIND_UNARCHIVER (user_defined_kernel)
	GINAC_DECLARE_UNARCHIVER (integration_kernel)
	GINAC_DECLARE_UNARCHIVER (basic_log_kernel)
	GINAC_DECLARE_UNARCHIVER (multiple_polylog_kernel)
	GINAC_DECLARE_UNARCHIVER (ELi_kernel)
	GINAC_DECLARE_UNARCHIVER (Ebar_kernel)
	GINAC_DECLARE_UNARCHIVER (Kronecker_dtau_kernel)
	GINAC_DECLARE_UNARCHIVER (Kronecker_dz_kernel)
	GINAC_DECLARE_UNARCHIVER (Eisenstein_kernel)
	GINAC_DECLARE_UNARCHIVER (Eisenstein_h_kernel)
	GINAC_DECLARE_UNARCHIVER (modular_form_kernel)
	GINAC_DECLARE_UNARCHIVER (user_defined_kernel)
	GINAC_DECLARE_UNARCHIVER (lst)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (matrix, basic, print_func< print_context >(&matrix::do_print). print_func< print_latex >(&matrix::do_print_latex). print_func< print_tree >(&matrix::do_print_tree). print_func< print_python_repr >(&matrix::do_print_python_repr)) matrix
	Default ctor.
	GINAC_BIND_UNARCHIVER (matrix)
ex	lst_to_matrix (const lst &l)
	Convert list of lists to matrix.
ex	diag_matrix (const lst &l)
	Convert list of diagonal elements to matrix.
ex	diag_matrix (std::initializer_list< ex > l)
ex	unit_matrix (unsigned r, unsigned c)
	Create an r times c unit matrix.
ex	symbolic_matrix (unsigned r, unsigned c, const std::string &base_name, const std::string &tex_base_name)
	Create an r times c matrix of newly generated symbols consisting of the given base name plus the numeric row/column position of each element.
ex	reduced_matrix (const matrix &m, unsigned r, unsigned c)
	Return the reduced matrix that is formed by deleting the rth row and cth column of matrix m.
ex	sub_matrix (const matrix &m, unsigned r, unsigned nr, unsigned c, unsigned nc)
	Return the nr times nc submatrix starting at position r, c of matrix m.
	GINAC_DECLARE_UNARCHIVER (matrix)
size_t	nops (const matrix &m)
ex	expand (const matrix &m, unsigned options=0)
ex	evalf (const matrix &m)
unsigned	rows (const matrix &m)
unsigned	cols (const matrix &m)
matrix	transpose (const matrix &m)
ex	determinant (const matrix &m, unsigned options=determinant_algo::automatic)
ex	trace (const matrix &m)
ex	charpoly (const matrix &m, const ex &lambda)
matrix	inverse (const matrix &m)
matrix	inverse (const matrix &m, unsigned algo)
unsigned	rank (const matrix &m)
unsigned	rank (const matrix &m, unsigned solve_algo)
ex	unit_matrix (unsigned x)
	Create a x times x unit matrix.
ex	symbolic_matrix (unsigned r, unsigned c, const std::string &base_name)
	Create an r times c matrix of newly generated symbols consisting of the given base name plus the numeric row/column position of each element.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (mul, expairseq, print_func< print_context >(&mul::do_print). print_func< print_latex >(&mul::do_print_latex). print_func< print_csrc >(&mul::do_print_csrc). print_func< print_tree >(&mul::do_print_tree). print_func< print_python_repr >(&mul::do_print_python_repr)) mul
bool	tryfactsubs (const ex &origfactor, const ex &patternfactor, int &nummatches, exmap &repls)
bool	algebraic_match_mul_with_mul (const mul &e, const ex &pat, exmap &repls, int factor, int &nummatches, const std::vector< bool > &subsed, std::vector< bool > &matched)
	Checks whether e matches to the pattern pat and the (possibly to be updated) list of replacements repls.
	GINAC_BIND_UNARCHIVER (mul)
	GINAC_DECLARE_UNARCHIVER (mul)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (ncmul, exprseq, print_func< print_context >(&ncmul::do_print). print_func< print_tree >(&ncmul::do_print_tree). print_func< print_csrc >(&ncmul::do_print_csrc). print_func< print_python_repr >(&ncmul::do_print_csrc)) ncmul
ex	reeval_ncmul (const exvector &v)
ex	hold_ncmul (const exvector &v)
	GINAC_BIND_UNARCHIVER (ncmul)
	GINAC_DECLARE_UNARCHIVER (ncmul)
static bool	get_first_symbol (const ex &e, ex &x)
	Return pointer to first symbol found in expression.
static void	add_symbol (const ex &s, sym_desc_vec &v)
static void	collect_symbols (const ex &e, sym_desc_vec &v)
static void	get_symbol_stats (const ex &a, const ex &b, sym_desc_vec &v)
	Collect statistical information about symbols in polynomials.
static numeric	lcmcoeff (const ex &e, const numeric &l)
static numeric	lcm_of_coefficients_denominators (const ex &e)
	Compute LCM of denominators of coefficients of a polynomial.
static ex	multiply_lcm (const ex &e, const numeric &lcm)
	Bring polynomial from Q[X] to Z[X] by multiplying in the previously determined LCM of the coefficient's denominators.
ex	quo (const ex &a, const ex &b, const ex &x, bool check_args)
	Quotient q(x) of polynomials a(x) and b(x) in Q[x].
ex	rem (const ex &a, const ex &b, const ex &x, bool check_args)
	Remainder r(x) of polynomials a(x) and b(x) in Q[x].
ex	decomp_rational (const ex &a, const ex &x)
	Decompose rational function a(x)=N(x)/D(x) into P(x)+n(x)/D(x) with degree(n, x) < degree(D, x).
ex	prem (const ex &a, const ex &b, const ex &x, bool check_args)
	Pseudo-remainder of polynomials a(x) and b(x) in Q[x].
ex	sprem (const ex &a, const ex &b, const ex &x, bool check_args)
	Sparse pseudo-remainder of polynomials a(x) and b(x) in Q[x].
bool	divide (const ex &a, const ex &b, ex &q, bool check_args)
	Exact polynomial division of a(X) by b(X) in Q[X].
static bool	divide_in_z (const ex &a, const ex &b, ex &q, sym_desc_vec::const_iterator var)
	Exact polynomial division of a(X) by b(X) in Z[X].
static ex	sr_gcd (const ex &a, const ex &b, sym_desc_vec::const_iterator var)
	Compute GCD of multivariate polynomials using the subresultant PRS algorithm.
static ex	interpolate (const ex &gamma, const numeric &xi, const ex &x, int degree_hint=1)
	xi-adic polynomial interpolation
static bool	heur_gcd_z (ex &res, const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
	Compute GCD of multivariate polynomials using the heuristic GCD algorithm.
static bool	heur_gcd (ex &res, const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
	Compute GCD of multivariate polynomials using the heuristic GCD algorithm.
static ex	gcd_pf_pow (const ex &a, const ex &b, ex *ca, ex *cb)
static ex	gcd_pf_mul (const ex &a, const ex &b, ex *ca, ex *cb)
ex	gcd (const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned options)
	Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X) and b(X) in Z[X].
static ex	gcd_pf_pow_pow (const ex &a, const ex &b, ex *ca, ex *cb)
ex	lcm (const ex &a, const ex &b, bool check_args)
	Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].
static epvector	sqrfree_yun (const ex &a, const symbol &x)
	Compute square-free factorization of multivariate polynomial a(x) using Yun's algorithm.
ex	sqrfree (const ex &a, const lst &l)
	Compute a square-free factorization of a multivariate polynomial in Q[X].
ex	sqrfree_parfrac (const ex &a, const symbol &x)
	Compute square-free partial fraction decomposition of rational function a(x).
static ex	replace_with_symbol (const ex &e, exmap &repl, exmap &rev_lookup, lst &modifier)
	Create a symbol for replacing the expression "e" (or return a previously assigned symbol).
static ex	replace_with_symbol (const ex &e, exmap &repl)
	Create a symbol for replacing the expression "e" (or return a previously assigned symbol).
static ex	frac_cancel (const ex &n, const ex &d)
	Fraction cancellation.
static ex	find_common_factor (const ex &e, ex &factor, exmap &repl)
	Remove the common factor in the terms of a sum 'e' by calculating the GCD, and multiply it into the expression 'factor' (which needs to be initialized to 1, unless you're accumulating factors).
ex	collect_common_factors (const ex &e)
	Collect common factors in sums.
ex	resultant (const ex &e1, const ex &e2, const ex &s)
	Resultant of two expressions e1,e2 with respect to symbol s.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (numeric, basic, print_func< print_context >(&numeric::do_print). print_func< print_latex >(&numeric::do_print_latex). print_func< print_csrc >(&numeric::do_print_csrc). print_func< print_csrc_cl_N >(&numeric::do_print_csrc_cl_N). print_func< print_tree >(&numeric::do_print_tree). print_func< print_python_repr >(&numeric::do_print_python_repr)) numeric
	default ctor.
static const cln::cl_F	make_real_float (const cln::cl_idecoded_float &dec)
	Construct a floating point number from sign, mantissa, and exponent.
static const cln::cl_F	read_real_float (std::istream &s)
	Read serialized floating point number.
	GINAC_BIND_UNARCHIVER (numeric)
static void	write_real_float (std::ostream &s, const cln::cl_R &n)
static void	print_real_number (const print_context &c, const cln::cl_R &x)
	Helper function to print a real number in a nicer way than is CLN's default.
static void	print_integer_csrc (const print_context &c, const cln::cl_I &x)
	Helper function to print integer number in C++ source format.
static void	print_real_csrc (const print_context &c, const cln::cl_R &x)
	Helper function to print real number in C++ source format.
template<typename T1 , typename T2 >
static bool	coerce (T1 &dst, const T2 &arg)
template<>
bool	coerce< int, cln::cl_I > (int &dst, const cln::cl_I &arg)
	Check if CLN integer can be converted into int.
template<>
bool	coerce< unsigned int, cln::cl_I > (unsigned int &dst, const cln::cl_I &arg)
static void	print_real_cl_N (const print_context &c, const cln::cl_R &x)
	Helper function to print real number in C++ source format using cl_N types.
const numeric	exp (const numeric &x)
	Exponential function.
const numeric	log (const numeric &x)
	Natural logarithm.
const numeric	sin (const numeric &x)
	Numeric sine (trigonometric function).
const numeric	cos (const numeric &x)
	Numeric cosine (trigonometric function).
const numeric	tan (const numeric &x)
	Numeric tangent (trigonometric function).
const numeric	asin (const numeric &x)
	Numeric inverse sine (trigonometric function).
const numeric	acos (const numeric &x)
	Numeric inverse cosine (trigonometric function).
const numeric	atan (const numeric &x)
	Numeric arcustangent.
const numeric	atan (const numeric &y, const numeric &x)
	Numeric arcustangent of two arguments, analytically continued in a suitable way.
const numeric	sinh (const numeric &x)
	Numeric hyperbolic sine (trigonometric function).
const numeric	cosh (const numeric &x)
	Numeric hyperbolic cosine (trigonometric function).
const numeric	tanh (const numeric &x)
	Numeric hyperbolic tangent (trigonometric function).
const numeric	asinh (const numeric &x)
	Numeric inverse hyperbolic sine (trigonometric function).
const numeric	acosh (const numeric &x)
	Numeric inverse hyperbolic cosine (trigonometric function).
const numeric	atanh (const numeric &x)
	Numeric inverse hyperbolic tangent (trigonometric function).
static cln::cl_N	Li2_series (const cln::cl_N &x, const cln::float_format_t &prec)
	Numeric evaluation of Dilogarithm within circle of convergence (unit circle) using a power series.
static cln::cl_N	Li2_projection (const cln::cl_N &x, const cln::float_format_t &prec)
	Folds Li2's argument inside a small rectangle to enhance convergence.
const cln::cl_N	Li2_ (const cln::cl_N &value)
	Numeric evaluation of Dilogarithm.
const numeric	Li2 (const numeric &x)
const numeric	zeta (const numeric &x)
	Numeric evaluation of Riemann's Zeta function.
static cln::float_format_t	guess_precision (const cln::cl_N &x)
const cln::cl_N	lgamma (const cln::cl_N &x)
	The Gamma function.
const numeric	lgamma (const numeric &x)
const cln::cl_N	tgamma (const cln::cl_N &x)
const numeric	tgamma (const numeric &x)
const numeric	psi (const numeric &x)
	The psi function (aka polygamma function).
const numeric	psi (const numeric &n, const numeric &x)
	The psi functions (aka polygamma functions).
const numeric	factorial (const numeric &n)
	Factorial combinatorial function.
const numeric	doublefactorial (const numeric &n)
	The double factorial combinatorial function.
const numeric	binomial (const numeric &n, const numeric &k)
	The Binomial coefficients.
const numeric	bernoulli (const numeric &nn)
	Bernoulli number.
const numeric	fibonacci (const numeric &n)
	Fibonacci number.
const numeric	abs (const numeric &x)
	Absolute value.
const numeric	mod (const numeric &a, const numeric &b)
	Modulus (in positive representation).
const numeric	smod (const numeric &a_, const numeric &b_)
	Modulus (in symmetric representation).
const numeric	irem (const numeric &a, const numeric &b)
	Numeric integer remainder.
const numeric	irem (const numeric &a, const numeric &b, numeric &q)
	Numeric integer remainder.
const numeric	iquo (const numeric &a, const numeric &b)
	Numeric integer quotient.
const numeric	iquo (const numeric &a, const numeric &b, numeric &r)
	Numeric integer quotient.
const numeric	gcd (const numeric &a, const numeric &b)
	Greatest Common Divisor.
const numeric	lcm (const numeric &a, const numeric &b)
	Least Common Multiple.
const numeric	sqrt (const numeric &x)
	Numeric square root.
const numeric	isqrt (const numeric &x)
	Integer numeric square root.
ex	PiEvalf ()
	Floating point evaluation of Archimedes' constant Pi.
ex	EulerEvalf ()
	Floating point evaluation of Euler's constant gamma.
ex	CatalanEvalf ()
	Floating point evaluation of Catalan's constant.
std::ostream &	operator<< (std::ostream &os, const _numeric_digits &e)
	GINAC_DECLARE_UNARCHIVER (numeric)
const numeric	pow (const numeric &x, const numeric &y)
const numeric	inverse (const numeric &x)
numeric	step (const numeric &x)
int	csgn (const numeric &x)
bool	is_zero (const numeric &x)
bool	is_positive (const numeric &x)
bool	is_negative (const numeric &x)
bool	is_integer (const numeric &x)
bool	is_pos_integer (const numeric &x)
bool	is_nonneg_integer (const numeric &x)
bool	is_even (const numeric &x)
bool	is_odd (const numeric &x)
bool	is_prime (const numeric &x)
bool	is_rational (const numeric &x)
bool	is_real (const numeric &x)
bool	is_cinteger (const numeric &x)
bool	is_crational (const numeric &x)
int	to_int (const numeric &x)
long	to_long (const numeric &x)
double	to_double (const numeric &x)
const numeric	real (const numeric &x)
const numeric	imag (const numeric &x)
const numeric	numer (const numeric &x)
const numeric	denom (const numeric &x)
static const ex	exadd (const ex &lh, const ex &rh)
	Used internally by operator+() to add two ex objects.
static const ex	exmul (const ex &lh, const ex &rh)
	Used internally by operator*() to multiply two ex objects.
static const ex	exminus (const ex &lh)
	Used internally by operator-() and friends to change the sign of an argument.
const ex	operator+ (const ex &lh, const ex &rh)
const ex	operator- (const ex &lh, const ex &rh)
const ex	operator* (const ex &lh, const ex &rh)
const ex	operator/ (const ex &lh, const ex &rh)
const numeric	operator+ (const numeric &lh, const numeric &rh)
const numeric	operator- (const numeric &lh, const numeric &rh)
const numeric	operator* (const numeric &lh, const numeric &rh)
const numeric	operator/ (const numeric &lh, const numeric &rh)
ex &	operator+= (ex &lh, const ex &rh)
ex &	operator-= (ex &lh, const ex &rh)
ex &	operator*= (ex &lh, const ex &rh)
ex &	operator/= (ex &lh, const ex &rh)
numeric &	operator+= (numeric &lh, const numeric &rh)
numeric &	operator-= (numeric &lh, const numeric &rh)
numeric &	operator*= (numeric &lh, const numeric &rh)
numeric &	operator/= (numeric &lh, const numeric &rh)
const ex	operator+ (const ex &lh)
const ex	operator- (const ex &lh)
const numeric	operator+ (const numeric &lh)
const numeric	operator- (const numeric &lh)
ex &	operator++ (ex &rh)
	Expression prefix increment.
ex &	operator-- (ex &rh)
	Expression prefix decrement.
const ex	operator++ (ex &lh, int)
	Expression postfix increment.
const ex	operator-- (ex &lh, int)
	Expression postfix decrement.
numeric &	operator++ (numeric &rh)
	Numeric prefix increment.
numeric &	operator-- (numeric &rh)
	Numeric prefix decrement.
const numeric	operator++ (numeric &lh, int)
	Numeric postfix increment.
const numeric	operator-- (numeric &lh, int)
	Numeric postfix decrement.
const relational	operator== (const ex &lh, const ex &rh)
const relational	operator!= (const ex &lh, const ex &rh)
const relational	operator< (const ex &lh, const ex &rh)
const relational	operator<= (const ex &lh, const ex &rh)
const relational	operator> (const ex &lh, const ex &rh)
const relational	operator>= (const ex &lh, const ex &rh)
static int	my_ios_index ()
static void	my_ios_callback (std::ios_base::event ev, std::ios_base &s, int i)
static print_context *	get_print_context (std::ios_base &s)
static void	set_print_context (std::ios_base &s, const print_context &c)
static unsigned	get_print_options (std::ios_base &s)
static void	set_print_options (std::ostream &s, unsigned options)
std::ostream &	operator<< (std::ostream &os, const ex &e)
std::istream &	operator>> (std::istream &is, ex &e)
std::ostream &	dflt (std::ostream &os)
std::ostream &	latex (std::ostream &os)
std::ostream &	python (std::ostream &os)
std::ostream &	python_repr (std::ostream &os)
std::ostream &	tree (std::ostream &os)
std::ostream &	csrc (std::ostream &os)
std::ostream &	csrc_float (std::ostream &os)
std::ostream &	csrc_double (std::ostream &os)
std::ostream &	csrc_cl_N (std::ostream &os)
std::ostream &	index_dimensions (std::ostream &os)
std::ostream &	no_index_dimensions (std::ostream &os)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (power, basic, print_func< print_dflt >(&power::do_print_dflt). print_func< print_latex >(&power::do_print_latex). print_func< print_csrc >(&power::do_print_csrc). print_func< print_python >(&power::do_print_python). print_func< print_python_repr >(&power::do_print_python_repr). print_func< print_csrc_cl_N >(&power::do_print_csrc_cl_N)) power
static void	print_sym_pow (const print_context &c, const symbol &x, int exp)
	GINAC_BIND_UNARCHIVER (power)
	GINAC_DECLARE_UNARCHIVER (power)
ex	pow (const ex &b, const ex &e)
	Symbolic exponentiation.
template<typename T1 , typename T2 >
ex	pow (const T1 &b, const T2 &e)
ex	sqrt (const ex &a)
	Square root expression.
template<class T >
bool	is_a (const print_context &obj)
	Check if obj is a T, including base classes.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (pseries, basic, print_func< print_context >(&pseries::do_print). print_func< print_latex >(&pseries::do_print_latex). print_func< print_tree >(&pseries::do_print_tree). print_func< print_python >(&pseries::do_print_python). print_func< print_python_repr >(&pseries::do_print_python_repr)) pseries
	GINAC_BIND_UNARCHIVER (pseries)
	GINAC_DECLARE_UNARCHIVER (pseries)
ex	series_to_poly (const ex &e)
	Convert the pseries object embedded in an expression to an ordinary polynomial in the expansion variable.
bool	is_terminating (const pseries &s)
template<typename T >
return_type_t	make_return_type_t (const unsigned rl=0)
template<class Alg , class Ctx , class T , class C >
void	set_print_func (void f(const T &, const C &c, unsigned))
	Add or replace a print method.
template<class Alg , class Ctx , class T , class C >
void	set_print_func (void(T::*f)(const C &, unsigned))
	Add or replace a print method.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (relational, basic, print_func< print_context >(&relational::do_print). print_func< print_tree >(&relational::do_print_tree). print_func< print_python_repr >(&relational::do_print_python_repr)) relational
	GINAC_BIND_UNARCHIVER (relational)
static void	print_operator (const print_context &c, relational::operators o)
	GINAC_DECLARE_UNARCHIVER (relational)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (symbol, basic, print_func< print_context >(&symbol::do_print). print_func< print_latex >(&symbol::do_print_latex). print_func< print_tree >(&symbol::do_print_tree). print_func< print_python_repr >(&symbol::do_print_python_repr)) symbol
static const std::string &	get_default_TeX_name (const std::string &name)
	Return default TeX name for symbol.
	GINAC_BIND_UNARCHIVER (symbol)
	GINAC_BIND_UNARCHIVER (realsymbol)
	GINAC_BIND_UNARCHIVER (possymbol)
	GINAC_DECLARE_UNARCHIVER (symbol)
	GINAC_DECLARE_UNARCHIVER (realsymbol)
	GINAC_DECLARE_UNARCHIVER (possymbol)
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (symmetry, basic, print_func< print_context >(&symmetry::do_print). print_func< print_tree >(&symmetry::do_print_tree)) symmetry
	GINAC_BIND_UNARCHIVER (symmetry)
static const symmetry &	index0 ()
static const symmetry &	index1 ()
static const symmetry &	index2 ()
static const symmetry &	index3 ()
const symmetry &	not_symmetric ()
const symmetry &	symmetric2 ()
const symmetry &	symmetric3 ()
const symmetry &	symmetric4 ()
const symmetry &	antisymmetric2 ()
const symmetry &	antisymmetric3 ()
const symmetry &	antisymmetric4 ()
int	canonicalize (exvector::iterator v, const symmetry &symm)
	Canonicalize the order of elements of an expression vector, according to the symmetry properties defined in a symmetry tree.
static ex	symm (const ex &e, exvector::const_iterator first, exvector::const_iterator last, bool asymmetric)
ex	symmetrize (const ex &e, exvector::const_iterator first, exvector::const_iterator last)
	Symmetrize expression over a set of objects (symbols, indices).
ex	antisymmetrize (const ex &e, exvector::const_iterator first, exvector::const_iterator last)
	Antisymmetrize expression over a set of objects (symbols, indices).
ex	symmetrize_cyclic (const ex &e, exvector::const_iterator first, exvector::const_iterator last)
	Symmetrize expression by cyclic permutation over a set of objects (symbols, indices).
	GINAC_DECLARE_UNARCHIVER (symmetry)
symmetry	sy_none ()
symmetry	sy_none (const symmetry &c1, const symmetry &c2)
symmetry	sy_none (const symmetry &c1, const symmetry &c2, const symmetry &c3)
symmetry	sy_none (const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4)
symmetry	sy_symm ()
symmetry	sy_symm (const symmetry &c1, const symmetry &c2)
symmetry	sy_symm (const symmetry &c1, const symmetry &c2, const symmetry &c3)
symmetry	sy_symm (const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4)
symmetry	sy_anti ()
symmetry	sy_anti (const symmetry &c1, const symmetry &c2)
symmetry	sy_anti (const symmetry &c1, const symmetry &c2, const symmetry &c3)
symmetry	sy_anti (const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4)
symmetry	sy_cycl ()
symmetry	sy_cycl (const symmetry &c1, const symmetry &c2)
symmetry	sy_cycl (const symmetry &c1, const symmetry &c2, const symmetry &c3)
symmetry	sy_cycl (const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4)
ex	symmetrize (const ex &e, const exvector &v)
	Symmetrize expression over a set of objects (symbols, indices).
ex	antisymmetrize (const ex &e, const exvector &v)
	Antisymmetrize expression over a set of objects (symbols, indices).
ex	symmetrize_cyclic (const ex &e, const exvector &v)
	Symmetrize expression by cyclic permutation over a set of objects (symbols, indices).
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (tensdelta, tensor, print_func< print_dflt >(&tensdelta::do_print). print_func< print_latex >(&tensdelta::do_print_latex)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensmetric
	print_func< print_dflt > (&tensmetric::do_print). print_func< print_latex >(&tensmetric
	GINAC_BIND_UNARCHIVER (minkmetric)
	GINAC_BIND_UNARCHIVER (tensepsilon)
	GINAC_BIND_UNARCHIVER (tensdelta)
	GINAC_BIND_UNARCHIVER (tensmetric)
	GINAC_BIND_UNARCHIVER (spinmetric)
ex	delta_tensor (const ex &i1, const ex &i2)
	Create a delta tensor with specified indices.
ex	metric_tensor (const ex &i1, const ex &i2)
	Create a symmetric metric tensor with specified indices.
ex	lorentz_g (const ex &i1, const ex &i2, bool pos_sig=false)
	Create a Minkowski metric tensor with specified indices.
ex	spinor_metric (const ex &i1, const ex &i2)
	Create a spinor metric tensor with specified indices.
ex	epsilon_tensor (const ex &i1, const ex &i2)
	Create an epsilon tensor in a Euclidean space with two indices.
ex	epsilon_tensor (const ex &i1, const ex &i2, const ex &i3)
	Create an epsilon tensor in a Euclidean space with three indices.
ex	lorentz_eps (const ex &i1, const ex &i2, const ex &i3, const ex &i4, bool pos_sig=false)
	Create an epsilon tensor in a Minkowski space with four indices.
	GINAC_DECLARE_UNARCHIVER (tensdelta)
	GINAC_DECLARE_UNARCHIVER (tensmetric)
	GINAC_DECLARE_UNARCHIVER (minkmetric)
	GINAC_DECLARE_UNARCHIVER (spinmetric)
	GINAC_DECLARE_UNARCHIVER (tensepsilon)
unsigned	log2 (unsigned n)
	Integer binary logarithm.
const numeric	multinomial_coefficient (const std::vector< unsigned > &p)
	Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where n = p1+p2+...+pk, i.e.
unsigned	rotate_left (unsigned n)
	Rotate bits of unsigned value by one bit to the left.
template<class T >
int	compare_pointers (const T *a, const T *b)
	Compare two pointers (just to establish some sort of canonical order).
unsigned	golden_ratio_hash (uintptr_t n)
	Truncated multiplication with golden ratio, for computing hash values.
template<class It >
int	permutation_sign (It first, It last)
template<class It , class Cmp , class Swap >
int	permutation_sign (It first, It last, Cmp comp, Swap swapit)
template<class It , class Cmp , class Swap >
void	shaker_sort (It first, It last, Cmp comp, Swap swapit)
template<class It , class Swap >
void	cyclic_permutation (It first, It last, It new_first, Swap swapit)
template<typename T >
std::enable_if< has_distance< T >::value, typenamestd::iterator_traits< T >::difference_type >::type	format_index_value (const T &a, const T &b)
	For printing a multi-index: If the templates are used, where T is an iterator, printing the address where the iterator points to is not meaningful.
template<typename T >
std::enable_if<!has_distance< T >::value, T >::type	format_index_value (const T &a, const T &b)
	For all other cases we simply print the value.
template<class T >
std::ostream &	operator<< (std::ostream &os, const basic_multi_iterator< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_ordered< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_ordered_eq< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_ordered_eq_indv< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_counter< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_counter_indv< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_permutation< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_shuffle< T > &v)
	Output operator.
template<class T >
std::ostream &	operator<< (std::ostream &os, const multi_iterator_shuffle_prime< T > &v)
	Output operator.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (wildcard, basic, print_func< print_context >(&wildcard::do_print). print_func< print_tree >(&wildcard::do_print_tree). print_func< print_python_repr >(&wildcard::do_print_python_repr)) wildcard
	GINAC_BIND_UNARCHIVER (wildcard)
bool	haswild (const ex &x)
	Check whether x has a wildcard anywhere as a subexpression.
	GINAC_DECLARE_UNARCHIVER (wildcard)
ex	wild (unsigned label=0)
	Create a wildcard object with the specified label.

Variables
static unarchive_table_t	unarch_table_instance
GiNaC::evalm_map_function	map_evalm
GiNaC::eval_integ_map_function	map_eval_integ
	tensor
const constant	Pi ("Pi", PiEvalf, "\\pi", domain::positive)
	Pi.
const constant	Euler ("Euler", EulerEvalf, "\\gamma_E", domain::positive)
	Euler's constant.
const constant	Catalan ("Catalan", CatalanEvalf, "G", domain::positive)
	Catalan's constant.
static unsigned const	crctab [256]
static library_init	library_initializer
	For construction of flyweights, etc.
const basic *	_num0_bp
	idx
unsigned	force_include_tgamma = tgamma_SERIAL::serial
unsigned	force_include_zeta1 = zeta1_SERIAL::serial
template<>
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT_T(lst, basic, print_func< print_context >(&lst::do_print). print_func< print_tree >(&lst::do_print_tree)) template<> bool lst	GINAC_BIND_UNARCHIVER (lst)
	Specialization of container::info() for lst.
const numeric	I = numeric(cln::complex(cln::cl_I(0),cln::cl_I(1)))
	Imaginary unit.
_numeric_digits	Digits
	Accuracy in decimal digits.
unsigned	next_print_context_id = 0
	Next free ID for print_context types.
const int	version_major = GINACLIB_MAJOR_VERSION
const int	version_minor = GINACLIB_MINOR_VERSION
const int	version_micro = GINACLIB_MICRO_VERSION
const numeric *	_num_120_p
const ex	_ex_120 = ex(*_num_120_p)
const numeric *	_num_60_p
const ex	_ex_60 = ex(*_num_60_p)
const numeric *	_num_48_p
const ex	_ex_48 = ex(*_num_48_p)
const numeric *	_num_30_p
const ex	_ex_30 = ex(*_num_30_p)
const numeric *	_num_25_p
const ex	_ex_25 = ex(*_num_25_p)
const numeric *	_num_24_p
const ex	_ex_24 = ex(*_num_24_p)
const numeric *	_num_20_p
const ex	_ex_20 = ex(*_num_20_p)
const numeric *	_num_18_p
const ex	_ex_18 = ex(*_num_18_p)
const numeric *	_num_15_p
const ex	_ex_15 = ex(*_num_15_p)
const numeric *	_num_12_p
const ex	_ex_12 = ex(*_num_12_p)
const numeric *	_num_11_p
const ex	_ex_11 = ex(*_num_11_p)
const numeric *	_num_10_p
const ex	_ex_10 = ex(*_num_10_p)
const numeric *	_num_9_p
const ex	_ex_9 = ex(*_num_9_p)
const numeric *	_num_8_p
const ex	_ex_8 = ex(*_num_8_p)
const numeric *	_num_7_p
const ex	_ex_7 = ex(*_num_7_p)
const numeric *	_num_6_p
const ex	_ex_6 = ex(*_num_6_p)
const numeric *	_num_5_p
const ex	_ex_5 = ex(*_num_5_p)
const numeric *	_num_4_p
const ex	_ex_4 = ex(*_num_4_p)
const numeric *	_num_3_p
const ex	_ex_3 = ex(*_num_3_p)
const numeric *	_num_2_p
const ex	_ex_2 = ex(*_num_2_p)
const numeric *	_num_1_p
const ex	_ex_1 = ex(*_num_1_p)
const numeric *	_num_1_2_p
const ex	_ex_1_2 = ex(*_num_1_2_p)
const numeric *	_num_1_3_p
const ex	_ex_1_3 = ex(*_num_1_3_p)
const numeric *	_num_1_4_p
const ex	_ex_1_4 = ex(*_num_1_4_p)
const numeric *	_num0_p
const ex	_ex0 = ex(*_num0_p)
const numeric *	_num1_4_p
const ex	_ex1_4 = ex(*_num1_4_p)
const numeric *	_num1_3_p
const ex	_ex1_3 = ex(*_num1_3_p)
const numeric *	_num1_2_p
const ex	_ex1_2 = ex(*_num1_2_p)
const numeric *	_num1_p
const ex	_ex1 = ex(*_num1_p)
const numeric *	_num2_p
const ex	_ex2 = ex(*_num2_p)
const numeric *	_num3_p
const ex	_ex3 = ex(*_num3_p)
const numeric *	_num4_p
const ex	_ex4 = ex(*_num4_p)
const numeric *	_num5_p
const ex	_ex5 = ex(*_num5_p)
const numeric *	_num6_p
const ex	_ex6 = ex(*_num6_p)
const numeric *	_num7_p
const ex	_ex7 = ex(*_num7_p)
const numeric *	_num8_p
const ex	_ex8 = ex(*_num8_p)
const numeric *	_num9_p
const ex	_ex9 = ex(*_num9_p)
const numeric *	_num10_p
const ex	_ex10 = ex(*_num10_p)
const numeric *	_num11_p
const ex	_ex11 = ex(*_num11_p)
const numeric *	_num12_p
const ex	_ex12 = ex(*_num12_p)
const numeric *	_num15_p
const ex	_ex15 = ex(*_num15_p)
const numeric *	_num18_p
const ex	_ex18 = ex(*_num18_p)
const numeric *	_num20_p
const ex	_ex20 = ex(*_num20_p)
const numeric *	_num24_p
const ex	_ex24 = ex(*_num24_p)
const numeric *	_num25_p
const ex	_ex25 = ex(*_num25_p)
const numeric *	_num30_p
const ex	_ex30 = ex(*_num30_p)
const numeric *	_num48_p
const ex	_ex48 = ex(*_num48_p)
const numeric *	_num60_p
const ex	_ex60 = ex(*_num60_p)
const numeric *	_num120_p
const ex	_ex120 = ex(*_num120_p)

Typedef Documentation

archive_node_id

typedef unsigned GiNaC::archive_node_id

Numerical ID value to refer to an archive_node.

Definition at line 39 of file archive.h.

archive_atom

typedef unsigned GiNaC::archive_atom

Numerical ID value to refer to a string.

Definition at line 42 of file archive.h.

synthesize_func

typedef basic *(* GiNaC::synthesize_func) ()

Definition at line 166 of file archive.h.

unarchive_map_t

typedef std::map<std::string, synthesize_func> GiNaC::unarchive_map_t

Definition at line 167 of file archive.h.

exvector

typedef std::vector<ex> GiNaC::exvector

Definition at line 48 of file basic.h.

exset

typedef std::set<ex, ex_is_less> GiNaC::exset

Definition at line 49 of file basic.h.

exmap

typedef std::map<ex, ex, ex_is_less> GiNaC::exmap

Definition at line 50 of file basic.h.

evalffunctype

typedef ex(* GiNaC::evalffunctype) ()

Definition at line 34 of file constant.h.

FUNCP_1P

typedef double(* GiNaC::FUNCP_1P) (double)

Function pointer with one function parameter.

Definition at line 39 of file excompiler.h.

FUNCP_2P

typedef double(* GiNaC::FUNCP_2P) (double, double)

Function pointer with two function parameters.

Definition at line 44 of file excompiler.h.

FUNCP_CUBA

typedef void(* GiNaC::FUNCP_CUBA) (const int *, const double[], const int *, double[])

Function pointer for use with the CUBA library (http://www.feynarts.de/cuba).

Definition at line 49 of file excompiler.h.

epvector

typedef std::vector<expair> GiNaC::epvector

expair-vector

Definition at line 33 of file expairseq.h.

epp

typedef epvector::iterator GiNaC::epp

expair-vector pointer

Definition at line 34 of file expairseq.h.

exprseq

typedef container<std::vector> GiNaC::exprseq

Definition at line 32 of file exprseq.h.

paramset

typedef std::multiset<unsigned> GiNaC::paramset

Definition at line 32 of file fderivative.h.

eval_funcp

typedef ex(* GiNaC::eval_funcp) ()

Definition at line 129 of file function.h.

evalf_funcp

typedef ex(* GiNaC::evalf_funcp) ()

Definition at line 130 of file function.h.

conjugate_funcp

typedef ex(* GiNaC::conjugate_funcp) ()

Definition at line 131 of file function.h.

real_part_funcp

typedef ex(* GiNaC::real_part_funcp) ()

Definition at line 132 of file function.h.

imag_part_funcp

typedef ex(* GiNaC::imag_part_funcp) ()

Definition at line 133 of file function.h.

expand_funcp

typedef ex(* GiNaC::expand_funcp) ()

Definition at line 134 of file function.h.

derivative_funcp

typedef ex(* GiNaC::derivative_funcp) ()

Definition at line 135 of file function.h.

expl_derivative_funcp

typedef ex(* GiNaC::expl_derivative_funcp) ()

Definition at line 136 of file function.h.

power_funcp

typedef ex(* GiNaC::power_funcp) ()

Definition at line 137 of file function.h.

series_funcp

typedef ex(* GiNaC::series_funcp) ()

Definition at line 138 of file function.h.

print_funcp

typedef void(* GiNaC::print_funcp) ()

Definition at line 139 of file function.h.

info_funcp

typedef bool(* GiNaC::info_funcp) ()

Definition at line 140 of file function.h.

eval_funcp_1

typedef ex(* GiNaC::eval_funcp_1) (const ex &)

Definition at line 143 of file function.h.

evalf_funcp_1

typedef ex(* GiNaC::evalf_funcp_1) (const ex &)

Definition at line 144 of file function.h.

conjugate_funcp_1

typedef ex(* GiNaC::conjugate_funcp_1) (const ex &)

Definition at line 145 of file function.h.

real_part_funcp_1

typedef ex(* GiNaC::real_part_funcp_1) (const ex &)

Definition at line 146 of file function.h.

imag_part_funcp_1

typedef ex(* GiNaC::imag_part_funcp_1) (const ex &)

Definition at line 147 of file function.h.

expand_funcp_1

typedef ex(* GiNaC::expand_funcp_1) (const ex &, unsigned)

Definition at line 148 of file function.h.

derivative_funcp_1

typedef ex(* GiNaC::derivative_funcp_1) (const ex &, unsigned)

Definition at line 149 of file function.h.

expl_derivative_funcp_1

typedef ex(* GiNaC::expl_derivative_funcp_1) (const ex &, const symbol &)

Definition at line 150 of file function.h.

power_funcp_1

typedef ex(* GiNaC::power_funcp_1) (const ex &, const ex &)

Definition at line 151 of file function.h.

series_funcp_1

typedef ex(* GiNaC::series_funcp_1) (const ex &, const relational &, int, unsigned)

Definition at line 152 of file function.h.

print_funcp_1

typedef void(* GiNaC::print_funcp_1) (const ex &, const print_context &)

Definition at line 153 of file function.h.

info_funcp_1

typedef bool(* GiNaC::info_funcp_1) (const ex &, unsigned)

Definition at line 154 of file function.h.

eval_funcp_2

typedef ex(* GiNaC::eval_funcp_2) (const ex &, const ex &)

Definition at line 155 of file function.h.

evalf_funcp_2

typedef ex(* GiNaC::evalf_funcp_2) (const ex &, const ex &)

Definition at line 156 of file function.h.

conjugate_funcp_2

typedef ex(* GiNaC::conjugate_funcp_2) (const ex &, const ex &)

Definition at line 157 of file function.h.

real_part_funcp_2

typedef ex(* GiNaC::real_part_funcp_2) (const ex &, const ex &)

Definition at line 158 of file function.h.

imag_part_funcp_2

typedef ex(* GiNaC::imag_part_funcp_2) (const ex &, const ex &)

Definition at line 159 of file function.h.

expand_funcp_2

typedef ex(* GiNaC::expand_funcp_2) (const ex &, const ex &, unsigned)

Definition at line 160 of file function.h.

derivative_funcp_2

typedef ex(* GiNaC::derivative_funcp_2) (const ex &, const ex &, unsigned)

Definition at line 161 of file function.h.

expl_derivative_funcp_2

typedef ex(* GiNaC::expl_derivative_funcp_2) (const ex &, const ex &, const symbol &)

Definition at line 162 of file function.h.

power_funcp_2

typedef ex(* GiNaC::power_funcp_2) (const ex &, const ex &, const ex &)

Definition at line 163 of file function.h.

series_funcp_2

typedef ex(* GiNaC::series_funcp_2) (const ex &, const ex &, const relational &, int, unsigned)

Definition at line 164 of file function.h.

print_funcp_2

typedef void(* GiNaC::print_funcp_2) (const ex &, const ex &, const print_context &)

Definition at line 165 of file function.h.

info_funcp_2

typedef bool(* GiNaC::info_funcp_2) (const ex &, const ex &, unsigned)

Definition at line 166 of file function.h.

eval_funcp_3

typedef ex(* GiNaC::eval_funcp_3) (const ex &, const ex &, const ex &)

Definition at line 167 of file function.h.

evalf_funcp_3

typedef ex(* GiNaC::evalf_funcp_3) (const ex &, const ex &, const ex &)

Definition at line 168 of file function.h.

conjugate_funcp_3

typedef ex(* GiNaC::conjugate_funcp_3) (const ex &, const ex &, const ex &)

Definition at line 169 of file function.h.

real_part_funcp_3

typedef ex(* GiNaC::real_part_funcp_3) (const ex &, const ex &, const ex &)

Definition at line 170 of file function.h.

imag_part_funcp_3

typedef ex(* GiNaC::imag_part_funcp_3) (const ex &, const ex &, const ex &)

Definition at line 171 of file function.h.

expand_funcp_3

typedef ex(* GiNaC::expand_funcp_3) (const ex &, const ex &, const ex &, unsigned)

Definition at line 172 of file function.h.

derivative_funcp_3

typedef ex(* GiNaC::derivative_funcp_3) (const ex &, const ex &, const ex &, unsigned)

Definition at line 173 of file function.h.

expl_derivative_funcp_3

typedef ex(* GiNaC::expl_derivative_funcp_3) (const ex &, const ex &, const ex &, const symbol &)

Definition at line 174 of file function.h.

power_funcp_3

typedef ex(* GiNaC::power_funcp_3) (const ex &, const ex &, const ex &, const ex &)

Definition at line 175 of file function.h.

series_funcp_3

typedef ex(* GiNaC::series_funcp_3) (const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 176 of file function.h.

print_funcp_3

typedef void(* GiNaC::print_funcp_3) (const ex &, const ex &, const ex &, const print_context &)

Definition at line 177 of file function.h.

info_funcp_3

typedef bool(* GiNaC::info_funcp_3) (const ex &, const ex &, const ex &, unsigned)

Definition at line 178 of file function.h.

eval_funcp_4

typedef ex(* GiNaC::eval_funcp_4) (const ex &, const ex &, const ex &, const ex &)

Definition at line 179 of file function.h.

evalf_funcp_4

typedef ex(* GiNaC::evalf_funcp_4) (const ex &, const ex &, const ex &, const ex &)

Definition at line 180 of file function.h.

conjugate_funcp_4

typedef ex(* GiNaC::conjugate_funcp_4) (const ex &, const ex &, const ex &, const ex &)

Definition at line 181 of file function.h.

real_part_funcp_4

typedef ex(* GiNaC::real_part_funcp_4) (const ex &, const ex &, const ex &, const ex &)

Definition at line 182 of file function.h.

imag_part_funcp_4

typedef ex(* GiNaC::imag_part_funcp_4) (const ex &, const ex &, const ex &, const ex &)

Definition at line 183 of file function.h.

expand_funcp_4

typedef ex(* GiNaC::expand_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 184 of file function.h.

derivative_funcp_4

typedef ex(* GiNaC::derivative_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 185 of file function.h.

expl_derivative_funcp_4

typedef ex(* GiNaC::expl_derivative_funcp_4) (const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 186 of file function.h.

power_funcp_4

typedef ex(* GiNaC::power_funcp_4) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 187 of file function.h.

series_funcp_4

typedef ex(* GiNaC::series_funcp_4) (const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 188 of file function.h.

print_funcp_4

typedef void(* GiNaC::print_funcp_4) (const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 189 of file function.h.

info_funcp_4

typedef bool(* GiNaC::info_funcp_4) (const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 190 of file function.h.

eval_funcp_5

typedef ex(* GiNaC::eval_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 191 of file function.h.

evalf_funcp_5

typedef ex(* GiNaC::evalf_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 192 of file function.h.

conjugate_funcp_5

typedef ex(* GiNaC::conjugate_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 193 of file function.h.

real_part_funcp_5

typedef ex(* GiNaC::real_part_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 194 of file function.h.

imag_part_funcp_5

typedef ex(* GiNaC::imag_part_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 195 of file function.h.

expand_funcp_5

typedef ex(* GiNaC::expand_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 196 of file function.h.

derivative_funcp_5

typedef ex(* GiNaC::derivative_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 197 of file function.h.

expl_derivative_funcp_5

typedef ex(* GiNaC::expl_derivative_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 198 of file function.h.

power_funcp_5

typedef ex(* GiNaC::power_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 199 of file function.h.

series_funcp_5

typedef ex(* GiNaC::series_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 200 of file function.h.

print_funcp_5

typedef void(* GiNaC::print_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 201 of file function.h.

info_funcp_5

typedef bool(* GiNaC::info_funcp_5) (const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 202 of file function.h.

eval_funcp_6

typedef ex(* GiNaC::eval_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 203 of file function.h.

evalf_funcp_6

typedef ex(* GiNaC::evalf_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 204 of file function.h.

conjugate_funcp_6

typedef ex(* GiNaC::conjugate_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 205 of file function.h.

real_part_funcp_6

typedef ex(* GiNaC::real_part_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 206 of file function.h.

imag_part_funcp_6

typedef ex(* GiNaC::imag_part_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 207 of file function.h.

expand_funcp_6

typedef ex(* GiNaC::expand_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 208 of file function.h.

derivative_funcp_6

typedef ex(* GiNaC::derivative_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 209 of file function.h.

expl_derivative_funcp_6

typedef ex(* GiNaC::expl_derivative_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 210 of file function.h.

power_funcp_6

typedef ex(* GiNaC::power_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 211 of file function.h.

series_funcp_6

typedef ex(* GiNaC::series_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 212 of file function.h.

print_funcp_6

typedef void(* GiNaC::print_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 213 of file function.h.

info_funcp_6

typedef bool(* GiNaC::info_funcp_6) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 214 of file function.h.

eval_funcp_7

typedef ex(* GiNaC::eval_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 215 of file function.h.

evalf_funcp_7

typedef ex(* GiNaC::evalf_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 216 of file function.h.

conjugate_funcp_7

typedef ex(* GiNaC::conjugate_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 217 of file function.h.

real_part_funcp_7

typedef ex(* GiNaC::real_part_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 218 of file function.h.

imag_part_funcp_7

typedef ex(* GiNaC::imag_part_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 219 of file function.h.

expand_funcp_7

typedef ex(* GiNaC::expand_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 220 of file function.h.

derivative_funcp_7

typedef ex(* GiNaC::derivative_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 221 of file function.h.

expl_derivative_funcp_7

typedef ex(* GiNaC::expl_derivative_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 222 of file function.h.

power_funcp_7

typedef ex(* GiNaC::power_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 223 of file function.h.

series_funcp_7

typedef ex(* GiNaC::series_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 224 of file function.h.

print_funcp_7

typedef void(* GiNaC::print_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 225 of file function.h.

info_funcp_7

typedef bool(* GiNaC::info_funcp_7) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 226 of file function.h.

eval_funcp_8

typedef ex(* GiNaC::eval_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 227 of file function.h.

evalf_funcp_8

typedef ex(* GiNaC::evalf_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 228 of file function.h.

conjugate_funcp_8

typedef ex(* GiNaC::conjugate_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 229 of file function.h.

real_part_funcp_8

typedef ex(* GiNaC::real_part_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 230 of file function.h.

imag_part_funcp_8

typedef ex(* GiNaC::imag_part_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 231 of file function.h.

expand_funcp_8

typedef ex(* GiNaC::expand_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 232 of file function.h.

derivative_funcp_8

typedef ex(* GiNaC::derivative_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 233 of file function.h.

expl_derivative_funcp_8

typedef ex(* GiNaC::expl_derivative_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 234 of file function.h.

power_funcp_8

typedef ex(* GiNaC::power_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 235 of file function.h.

series_funcp_8

typedef ex(* GiNaC::series_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 236 of file function.h.

print_funcp_8

typedef void(* GiNaC::print_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 237 of file function.h.

info_funcp_8

typedef bool(* GiNaC::info_funcp_8) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 238 of file function.h.

eval_funcp_9

typedef ex(* GiNaC::eval_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 239 of file function.h.

evalf_funcp_9

typedef ex(* GiNaC::evalf_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 240 of file function.h.

conjugate_funcp_9

typedef ex(* GiNaC::conjugate_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 241 of file function.h.

real_part_funcp_9

typedef ex(* GiNaC::real_part_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 242 of file function.h.

imag_part_funcp_9

typedef ex(* GiNaC::imag_part_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 243 of file function.h.

expand_funcp_9

typedef ex(* GiNaC::expand_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 244 of file function.h.

derivative_funcp_9

typedef ex(* GiNaC::derivative_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 245 of file function.h.

expl_derivative_funcp_9

typedef ex(* GiNaC::expl_derivative_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 246 of file function.h.

power_funcp_9

typedef ex(* GiNaC::power_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 247 of file function.h.

series_funcp_9

typedef ex(* GiNaC::series_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 248 of file function.h.

print_funcp_9

typedef void(* GiNaC::print_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 249 of file function.h.

info_funcp_9

typedef bool(* GiNaC::info_funcp_9) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 250 of file function.h.

eval_funcp_10

typedef ex(* GiNaC::eval_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 251 of file function.h.

evalf_funcp_10

typedef ex(* GiNaC::evalf_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 252 of file function.h.

conjugate_funcp_10

typedef ex(* GiNaC::conjugate_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 253 of file function.h.

real_part_funcp_10

typedef ex(* GiNaC::real_part_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 254 of file function.h.

imag_part_funcp_10

typedef ex(* GiNaC::imag_part_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 255 of file function.h.

expand_funcp_10

typedef ex(* GiNaC::expand_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 256 of file function.h.

derivative_funcp_10

typedef ex(* GiNaC::derivative_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 257 of file function.h.

expl_derivative_funcp_10

typedef ex(* GiNaC::expl_derivative_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 258 of file function.h.

power_funcp_10

typedef ex(* GiNaC::power_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 259 of file function.h.

series_funcp_10

typedef ex(* GiNaC::series_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 260 of file function.h.

print_funcp_10

typedef void(* GiNaC::print_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 261 of file function.h.

info_funcp_10

typedef bool(* GiNaC::info_funcp_10) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 262 of file function.h.

eval_funcp_11

typedef ex(* GiNaC::eval_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 263 of file function.h.

evalf_funcp_11

typedef ex(* GiNaC::evalf_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 264 of file function.h.

conjugate_funcp_11

typedef ex(* GiNaC::conjugate_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 265 of file function.h.

real_part_funcp_11

typedef ex(* GiNaC::real_part_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 266 of file function.h.

imag_part_funcp_11

typedef ex(* GiNaC::imag_part_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 267 of file function.h.

expand_funcp_11

typedef ex(* GiNaC::expand_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 268 of file function.h.

derivative_funcp_11

typedef ex(* GiNaC::derivative_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 269 of file function.h.

expl_derivative_funcp_11

typedef ex(* GiNaC::expl_derivative_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 270 of file function.h.

power_funcp_11

typedef ex(* GiNaC::power_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 271 of file function.h.

series_funcp_11

typedef ex(* GiNaC::series_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 272 of file function.h.

print_funcp_11

typedef void(* GiNaC::print_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 273 of file function.h.

info_funcp_11

typedef bool(* GiNaC::info_funcp_11) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 274 of file function.h.

eval_funcp_12

typedef ex(* GiNaC::eval_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 275 of file function.h.

evalf_funcp_12

typedef ex(* GiNaC::evalf_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 276 of file function.h.

conjugate_funcp_12

typedef ex(* GiNaC::conjugate_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 277 of file function.h.

real_part_funcp_12

typedef ex(* GiNaC::real_part_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 278 of file function.h.

imag_part_funcp_12

typedef ex(* GiNaC::imag_part_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 279 of file function.h.

expand_funcp_12

typedef ex(* GiNaC::expand_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 280 of file function.h.

derivative_funcp_12

typedef ex(* GiNaC::derivative_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 281 of file function.h.

expl_derivative_funcp_12

typedef ex(* GiNaC::expl_derivative_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 282 of file function.h.

power_funcp_12

typedef ex(* GiNaC::power_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 283 of file function.h.

series_funcp_12

typedef ex(* GiNaC::series_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 284 of file function.h.

print_funcp_12

typedef void(* GiNaC::print_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 285 of file function.h.

info_funcp_12

typedef bool(* GiNaC::info_funcp_12) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 286 of file function.h.

eval_funcp_13

typedef ex(* GiNaC::eval_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 287 of file function.h.

evalf_funcp_13

typedef ex(* GiNaC::evalf_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 288 of file function.h.

conjugate_funcp_13

typedef ex(* GiNaC::conjugate_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 289 of file function.h.

real_part_funcp_13

typedef ex(* GiNaC::real_part_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 290 of file function.h.

imag_part_funcp_13

typedef ex(* GiNaC::imag_part_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 291 of file function.h.

expand_funcp_13

typedef ex(* GiNaC::expand_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 292 of file function.h.

derivative_funcp_13

typedef ex(* GiNaC::derivative_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 293 of file function.h.

expl_derivative_funcp_13

typedef ex(* GiNaC::expl_derivative_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 294 of file function.h.

power_funcp_13

typedef ex(* GiNaC::power_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 295 of file function.h.

series_funcp_13

typedef ex(* GiNaC::series_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 296 of file function.h.

print_funcp_13

typedef void(* GiNaC::print_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 297 of file function.h.

info_funcp_13

typedef bool(* GiNaC::info_funcp_13) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 298 of file function.h.

eval_funcp_14

typedef ex(* GiNaC::eval_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 299 of file function.h.

evalf_funcp_14

typedef ex(* GiNaC::evalf_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 300 of file function.h.

conjugate_funcp_14

typedef ex(* GiNaC::conjugate_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 301 of file function.h.

real_part_funcp_14

typedef ex(* GiNaC::real_part_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 302 of file function.h.

imag_part_funcp_14

typedef ex(* GiNaC::imag_part_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 303 of file function.h.

expand_funcp_14

typedef ex(* GiNaC::expand_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 304 of file function.h.

derivative_funcp_14

typedef ex(* GiNaC::derivative_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 305 of file function.h.

expl_derivative_funcp_14

typedef ex(* GiNaC::expl_derivative_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const symbol &)

Definition at line 306 of file function.h.

power_funcp_14

typedef ex(* GiNaC::power_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)

Definition at line 307 of file function.h.

series_funcp_14

typedef ex(* GiNaC::series_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)

Definition at line 308 of file function.h.

print_funcp_14

typedef void(* GiNaC::print_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)

Definition at line 309 of file function.h.

info_funcp_14

typedef bool(* GiNaC::info_funcp_14) (const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, unsigned)

Definition at line 310 of file function.h.

eval_funcp_exvector

typedef ex(* GiNaC::eval_funcp_exvector) (const exvector &)

Definition at line 315 of file function.h.

evalf_funcp_exvector

typedef ex(* GiNaC::evalf_funcp_exvector) (const exvector &)

Definition at line 316 of file function.h.

conjugate_funcp_exvector

typedef ex(* GiNaC::conjugate_funcp_exvector) (const exvector &)

Definition at line 317 of file function.h.

real_part_funcp_exvector

typedef ex(* GiNaC::real_part_funcp_exvector) (const exvector &)

Definition at line 318 of file function.h.

imag_part_funcp_exvector

typedef ex(* GiNaC::imag_part_funcp_exvector) (const exvector &)

Definition at line 319 of file function.h.

expand_funcp_exvector

typedef ex(* GiNaC::expand_funcp_exvector) (const exvector &, unsigned)

Definition at line 320 of file function.h.

derivative_funcp_exvector

typedef ex(* GiNaC::derivative_funcp_exvector) (const exvector &, unsigned)

Definition at line 321 of file function.h.

expl_derivative_funcp_exvector

typedef ex(* GiNaC::expl_derivative_funcp_exvector) (const exvector &, const symbol &)

Definition at line 322 of file function.h.

power_funcp_exvector

typedef ex(* GiNaC::power_funcp_exvector) (const exvector &, const ex &)

Definition at line 323 of file function.h.

series_funcp_exvector

typedef ex(* GiNaC::series_funcp_exvector) (const exvector &, const relational &, int, unsigned)

Definition at line 324 of file function.h.

print_funcp_exvector

typedef void(* GiNaC::print_funcp_exvector) (const exvector &, const print_context &)

Definition at line 325 of file function.h.

info_funcp_exvector

typedef bool(* GiNaC::info_funcp_exvector) (const exvector &, unsigned)

Definition at line 326 of file function.h.

exhashmap

template<typename T , class Hash = std::hash<ex>, class KeyEqual = std::equal_to<ex>, class Allocator = std::allocator<std::pair<const ex, T>>>

using GiNaC::exhashmap = typedef std::unordered_map<ex, T, Hash, KeyEqual, Allocator>

Definition at line 34 of file hash_map.h.

spmap

typedef std::map<spmapkey, ex> GiNaC::spmap

Definition at line 211 of file indexed.h.

lookup_map

typedef map<error_and_integral, ex, error_and_integral_is_less> GiNaC::lookup_map

Definition at line 210 of file integral.cpp.

lst

typedef container< std::list > GiNaC::lst

Definition at line 32 of file lst.h.

uintvector

typedef std::vector<std::size_t> GiNaC::uintvector

Definition at line 117 of file ncmul.cpp.

unsignedvector

typedef std::vector<unsigned> GiNaC::unsignedvector

Definition at line 275 of file ncmul.cpp.

exvectorvector

typedef std::vector<exvector> GiNaC::exvectorvector

Definition at line 276 of file ncmul.cpp.

sym_desc_vec

typedef std::vector<sym_desc> GiNaC::sym_desc_vec

Definition at line 160 of file normal.cpp.

digits_changed_callback

typedef void(* GiNaC::digits_changed_callback) (long)

Function pointer to implement callbacks in the case 'Digits' gets changed.

Main purpose of such callbacks is to adjust look-up tables of certain functions to the new precision. Parameter contains the signed difference between new Digits and old Digits.

Definition at line 40 of file numeric.h.

print_context_class_info

typedef class_info<print_context_options> GiNaC::print_context_class_info

Definition at line 49 of file print.h.

registered_class_info

typedef class_info<registered_class_options> GiNaC::registered_class_info

Definition at line 125 of file registrar.h.

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
callback_registered

Definition at line 295 of file operators.cpp.

Function Documentation

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [1/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	add	,
		expairseq	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 38 of file add.cpp.

GINAC_BIND_UNARCHIVER() [1/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

add

)

GINAC_DECLARE_UNARCHIVER() [1/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

add

)

write_unsigned()

static void GiNaC::write_unsigned ( std::ostream &  os, unsigned  val  )

static

Write unsigned integer quantity to stream.

Definition at line 173 of file archive.cpp.

read_unsigned()

static unsigned GiNaC::read_unsigned ( std::istream &  is )

static

Read unsigned integer quantity from stream.

Definition at line 183 of file archive.cpp.

operator<<() [1/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const archive_node &	n
	)

Write archive_node to binary data stream.

Definition at line 199 of file archive.cpp.

operator<<() [2/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const archive &	ar
	)

Write archive to binary data stream.

Definition at line 212 of file archive.cpp.

operator>>() [1/3]

std::istream & GiNaC::operator>>	(	std::istream &	is,
		archive_node &	n
	)

Read archive_node from binary data stream.

Definition at line 244 of file archive.cpp.

operator>>() [2/3]

std::istream & GiNaC::operator>>	(	std::istream &	is,
		archive &	ar
	)

Read archive from binary data stream.

Definition at line 259 of file archive.cpp.

find_factory_fcn()

static synthesize_func GiNaC::find_factory_fcn ( const std::string &  name )

static

Definition at line 535 of file archive.cpp.

References GiNaC::unarchive_table_t::find().

Referenced by GiNaC::archive_node::unarchive().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [2/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	basic	,
		void	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

basic copy constructor: implicitly assumes that the other class is of the exact same type (as it's used by duplicate()), so it can copy the tinfo_key and the hash value.

Definition at line 45 of file basic.cpp.

is_a() [1/3]

template<class T >

bool GiNaC::is_a ( const basic &  obj )

inline

Check if obj is a T, including base classes.

Definition at line 313 of file basic.h.

Referenced by GiNaC::container< C >::subs().

is_exactly_a() [1/2]

template<class T >

bool GiNaC::is_exactly_a ( const basic &  obj )

inline

Check if obj is a T, not including base classes.

Definition at line 320 of file basic.h.

dynallocate() [1/2]

template<class B , typename... Args>

B & GiNaC::dynallocate ( Args &&...  args )

inline

Constructs a new (class basic or derived) B object on the heap.

This function picks the object's ctor based on the given argument types.

This helps the constructor of ex from basic (or a derived class B) because then the constructor doesn't have to duplicate the object onto the heap. See ex::construct_from_basic(const basic &) for more information.

Definition at line 334 of file basic.h.

References GiNaC::status_flags::dynallocated.

dynallocate() [2/2]

template<class B >

B & GiNaC::dynallocate ( std::initializer_list< ex >  il )

inline

Constructs a new (class basic or derived) B object on the heap.

This function is needed for GiNaC classes which have public ctors from initializer lists of expressions (which are not a type and not captured by the variadic template version).

Definition at line 345 of file basic.h.

References GiNaC::status_flags::dynallocated.

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [3/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	clifford	,
		indexed	,
		print_func< print_dflt > &::do_print_dflt. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree
	)

print_func< print_dflt >() [1/3]

GiNaC::print_func< print_dflt >

(

&diracone::do_print

)

&

Definition at line 51 of file clifford.cpp.

GINAC_BIND_UNARCHIVER() [2/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

clifford

)

GINAC_BIND_UNARCHIVER() [3/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

cliffordunit

)

GINAC_BIND_UNARCHIVER() [4/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

diracone

)

GINAC_BIND_UNARCHIVER() [5/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgamma

)

GINAC_BIND_UNARCHIVER() [6/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgamma5

)

GINAC_BIND_UNARCHIVER() [7/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgammaL

)

GINAC_BIND_UNARCHIVER() [8/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgammaR

)

is_dirac_slash()

static bool GiNaC::is_dirac_slash ( const ex &  seq0 )

static

Definition at line 256 of file clifford.cpp.

Referenced by GiNaC::clifford::do_print_dflt(), and GiNaC::clifford::do_print_latex().

base_and_index()

static void GiNaC::base_and_index ( const ex &  c, ex &  b, ex &  i  )

static

This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix)

Definition at line 325 of file clifford.cpp.

dirac_ONE()

ex GiNaC::dirac_ONE

(

unsigned char

rl = 0

)

Create a Clifford unity object.

Parameters

rl	Representation label

Returns

newly constructed object

Definition at line 723 of file clifford.cpp.

Referenced by GiNaC::add::coeff().

get_dim_uint()

static unsigned GiNaC::get_dim_uint ( const ex &  e )

static

Definition at line 729 of file clifford.cpp.

clifford_unit()

ex GiNaC::clifford_unit	(	const ex &	mu,
		const ex &	metr,
		unsigned char	rl = 0
	)

Create a Clifford unit object.

Parameters

mu	Index (must be of class varidx or a derived class)
metr	Metric (should be indexed, tensmetric or a derived class, or a matrix)
rl	Representation label

Returns

newly constructed Clifford unit object

Definition at line 740 of file clifford.cpp.

dirac_gamma()

ex GiNaC::dirac_gamma	(	const ex &	mu,
		unsigned char	rl = 0
	)

Create a Dirac gamma object.

Parameters

mu	Index (must be of class varidx or a derived class)
rl	Representation label

Returns

newly constructed gamma object

Definition at line 782 of file clifford.cpp.

dirac_gamma5()

ex GiNaC::dirac_gamma5

(

unsigned char

rl = 0

)

Create a Dirac gamma5 object.

Parameters

rl	Representation label

Returns

newly constructed object

Definition at line 794 of file clifford.cpp.

dirac_gammaL()

ex GiNaC::dirac_gammaL

(

unsigned char

rl = 0

)

Create a Dirac gammaL object.

Parameters

rl	Representation label

Returns

newly constructed object

Definition at line 800 of file clifford.cpp.

dirac_gammaR()

ex GiNaC::dirac_gammaR

(

unsigned char

rl = 0

)

Create a Dirac gammaR object.

Parameters

rl	Representation label

Returns

newly constructed object

Definition at line 806 of file clifford.cpp.

dirac_slash()

ex GiNaC::dirac_slash	(	const ex &	e,
		const ex &	dim,
		unsigned char	rl = 0
	)

Create a term of the form e_mu * gamma~mu with a unique index mu.

Parameters

e	Original expression
dim	Dimension of index
rl	Representation label

Definition at line 812 of file clifford.cpp.

get_representation_label() [1/2]

static unsigned char GiNaC::get_representation_label ( const return_type_t &  ti )

static

Extract representation label from tinfo key (as returned by return_type_tinfo()).

Definition at line 825 of file clifford.cpp.

Referenced by color_trace(), GiNaC::su3f::contract_with(), and GiNaC::su3d::contract_with().

trace_string()

static ex GiNaC::trace_string ( exvector::const_iterator  ix, size_t  num  )

static

Take trace of a string of an even number of Dirac gammas given a vector of indices.

Definition at line 832 of file clifford.cpp.

dirac_trace() [1/3]

ex GiNaC::dirac_trace	(	const ex &	e,
		const std::set< unsigned char > &	rls,
		const ex &	trONE = 4
	)

Calculate dirac traces over the specified set of representation labels.

The computed trace is a linear functional that is equal to the usual trace only in D = 4 dimensions. In particular, the functional is not always cyclic in D != 4 dimensions when gamma5 is involved.

Parameters

e	Expression to take the trace of
rls	Set of representation labels
trONE	Expression to be returned as the trace of the unit matrix

Definition at line 866 of file clifford.cpp.

dirac_trace() [2/3]

ex GiNaC::dirac_trace	(	const ex &	e,
		const lst &	rll,
		const ex &	trONE = 4
	)

Calculate dirac traces over the specified list of representation labels.

The computed trace is a linear functional that is equal to the usual trace only in D = 4 dimensions. In particular, the functional is not always cyclic in D != 4 dimensions when gamma5 is involved.

Parameters

e	Expression to take the trace of
rll	List of representation labels
trONE	Expression to be returned as the trace of the unit matrix

Definition at line 1003 of file clifford.cpp.

dirac_trace() [3/3]

ex GiNaC::dirac_trace	(	const ex &	e,
		unsigned char	rl = 0,
		const ex &	trONE = 4
	)

Calculate the trace of an expression containing gamma objects with a specified representation label.

The computed trace is a linear functional that is equal to the usual trace only in D = 4 dimensions. In particular, the functional is not always cyclic in D != 4 dimensions when gamma5 is involved.

Parameters

e	Expression to take the trace of
rl	Representation label
trONE	Expression to be returned as the trace of the unit matrix

Definition at line 1015 of file clifford.cpp.

canonicalize_clifford()

ex GiNaC::canonicalize_clifford

(

const ex &

e

)

Bring all products of clifford objects in an expression into a canonical order.

This is not necessarily the most simple form but it will allow to check two expressions for equality.

Definition at line 1025 of file clifford.cpp.

clifford_star_bar()

ex GiNaC::clifford_star_bar	(	const ex &	e,
		bool	do_bar,
		unsigned	options
	)

An auxillary function performing clifford_star() and clifford_bar().

Definition at line 1091 of file clifford.cpp.

Referenced by clifford_bar(), and clifford_star().

clifford_prime()

ex GiNaC::clifford_prime

(

const ex &

e

)

Automorphism of the Clifford algebra, simply changes signs of all clifford units.

Definition at line 1132 of file clifford.cpp.

remove_dirac_ONE()

ex GiNaC::remove_dirac_ONE	(	const ex &	e,
		unsigned char	rl = 0,
		unsigned	options = 0
	)

Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1.

For the default value rl = 0 remove all of them. Aborts if e contains any clifford_unit with representation_label to be removed.

Parameters

e	Expression to be processed
rl	Value of representation label
options	Defines some internal use

Definition at line 1146 of file clifford.cpp.

clifford_max_label()

int GiNaC::clifford_max_label	(	const ex &	e,
		bool	ignore_ONE = false
	)

Returns the maximal representation label of a clifford object if e contains at least one, otherwise returns -1.

Parameters

e	Expression to be processed
ignore_ONE	defines if clifford_ONE should be ignored in the search

Definition at line 1187 of file clifford.cpp.

Referenced by GiNaC::add::coeff().

clifford_norm()

ex GiNaC::clifford_norm

(

const ex &

e

)

Calculation of the norm in the Clifford algebra.

Definition at line 1202 of file clifford.cpp.

clifford_inverse()

ex GiNaC::clifford_inverse

(

const ex &

e

)

Calculation of the inverse in the Clifford algebra.

Definition at line 1207 of file clifford.cpp.

lst_to_clifford() [1/2]

ex GiNaC::lst_to_clifford	(	const ex &	v,
		const ex &	mu,
		const ex &	metr,
		unsigned char	rl = 0
	)

List or vector conversion into the Clifford vector.

Parameters

v	List or vector of coordinates
mu	Index (must be of class varidx or a derived class)
metr	Metric (should be indexed, tensmetric or a derived class, or a matrix)
rl	Representation label

Returns

Clifford vector with given components

Definition at line 1216 of file clifford.cpp.

lst_to_clifford() [2/2]

ex GiNaC::lst_to_clifford	(	const ex &	v,
		const ex &	e
	)

List or vector conversion into the Clifford vector.

Parameters

v	List or vector of coordinates
e	Clifford unit object

Returns

Clifford vector with given components

Definition at line 1224 of file clifford.cpp.

get_clifford_comp()

static ex GiNaC::get_clifford_comp ( const ex &  e, const ex &  c, bool  root = true  )

static

Auxiliary structure to define a function for striping one Clifford unit from vectors.

Used in clifford_to_lst().

Definition at line 1268 of file clifford.cpp.

clifford_to_lst()

lst GiNaC::clifford_to_lst	(	const ex &	e,
		const ex &	c,
		bool	algebraic = true
	)

An inverse function to lst_to_clifford().

For given Clifford vector extracts its components with respect to given Clifford unit. Obtained components may contain Clifford units with a different metric. Extraction is based on the algebraic formula (e * c.i + c.i * e)/ pow(e.i, 2) for non-degenerate cases (i.e. neither pow(e.i, 2) = 0).

Parameters

e	Clifford expression to be decomposed into components
c	Clifford unit defining the metric for splitting (should have numeric dimension of indices)
algebraic	Use algebraic or symbolic algorithm for extractions

Returns

List of components of a Clifford vector

Definition at line 1331 of file clifford.cpp.

clifford_moebius_map() [1/2]

ex GiNaC::clifford_moebius_map	(	const ex &	a,
		const ex &	b,
		const ex &	c,
		const ex &	d,
		const ex &	v,
		const ex &	G,
		unsigned char	rl = 0
	)

Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix (a b\c d) in linear spaces with arbitrary signature.

The expression is (a * x + b)/(c * x + d), where x is a vector build from list v with metric G. (see Jan Cnops. An introduction to {D}irac operators on manifolds, v.24 of Progress in Mathematical Physics. Birkhauser Boston Inc., Boston, MA, 2002.)

Parameters

a	(1,1) entry of the defining matrix
b	(1,2) entry of the defining matrix
c	(2,1) entry of the defining matrix
d	(2,2) entry of the defining matrix
v	Vector to be transformed
G	Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
rl	Representation label

Returns

List of components of the transformed vector

Definition at line 1375 of file clifford.cpp.

clifford_moebius_map() [2/2]

ex GiNaC::clifford_moebius_map	(	const ex &	M,
		const ex &	v,
		const ex &	G,
		unsigned char	rl = 0
	)

The second form of Moebius transformations defined by a 2x2 Clifford matrix M This function takes the transformation matrix M as a single entity.

Parameters

M	the defining matrix
v	Vector to be transformed
G	Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
rl	Representation label

Returns

List of components of the transformed vector

Definition at line 1402 of file clifford.cpp.

GINAC_DECLARE_UNARCHIVER() [2/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

clifford

)

GINAC_DECLARE_UNARCHIVER() [3/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracone

)

GINAC_DECLARE_UNARCHIVER() [4/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

cliffordunit

)

GINAC_DECLARE_UNARCHIVER() [5/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgamma

)

GINAC_DECLARE_UNARCHIVER() [6/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgamma5

)

GINAC_DECLARE_UNARCHIVER() [7/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgammaL

)

GINAC_DECLARE_UNARCHIVER() [8/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgammaR

)

is_clifford_tinfo()

bool GiNaC::is_clifford_tinfo ( const return_type_t &  ti )

inline

Check whether a given return_type_t object (as returned by return_type_tinfo() is that of a clifford object (with an arbitrary representation label).

Parameters

ti

tinfo key

Definition at line 194 of file clifford.h.

References GiNaC::return_type_t::tinfo.

Referenced by GiNaC::ncmul::conjugate().

clifford_bar()

ex GiNaC::clifford_bar ( const ex &  e )

inline

Main anti-automorphism of the Clifford algebra: makes reversion and changes signs of all clifford units.

Definition at line 290 of file clifford.h.

References clifford_star_bar().

clifford_star()

ex GiNaC::clifford_star ( const ex &  e )

inline

Reversion of the Clifford algebra, reverse the order of all clifford units in ncmul.

Definition at line 294 of file clifford.h.

References clifford_star_bar().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [4/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	su3one	,
		tensor	,
		print_func< print_dflt > &::do_print. print_func< print_latex > &::do_print_latex
	)

print_func< print_dflt >() [2/3]

GiNaC::print_func< print_dflt >

(

&su3t::do_print

)

&

Definition at line 45 of file color.cpp.

GINAC_BIND_UNARCHIVER() [9/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

color

)

GINAC_BIND_UNARCHIVER() [10/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

su3one

)

GINAC_BIND_UNARCHIVER() [11/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

su3t

)

GINAC_BIND_UNARCHIVER() [12/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

su3f

)

GINAC_BIND_UNARCHIVER() [13/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

su3d

)

permute_free_index_to_front()

static ex GiNaC::permute_free_index_to_front ( const exvector &  iv3, const exvector &  iv2, int &  sig  )

static

Given a vector iv3 of three indices and a vector iv2 of two indices that is a subset of iv3, return the (free) index that is in iv3 but not in iv2 and the sign introduced by permuting that index to the front.

Parameters

iv3	Vector of 3 indices
iv2	Vector of 2 indices, must be a subset of iv3
sig	Returns sign introduced by index permutation

Returns

the free index (the one that is in iv3 but not in iv2)

Definition at line 197 of file color.cpp.

References GINAC_ASSERT, and TEST_PERMUTATION.

Referenced by GiNaC::su3f::contract_with(), and GiNaC::su3d::contract_with().

color_ONE()

ex GiNaC::color_ONE

(

unsigned char

rl = 0

)

Create the su(3) unity element.

This is an indexed object, although it has no indices.

Parameters

rl	Representation label

Returns

newly constructed unity element

Definition at line 470 of file color.cpp.

Referenced by GiNaC::su3t::contract_with().

color_T()

ex GiNaC::color_T	(	const ex &	a,
		unsigned char	rl = 0
	)

Create an su(3) generator.

Parameters

a	Index
rl	Representation label

Returns

newly constructed unity generator

Definition at line 476 of file color.cpp.

Referenced by color_trace(), GiNaC::su3f::contract_with(), and GiNaC::su3d::contract_with().

color_f()

ex GiNaC::color_f	(	const ex &	a,
		const ex &	b,
		const ex &	c
	)

Create an su(3) antisymmetric structure constant.

Parameters

a	First index
b	Second index
c	Third index

Returns

newly constructed structure constant

Definition at line 488 of file color.cpp.

References antisymmetric3(), and c.

Referenced by color_h().

color_d()

ex GiNaC::color_d	(	const ex &	a,
		const ex &	b,
		const ex &	c
	)

Create an su(3) symmetric structure constant.

Parameters

a	First index
b	Second index
c	Third index

Returns

newly constructed structure constant

Definition at line 500 of file color.cpp.

References c, and symmetric3().

Referenced by color_h().

color_h()

ex GiNaC::color_h	(	const ex &	a,
		const ex &	b,
		const ex &	c
	)

This returns the linear combination d.a.b.c+I*f.a.b.c.

Definition at line 512 of file color.cpp.

References c, color_d(), color_f(), and I.

Referenced by color_trace().

is_color_tinfo()

static bool GiNaC::is_color_tinfo ( const return_type_t &  ti )

static

Check whether a given tinfo key (as returned by return_type_tinfo() is that of a color object (with an arbitrary representation label).

Definition at line 519 of file color.cpp.

References GiNaC::return_type_t::tinfo.

Referenced by color_trace().

get_representation_label() [2/2]

static unsigned char GiNaC::get_representation_label ( const return_type_t &  ti )

static

Extract representation label from tinfo key (as returned by return_type_tinfo()).

Definition at line 526 of file color.cpp.

References GiNaC::return_type_t::rl.

color_trace() [1/3]

ex GiNaC::color_trace	(	const ex &	e,
		const std::set< unsigned char > &	rls
	)

Calculate color traces over the specified set of representation labels.

Parameters

e	Expression to take the trace of
rls	Set of representation labels

Definition at line 531 of file color.cpp.

References _ex0, _ex1, _ex3, color_h(), color_T(), color_trace(), delta_tensor(), GiNaC::ex::expand(), get_representation_label(), is_color_tinfo(), GiNaC::ex::map(), GiNaC::ex::nops(), GiNaC::ex::op(), and GiNaC::ex::return_type_tinfo().

Referenced by color_trace(), color_trace(), color_trace(), and GiNaC::su3t::contract_with().

color_trace() [2/3]

ex GiNaC::color_trace	(	const ex &	e,
		const lst &	rll
	)

Calculate color traces over the specified list of representation labels.

Parameters

e	Expression to take the trace of
rll	List of representation labels

Definition at line 617 of file color.cpp.

References color_trace(), and GiNaC::info_flags::nonnegint.

color_trace() [3/3]

ex GiNaC::color_trace	(	const ex &	e,
		unsigned char	rl = 0
	)

Calculate the trace of an expression containing color objects with a specified representation label.

Parameters

e	Expression to take the trace of
rl	Representation label

Definition at line 629 of file color.cpp.

References color_trace().

GINAC_DECLARE_UNARCHIVER() [9/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

color

)

GINAC_DECLARE_UNARCHIVER() [10/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3one

)

GINAC_DECLARE_UNARCHIVER() [11/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3t

)

GINAC_DECLARE_UNARCHIVER() [12/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3f

)

GINAC_DECLARE_UNARCHIVER() [13/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3d

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [5/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	constant	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)		const

Definition at line 35 of file constant.cpp.

References GiNaC::status_flags::evaluated, and GiNaC::status_flags::expanded.

GINAC_BIND_UNARCHIVER() [14/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

constant

)

GINAC_DECLARE_UNARCHIVER() [14/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

constant

)

crc32()

static unsigned GiNaC::crc32 ( const char *  c, const unsigned  len, const unsigned  crcinit  )

static

Definition at line 66 of file crc32.h.

References c, crctab, and len.

are_ex_trivially_equal()

bool GiNaC::are_ex_trivially_equal ( const ex &  e1, const ex &  e2  )

inline

Compare two objects of class quickly without doing a deep tree traversal.

Returns

"true" if they are equal "false" if equality cannot be established quickly (e1 and e2 may still be equal, in this case.

Definition at line 700 of file ex.h.

Referenced by GiNaC::expair::conjugate(), GiNaC::add::conjugate(), GiNaC::container< C >::conjugate(), GiNaC::expairseq::conjugate(), GiNaC::integral::conjugate(), GiNaC::matrix::conjugate(), GiNaC::mul::conjugate(), GiNaC::power::conjugate(), GiNaC::pseries::conjugate(), GiNaC::pseries::eval_integ(), GiNaC::integral::evalf(), GiNaC::pseries::evalm(), GiNaC::indexed::expand(), GiNaC::integral::expand(), GiNaC::power::expand(), GiNaC::expairseq::expandchildren(), GiNaC::mul::expandchildren(), GiNaC::ncmul::expandchildren(), GiNaC::expairseq::make_flat(), GiNaC::make_flat_inserter::make_flat_inserter(), GiNaC::basic::map(), GiNaC::idx::map(), GiNaC::power::map(), GiNaC::relational::map(), GiNaC::internal::_iter_rep::operator==(), GiNaC::const_iterator::operator==(), GiNaC::basic::subs(), GiNaC::clifford::subs(), GiNaC::idx::subs(), GiNaC::power::subs(), GiNaC::relational::subs(), GiNaC::container< C >::subschildren(), and GiNaC::expairseq::subschildren().

operator<<() [3/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const exvector &	e
	)

Definition at line 350 of file operators.cpp.

References get_print_context().

operator<<() [4/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const exset &	e
	)

Definition at line 377 of file operators.cpp.

References get_print_context().

operator<<() [5/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const exmap &	e
	)

Definition at line 404 of file operators.cpp.

References get_print_context().

nops() [1/2]

size_t GiNaC::nops ( const ex &  thisex )

inline

Definition at line 728 of file ex.h.

References GiNaC::ex::nops().

Referenced by GiNaC::basic::calchash(), GiNaC::basic::derivative(), GiNaC::basic::do_print_tree(), GiNaC::container< C >::do_print_tree(), GiNaC::basic::eval_integ(), GiNaC::basic::evalf(), GiNaC::basic::evalm(), GiNaC::basic::expand(), GiNaC::basic::has(), GiNaC::container< C >::let_op(), GiNaC::basic::map(), GiNaC::basic::match(), GiNaC::container< C >::op(), and GiNaC::basic::subs().

expand() [1/2]

ex GiNaC::expand ( const ex &  thisex, unsigned  options = 0  )

inline

Definition at line 731 of file ex.h.

References GiNaC::ex::expand(), and options.

Referenced by GiNaC::basic::collect(), divide(), divide_in_z(), gcd(), gcd_pf_pow(), log_expand(), prem(), quo(), rem(), and sprem().

conjugate()

ex GiNaC::conjugate ( const ex &  thisex )

inline

Definition at line 734 of file ex.h.

References GiNaC::ex::conjugate().

Referenced by conjugate_expl_derivative().

real_part()

ex GiNaC::real_part ( const ex &  thisex )

inline

Definition at line 737 of file ex.h.

References GiNaC::ex::real_part().

Referenced by cos_imag_part(), cos_real_part(), cosh_imag_part(), cosh_real_part(), exp_imag_part(), exp_real_part(), log_imag_part(), real_part_expl_derivative(), sin_imag_part(), sin_real_part(), sinh_imag_part(), sinh_real_part(), tan_imag_part(), tan_real_part(), tanh_imag_part(), and tanh_real_part().

imag_part()

ex GiNaC::imag_part ( const ex &  thisex )

inline

Definition at line 740 of file ex.h.

References GiNaC::ex::imag_part().

Referenced by cos_imag_part(), cos_real_part(), cosh_imag_part(), cosh_real_part(), exp_imag_part(), exp_real_part(), imag_part_expl_derivative(), log_imag_part(), sin_imag_part(), sin_real_part(), sinh_imag_part(), sinh_real_part(), tan_imag_part(), tan_real_part(), tanh_imag_part(), and tanh_real_part().

has()

bool GiNaC::has ( const ex &  thisex, const ex &  pattern, unsigned  options = 0  )

inline

Definition at line 743 of file ex.h.

References GiNaC::ex::has(), and options.

Referenced by GiNaC::basic::is_polynomial().

find()

bool GiNaC::find ( const ex &  thisex, const ex &  pattern, exset &  found  )

inline

Definition at line 746 of file ex.h.

References GiNaC::ex::find().

is_polynomial()

bool GiNaC::is_polynomial ( const ex &  thisex, const ex &  vars  )

inline

Definition at line 749 of file ex.h.

References GiNaC::ex::is_polynomial().

degree()

int GiNaC::degree ( const ex &  thisex, const ex &  s  )

inline

Definition at line 752 of file ex.h.

References GiNaC::ex::degree().

Referenced by GiNaC::basic::collect(), replace_with_symbol(), and sqrfree_parfrac().

ldegree()

int GiNaC::ldegree ( const ex &  thisex, const ex &  s  )

inline

Definition at line 755 of file ex.h.

References GiNaC::ex::ldegree().

Referenced by GiNaC::basic::collect().

coeff()

ex GiNaC::coeff ( const ex &  thisex, const ex &  s, int  n = 1  )

inline

Definition at line 758 of file ex.h.

References GiNaC::ex::coeff(), and n.

Referenced by GiNaC::basic::collect(), GiNaC::make_flat_inserter::handle_factor(), iterated_integral_evalf_impl(), log_series(), and sqrfree_parfrac().

numer() [1/2]

ex GiNaC::numer ( const ex &  thisex )

inline

Definition at line 761 of file ex.h.

References GiNaC::ex::numer().

Referenced by decomp_rational(), GiNaC::power::imag_part(), GiNaC::add::integer_content(), print_real_csrc(), GiNaC::power::real_part(), replace_with_symbol(), and sqrfree_parfrac().

denom() [1/2]

ex GiNaC::denom ( const ex &  thisex )

inline

Definition at line 764 of file ex.h.

References GiNaC::ex::denom().

Referenced by decomp_rational(), GiNaC::add::integer_content(), lcmcoeff(), print_real_csrc(), replace_with_symbol(), and sqrfree_parfrac().

numer_denom()

ex GiNaC::numer_denom ( const ex &  thisex )

inline

Definition at line 767 of file ex.h.

References GiNaC::ex::numer_denom().

Referenced by decomp_rational(), and sqrfree_parfrac().

normal()

ex GiNaC::normal ( const ex &  thisex )

inline

Definition at line 770 of file ex.h.

References GiNaC::ex::normal().

Referenced by fsolve(), GiNaC::normal_map_function::operator()(), and replace_with_symbol().

to_rational()

ex GiNaC::to_rational ( const ex &  thisex, exmap &  repl  )

inline

Definition at line 773 of file ex.h.

References GiNaC::ex::to_rational().

to_polynomial()

ex GiNaC::to_polynomial ( const ex &  thisex, exmap &  repl  )

inline

Definition at line 776 of file ex.h.

References GiNaC::ex::to_polynomial().

collect()

ex GiNaC::collect ( const ex &  thisex, const ex &  s, bool  distributed = false  )

inline

Definition at line 779 of file ex.h.

References GiNaC::ex::collect().

Referenced by GiNaC::basic::collect().

eval()

ex GiNaC::eval ( const ex &  thisex )

inline

Definition at line 782 of file ex.h.

References GiNaC::ex::eval().

evalf() [1/2]

ex GiNaC::evalf ( const ex &  thisex )

inline

Definition at line 785 of file ex.h.

References GiNaC::ex::evalf().

Referenced by beta_eval(), eta_evalf(), GiNaC::evalf_map_function::operator()(), and zeta2_evalf().

evalm()

ex GiNaC::evalm ( const ex &  thisex )

inline

Definition at line 788 of file ex.h.

References GiNaC::ex::evalm().

Referenced by GiNaC::evalm_map_function::operator()().

eval_integ()

ex GiNaC::eval_integ ( const ex &  thisex )

inline

Definition at line 791 of file ex.h.

References GiNaC::ex::eval_integ().

Referenced by GiNaC::eval_integ_map_function::operator()().

diff()

ex GiNaC::diff ( const ex &  thisex, const symbol &  s, unsigned  nth = 1  )

inline

Definition at line 794 of file ex.h.

References GiNaC::ex::diff().

Referenced by GiNaC::derivative_map_function::operator()().

series()

ex GiNaC::series ( const ex &  thisex, const ex &  r, int  order, unsigned  options = 0  )

inline

Definition at line 797 of file ex.h.

References options, order, r, and GiNaC::ex::series().

Referenced by atan_series(), atanh_series(), Li2_series(), and log_series().

match()

bool GiNaC::match ( const ex &  thisex, const ex &  pattern, exmap &  repl_lst  )

inline

Definition at line 800 of file ex.h.

References GiNaC::ex::match().

Referenced by GiNaC::basic::has(), and GiNaC::basic::subs_one_level().

simplify_indexed() [1/3]

ex GiNaC::simplify_indexed ( const ex &  thisex, unsigned  options = 0  )

inline

Definition at line 803 of file ex.h.

References options, and GiNaC::ex::simplify_indexed().

Referenced by GiNaC::ex::simplify_indexed(), and GiNaC::ex::simplify_indexed().

simplify_indexed() [2/3]

ex GiNaC::simplify_indexed ( const ex &  thisex, const scalar_products &  sp, unsigned  options = 0  )

inline

Definition at line 806 of file ex.h.

References options, and GiNaC::ex::simplify_indexed().

symmetrize() [1/4]

ex GiNaC::symmetrize ( const ex &  thisex )

inline

Definition at line 809 of file ex.h.

References GiNaC::ex::symmetrize().

Referenced by idx_symmetrization(), GiNaC::ex::symmetrize(), symmetrize(), and symmetrize_cyclic().

symmetrize() [2/4]

ex GiNaC::symmetrize ( const ex &  thisex, const lst &  l  )

inline

Definition at line 812 of file ex.h.

References GiNaC::ex::symmetrize().

antisymmetrize() [1/4]

ex GiNaC::antisymmetrize ( const ex &  thisex )

inline

Definition at line 815 of file ex.h.

References GiNaC::ex::antisymmetrize().

Referenced by GiNaC::ex::antisymmetrize(), and antisymmetrize().

antisymmetrize() [2/4]

ex GiNaC::antisymmetrize ( const ex &  thisex, const lst &  l  )

inline

Definition at line 818 of file ex.h.

References GiNaC::ex::antisymmetrize().

symmetrize_cyclic() [1/4]

ex GiNaC::symmetrize_cyclic ( const ex &  thisex )

inline

Definition at line 821 of file ex.h.

References GiNaC::ex::symmetrize_cyclic().

Referenced by GiNaC::ex::symmetrize_cyclic(), and GiNaC::ex::symmetrize_cyclic().

symmetrize_cyclic() [2/4]

ex GiNaC::symmetrize_cyclic ( const ex &  thisex, const lst &  l  )

inline

Definition at line 824 of file ex.h.

References GiNaC::ex::symmetrize_cyclic().

op()

ex GiNaC::op ( const ex &  thisex, size_t  i  )

inline

Definition at line 827 of file ex.h.

References GiNaC::ex::op().

Referenced by GiNaC::basic::calchash(), GiNaC::basic::do_print_tree(), GiNaC::basic::has(), Li2_series(), GiNaC::basic::map(), GiNaC::basic::match(), GiNaC::basic::operator[](), GiNaC::basic::operator[](), rename_dummy_indices(), and GiNaC::basic::subs().

lhs()

ex GiNaC::lhs ( const ex &  thisex )

inline

Definition at line 830 of file ex.h.

References GiNaC::ex::lhs().

rhs()

ex GiNaC::rhs ( const ex &  thisex )

inline

Definition at line 833 of file ex.h.

References GiNaC::ex::rhs().

Referenced by lsolve(), GiNaC::ptr< T >::operator!=(), GiNaC::ptr< T >::operator==(), GiNaC::matrix::solve(), and sqrfree_parfrac().

is_zero() [1/2]

bool GiNaC::is_zero ( const ex &  thisex )

inline

Definition at line 836 of file ex.h.

References GiNaC::ex::is_zero().

Referenced by cosh_eval(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::tensepsilon::eval_indexed(), GiNaC::matrix::gauss_elimination(), GiNaC::matrix::markowitz_elimination(), GiNaC::matrix::mul(), GiNaC::relational::operator safe_bool(), GiNaC::matrix::pivot(), sinh_eval(), and tanh_eval().

swap() [1/2]

void GiNaC::swap ( ex &  e1, ex &  e2  )

inline

Definition at line 839 of file ex.h.

References GiNaC::ex::swap().

Referenced by permutation_sign(), and GiNaC::matrix::pivot().

subs() [1/3]

ex GiNaC::subs ( const ex &  thisex, const exmap &  m, unsigned  options = 0  )

inline

Definition at line 847 of file ex.h.

References m, options, and GiNaC::ex::subs().

Referenced by Li2_series().

subs() [2/3]

ex GiNaC::subs ( const ex &  thisex, const lst &  ls, const lst &  lr, unsigned  options = 0  )

inline

Definition at line 850 of file ex.h.

References lr, options, and GiNaC::ex::subs().

subs() [3/3]

ex GiNaC::subs ( const ex &  thisex, const ex &  e, unsigned  options = 0  )

inline

Definition at line 853 of file ex.h.

References options, and GiNaC::ex::subs().

is_a() [2/3]

template<class T >

bool GiNaC::is_a ( const ex &  obj )

inline

Check if ex is a handle to a T, including base classes.

Definition at line 955 of file ex.h.

is_exactly_a() [2/2]

template<class T >

bool GiNaC::is_exactly_a ( const ex &  obj )

inline

Check if ex is a handle to a T, not including base classes.

Definition at line 962 of file ex.h.

ex_to()

template<class T >

attribute_pure const T & GiNaC::ex_to ( const ex &  e )

inline

Return a reference to the basic-derived class T object embedded in an expression.

This is fast but unsafe: the result is undefined if the expression does not contain a T object at its top level. Hence, you should generally check the type of e first. Also, you shouldn't cache the returned reference because GiNaC's garbage collector may destroy the referenced object any time it's used in another expression.

Parameters

e	expression

Returns

reference to object of class T

See also

is_exactly_a<class T>()

Definition at line 978 of file ex.h.

compile_ex() [1/3]

void GiNaC::compile_ex	(	const ex &	expr,
		const symbol &	sym,
		FUNCP_1P &	fp,
		const std::string	filename = ""
	)

Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.

The function pointer has type FUNCP_1P.

Parameters

expr	Expression to be compiled
sym	Symbol from the expression to become the function parameter
fp	Returned function pointer
filename	Name of the intermediate source code and so-file. If supplied, these intermediate files will not be deleted

Definition at line 323 of file excompiler.cpp.

compile_ex() [2/3]

void GiNaC::compile_ex	(	const ex &	expr,
		const symbol &	sym1,
		const symbol &	sym2,
		FUNCP_2P &	fp,
		const std::string	filename = ""
	)

Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.

The function pointer has type FUNCP_2P.

Parameters

expr	Expression to be compiled
sym1	Symbol from the expression to become the first function parameter
sym2	Symbol from the expression to become the second function parameter
fp	Returned function pointer
filename	Name of the intermediate source code and so-file. If supplied, these intermediate files will not be deleted

Definition at line 328 of file excompiler.cpp.

compile_ex() [3/3]

void GiNaC::compile_ex	(	const lst &	exprs,
		const lst &	syms,
		FUNCP_CUBA &	fp,
		const std::string	filename = ""
	)

Takes an expression and produces a function pointer to the compiled and linked C code equivalent in double precision.

The function pointer has type FUNCP_CUBA.

Parameters

exprs	List of expression to be compiled
syms	Symbols from the expression to become the function parameters
fp	Returned function pointer
filename	Name of the intermediate source code and so-file. If supplied, these intermediate files will not be deleted

Definition at line 333 of file excompiler.cpp.

link_ex() [1/3]

void GiNaC::link_ex	(	const std::string	filename,
		FUNCP_1P &	fp
	)

Opens an existing so-file and returns a function pointer of type FUNCP_1P to the contained function.

The so-file has to be generated by compile_ex in advance.

Parameters

filename	Name of the so-file to open and link
fp	Returned function pointer

Definition at line 338 of file excompiler.cpp.

link_ex() [2/3]

void GiNaC::link_ex	(	const std::string	filename,
		FUNCP_2P &	fp
	)

Opens an existing so-file and returns a function pointer of type FUNCP_2P to the contained function.

The so-file has to be generated by compile_ex in advance.

Parameters

filename	Name of the so-file to open and link
fp	Returned function pointer

Definition at line 343 of file excompiler.cpp.

link_ex() [3/3]

void GiNaC::link_ex	(	const std::string	filename,
		FUNCP_CUBA &	fp
	)

Opens an existing so-file and returns a function pointer of type FUNCP_CUBA to the contained function.

The so-file has to be generated by compile_ex in advance.

Parameters

filename	Name of the so-file to open and link
fp	Returned function pointer

Definition at line 348 of file excompiler.cpp.

unlink_ex()

void GiNaC::unlink_ex

(

const std::string

filename

)

Closes all linked .so files that have the supplied filename.

Parameters

filename

Name of the so-file to close

Definition at line 353 of file excompiler.cpp.

swap() [2/2]

void GiNaC::swap ( expair &  e1, expair &  e2  )

inline

Definition at line 111 of file expair.h.

References GiNaC::expair::swap().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [6/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	expairseq	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree
	)

Definition at line 47 of file expairseq.cpp.

conjugateepvector()

epvector * GiNaC::conjugateepvector

(

const epvector &

)

Complex conjugate every element of an epvector.

Returns zero if this does not change anything.

Definition at line 252 of file expairseq.cpp.

References GiNaC::ex::conjugate(), GiNaC::ex::is_equal(), and x.

Referenced by GiNaC::expairseq::conjugate(), and GiNaC::pseries::conjugate().

factor()

ex GiNaC::factor	(	const ex &	poly,
		unsigned	options
	)

Interface function to the outside world.

Factorizes univariate and multivariate polynomials.

It uses factor1() on each of the explicitly present factors of poly.

The default option is factor_options::polynomial, which means that factor() will only factorize an expression if it is a proper polynomial (i.e. the flag info_flags::polynomial is set). Given the option factor_options::all, factor() will factorize all subexpressions, e.g. polynomials containing functions or polynomials inside function arguments.

Parameters

[in]	poly	expression to factorize
[in]	options	see GiNaC::factor_options

Returns

factorized expression

Definition at line 2575 of file factor.cpp.

References options, poly, and pow().

Referenced by algebraic_match_mul_with_mul(), collect_common_factors(), GiNaC::ncmul::eval(), GiNaC::power::expand_add(), GiNaC::mul::expandchildren(), find_common_factor(), GiNaC::mul::find_real_imag(), GiNaC::mul::info(), GiNaC::mul::series(), and sqrfree_parfrac().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [7/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	fail	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree
	)

GINAC_DECLARE_UNARCHIVER() [15/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

fail

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [8/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	fderivative	,
		function	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_tree > &::do_print_tree
	)

Definition at line 30 of file fderivative.cpp.

GINAC_BIND_UNARCHIVER() [15/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

fderivative

)

GINAC_DECLARE_UNARCHIVER() [16/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

fderivative

)

GINAC_BIND_UNARCHIVER() [16/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

function

)

GINAC_DECLARE_UNARCHIVER() [17/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

function

)

is_the_function()

template<typename T >

bool GiNaC::is_the_function ( const ex &  x )

inline

Definition at line 758 of file function.h.

References x.

make_hash_seed()

static unsigned GiNaC::make_hash_seed ( const std::type_info &  tinfo )

inlinestatic

We need a hash function which gives different values for objects of different types.

Hence we need some unique integer for each type. Fortunately, standard C++ RTTI class ‘type_info’ stores a pointer to mangled type name. Normally this pointer is the same for all objects of the same type (although it changes from run to run), so it can be used for computing hashes. However, on some platforms (such as woe32) the pointer returned by type_info::name() might be different even for objects of the same type! Hence we need to resort to comparing string representation of the (mangled) type names. This is quite expensive, so we compare crc32 hashes of those strings. We might get more hash collisions (and slower evaluation as a result), but being a bit slower is much better than being wrong.

Definition at line 36 of file hash_seed.h.

References golden_ratio_hash().

Referenced by GiNaC::expairseq::calchash(), GiNaC::function::calchash(), GiNaC::idx::calchash(), GiNaC::relational::calchash(), GiNaC::symbol::calchash(), GiNaC::symmetry::calchash(), and GiNaC::wildcard::calchash().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [9/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	idx	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_tree > &::do_print_tree
	)

print_func< print_context >()

GiNaC::print_func< print_context >

(

&varidx::do_print

)

&

Definition at line 43 of file idx.cpp.

GINAC_BIND_UNARCHIVER() [17/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

idx

)

GINAC_BIND_UNARCHIVER() [18/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

varidx

)

GINAC_BIND_UNARCHIVER() [19/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

spinidx

)

is_dummy_pair() [1/2]

bool GiNaC::is_dummy_pair	(	const idx &	i1,
		const idx &	i2
	)

Check whether two indices form a dummy pair.

Definition at line 501 of file idx.cpp.

References GiNaC::idx::is_dummy_pair_same_type().

Referenced by GiNaC::matrix::contract_with(), GiNaC::spinmetric::contract_with(), GiNaC::matrix::eval_indexed(), GiNaC::tensdelta::eval_indexed(), find_free_and_dummy(), GiNaC::indexed::has_dummy_index_for(), is_dummy_pair(), GiNaC::is_summation_idx::operator()(), and GiNaC::tensor::replace_contr_index().

is_dummy_pair() [2/2]

bool GiNaC::is_dummy_pair	(	const ex &	e1,
		const ex &	e2
	)

Check whether two expressions form a dummy index pair.

Definition at line 511 of file idx.cpp.

References is_dummy_pair().

find_free_and_dummy() [1/2]

void GiNaC::find_free_and_dummy	(	exvector::const_iterator	it,
		exvector::const_iterator	itend,
		exvector &	out_free,
		exvector &	out_dummy
	)

Given a vector of indices, split them into two vectors, one containing the free indices, the other containing the dummy indices (numeric indices are neither free nor dummy ones).

Parameters

it	Pointer to start of index vector
itend	Pointer to end of index vector
out_free	Vector of free indices (returned, sorted)
out_dummy	Vector of dummy indices (returned, sorted)

Definition at line 520 of file idx.cpp.

References is_dummy_pair(), last, and shaker_sort().

Referenced by GiNaC::su3d::contract_with(), count_dummy_indices(), count_free_indices(), find_dummy_indices(), find_free_and_dummy(), get_all_dummy_indices_safely(), GiNaC::indexed::get_dummy_indices(), GiNaC::indexed::get_free_indices(), GiNaC::mul::get_free_indices(), and GiNaC::ncmul::get_free_indices().

minimal_dim()

ex GiNaC::minimal_dim	(	const ex &	dim1,
		const ex &	dim2
	)

Return the minimum of two index dimensions.

If this is undecidable, throw an exception. Numeric dimensions are always considered "smaller" than symbolic dimensions.

Definition at line 560 of file idx.cpp.

References GiNaC::ex::is_equal().

Referenced by GiNaC::idx::minimal_dim().

GINAC_DECLARE_UNARCHIVER() [18/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

idx

)

GINAC_DECLARE_UNARCHIVER() [19/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

varidx

)

GINAC_DECLARE_UNARCHIVER() [20/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

spinidx

)

find_free_and_dummy() [2/2]

void GiNaC::find_free_and_dummy ( const exvector &  v, exvector &  out_free, exvector &  out_dummy  )

inline

Given a vector of indices, split them into two vectors, one containing the free indices, the other containing the dummy indices (numeric indices are neither free nor dummy ones).

Parameters

v	Index vector
out_free	Vector of free indices (returned, sorted)
out_dummy	Vector of dummy indices (returned, sorted)

Definition at line 236 of file idx.h.

References find_free_and_dummy().

find_dummy_indices()

void GiNaC::find_dummy_indices ( const exvector &  v, exvector &  out_dummy  )

inline

Given a vector of indices, find the dummy indices.

Parameters

v	Index vector
out_dummy	Vector of dummy indices (returned, sorted)

Definition at line 245 of file idx.h.

References find_free_and_dummy().

Referenced by GiNaC::indexed::get_dummy_indices().

count_dummy_indices()

size_t GiNaC::count_dummy_indices ( const exvector &  v )

inline

Count the number of dummy index pairs in an index vector.

Definition at line 252 of file idx.h.

References find_free_and_dummy().

count_free_indices()

size_t GiNaC::count_free_indices ( const exvector &  v )

inline

Count the number of dummy index pairs in an index vector.

Definition at line 260 of file idx.h.

References find_free_and_dummy().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [10/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	indexed	,
		exprseq	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree
	)

Definition at line 48 of file indexed.cpp.

GINAC_BIND_UNARCHIVER() [20/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

indexed

)

indices_consistent()

static bool GiNaC::indices_consistent ( const exvector &  v1, const exvector &  v2  )

static

Check whether two sorted index vectors are consistent (i.e.

equal).

Definition at line 415 of file indexed.cpp.

Referenced by GiNaC::add::get_free_indices().

number_of_type()

template<class T >

size_t GiNaC::number_of_type

(

const exvector &

v

)

Definition at line 524 of file indexed.cpp.

rename_dummy_indices()

template<class T >

static ex GiNaC::rename_dummy_indices ( const ex &  e, exvector &  global_dummy_indices, exvector &  local_dummy_indices  )

static

Rename dummy indices in an expression.

Parameters

e	Expression to work on
local_dummy_indices	The set of dummy indices that appear in the expression "e"
global_dummy_indices	The set of dummy indices that have appeared before and which we would like to use in "e", too. This gets updated by the function

Definition at line 541 of file indexed.cpp.

References GiNaC::ex::begin(), GINAC_ASSERT, GiNaC::subs_options::no_pattern, op(), shaker_sort(), and GiNaC::ex::subs().

find_variant_indices()

static void GiNaC::find_variant_indices ( const exvector &  v, exvector &  variant_indices  )

static

Given a set of indices, extract those of class varidx.

Definition at line 603 of file indexed.cpp.

reposition_dummy_indices()

bool GiNaC::reposition_dummy_indices	(	ex &	e,
		exvector &	variant_dummy_indices,
		exvector &	moved_indices
	)

Raise/lower dummy indices in a single indexed objects to canonicalize their variance.

Parameters

e	Object to work on
variant_dummy_indices	The set of indices that might need repositioning (will be changed by this function)
moved_indices	The set of indices that have been repositioned (will be changed by this function)

Returns

true if 'e' was changed

Definition at line 619 of file indexed.cpp.

product_to_exvector()

static void GiNaC::product_to_exvector ( const ex &  e, exvector &  v, bool &  non_commutative  )

static

Definition at line 732 of file indexed.cpp.

References _ex2, GINAC_ASSERT, GiNaC::ex::is_equal(), GiNaC::ex::nops(), and GiNaC::ex::op().

Referenced by get_all_dummy_indices().

idx_symmetrization()

template<class T >

ex GiNaC::idx_symmetrization	(	const ex &	r,
		const exvector &	local_dummy_indices
	)

Definition at line 763 of file indexed.cpp.

References r, and symmetrize().

simplify_indexed() [3/3]

ex GiNaC::simplify_indexed	(	const ex &	e,
		exvector &	free_indices,
		exvector &	dummy_indices,
		const scalar_products &	sp
	)

Simplify indexed expression, return list of free indices.

Definition at line 1045 of file indexed.cpp.

simplify_indexed_product()

ex GiNaC::simplify_indexed_product	(	const ex &	e,
		exvector &	free_indices,
		exvector &	dummy_indices,
		const scalar_products &	sp
	)

Simplify product of indexed expressions (commutative, noncommutative and simple squares), return list of free indices.

Definition at line 780 of file indexed.cpp.

hasindex()

bool GiNaC::hasindex	(	const ex &	x,
		const ex &	sym
	)

Definition at line 1033 of file indexed.cpp.

References hasindex(), GiNaC::ex::nops(), GiNaC::ex::op(), and x.

Referenced by hasindex().

get_all_dummy_indices_safely()

exvector GiNaC::get_all_dummy_indices_safely

(

const ex &

e

)

More reliable version of the form.

The former assumes that e is an expanded expression.

Definition at line 1395 of file indexed.cpp.

References find_free_and_dummy(), get_all_dummy_indices_safely(), GiNaC::ex::get_free_indices(), GiNaC::ex::nops(), and GiNaC::ex::op().

Referenced by GiNaC::mul::expand(), get_all_dummy_indices_safely(), GiNaC::make_flat_inserter::handle_factor(), rename_dummy_indices_uniquely(), and rename_dummy_indices_uniquely().

get_all_dummy_indices()

exvector GiNaC::get_all_dummy_indices

(

const ex &

e

)

Returns all dummy indices from the exvector.

Returns all dummy indices from the expression.

Definition at line 1436 of file indexed.cpp.

References product_to_exvector().

Referenced by expand_dummy_sum(), and GiNaC::power::expand_mul().

rename_dummy_indices_uniquely() [1/4]

lst GiNaC::rename_dummy_indices_uniquely	(	const exvector &	va,
		const exvector &	vb
	)

Similar to above, where va and vb are the same and the return value is a list of two lists for substitution in b.

Definition at line 1461 of file indexed.cpp.

References GiNaC::container_storage< C >::reserve().

Referenced by GiNaC::expairseq::construct_from_2_ex(), GiNaC::mul::expand(), GiNaC::ncmul::expand(), GiNaC::power::expand_mul(), GiNaC::make_flat_inserter::handle_factor(), rename_dummy_indices_uniquely(), rename_dummy_indices_uniquely(), and rename_dummy_indices_uniquely().

rename_dummy_indices_uniquely() [2/4]

ex GiNaC::rename_dummy_indices_uniquely	(	const exvector &	va,
		const exvector &	vb,
		const ex &	b
	)

Same as above, where va and vb contain the indices of a and b and are sorted.

Definition at line 1496 of file indexed.cpp.

References GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::container< C >::op(), rename_dummy_indices_uniquely(), and GiNaC::ex::subs().

rename_dummy_indices_uniquely() [3/4]

ex GiNaC::rename_dummy_indices_uniquely	(	const ex &	a,
		const ex &	b
	)

Returns b with all dummy indices, which are common with a, renamed.

Definition at line 1502 of file indexed.cpp.

References get_all_dummy_indices_safely(), GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::container< C >::op(), rename_dummy_indices_uniquely(), and GiNaC::ex::subs().

rename_dummy_indices_uniquely() [4/4]

ex GiNaC::rename_dummy_indices_uniquely	(	exvector &	va,
		const ex &	b,
		bool	modify_va
	)

Returns b with all dummy indices, which are listed in va, renamed if modify_va is set to TRUE all dummy indices of b will be appended to va.

Definition at line 1518 of file indexed.cpp.

References GiNaC::ex::begin(), GiNaC::ex::end(), get_all_dummy_indices_safely(), GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::container< C >::op(), rename_dummy_indices_uniquely(), and GiNaC::ex::subs().

expand_dummy_sum()

ex GiNaC::expand_dummy_sum	(	const ex &	e,
		bool	subs_idx = false
	)

This function returns the given expression with expanded sums for all dummy index summations, where the dimensionality of the dummy index is a nonnegative integer.

Optionally all indices with a variance will be substituted by indices with the corresponding numeric values without variance.

Parameters

e	the given expression
subs_idx	indicates if variance of dummy indices should be neglected

Definition at line 1542 of file indexed.cpp.

References GiNaC::ex::expand(), expand_dummy_sum(), get_all_dummy_indices(), GiNaC::ex::map(), GiNaC::info_flags::nonnegint, and GiNaC::ex::subs().

Referenced by expand_dummy_sum().

GINAC_DECLARE_UNARCHIVER() [21/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

indexed

)

conjugate_evalf()

static ex GiNaC::conjugate_evalf ( const ex &  arg )

static

Definition at line 47 of file inifcns.cpp.

References GiNaC::ex::conjugate().

conjugate_eval()

static ex GiNaC::conjugate_eval ( const ex &  arg )

static

Definition at line 55 of file inifcns.cpp.

References GiNaC::ex::conjugate().

conjugate_print_latex()

static void GiNaC::conjugate_print_latex ( const ex &  arg, const print_context &  c  )

static

Definition at line 60 of file inifcns.cpp.

References c, and GiNaC::ex::print().

conjugate_conjugate()

static ex GiNaC::conjugate_conjugate ( const ex &  arg )

static

Definition at line 65 of file inifcns.cpp.

conjugate_expl_derivative()

static ex GiNaC::conjugate_expl_derivative ( const ex &  arg, const symbol &  s  )

static

Definition at line 72 of file inifcns.cpp.

References conjugate(), GiNaC::ex::diff(), GiNaC::basic::hold(), GiNaC::symbol::info(), and GiNaC::info_flags::real.

conjugate_real_part()

static ex GiNaC::conjugate_real_part ( const ex &  arg )

static

Definition at line 83 of file inifcns.cpp.

References GiNaC::ex::real_part().

conjugate_imag_part()

static ex GiNaC::conjugate_imag_part ( const ex &  arg )

static

Definition at line 88 of file inifcns.cpp.

References GiNaC::ex::imag_part().

func_arg_info()

static bool GiNaC::func_arg_info ( const ex &  arg, unsigned  inf  )

static

Definition at line 93 of file inifcns.cpp.

References GiNaC::info_flags::cinteger, GiNaC::info_flags::cinteger_polynomial, GiNaC::info_flags::crational, GiNaC::info_flags::crational_polynomial, GiNaC::info_flags::even, GiNaC::info_flags::has_indices, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::info_flags::integer_polynomial, GiNaC::info_flags::negative, GiNaC::info_flags::negint, GiNaC::info_flags::nonnegative, GiNaC::info_flags::nonnegint, GiNaC::info_flags::odd, GiNaC::info_flags::polynomial, GiNaC::info_flags::posint, GiNaC::info_flags::positive, GiNaC::info_flags::prime, GiNaC::info_flags::rational, GiNaC::info_flags::rational_function, GiNaC::info_flags::rational_polynomial, and GiNaC::info_flags::real.

Referenced by conjugate_info().

conjugate_info()

static bool GiNaC::conjugate_info ( const ex &  arg, unsigned  inf  )

static

Definition at line 124 of file inifcns.cpp.

References func_arg_info().

REGISTER_FUNCTION() [1/36]

GiNaC::REGISTER_FUNCTION	(	conjugate_function	,
		eval_func(conjugate_eval). evalf_func(conjugate_evalf). expl_derivative_func(conjugate_expl_derivative). info_func(conjugate_info). print_func< print_latex >(conjugate_print_latex). conjugate_func(conjugate_conjugate). real_part_func(conjugate_real_part). imag_part_func(conjugate_imag_part). set_name("conjugate","conjugate")
	)

real_part_evalf()

static ex GiNaC::real_part_evalf ( const ex &  arg )

static

Definition at line 143 of file inifcns.cpp.

real_part_eval()

static ex GiNaC::real_part_eval ( const ex &  arg )

static

Definition at line 151 of file inifcns.cpp.

References GiNaC::ex::real_part().

real_part_print_latex()

static void GiNaC::real_part_print_latex ( const ex &  arg, const print_context &  c  )

static

Definition at line 156 of file inifcns.cpp.

References c, and GiNaC::ex::print().

real_part_conjugate()

static ex GiNaC::real_part_conjugate ( const ex &  arg )

static

Definition at line 161 of file inifcns.cpp.

real_part_real_part()

static ex GiNaC::real_part_real_part ( const ex &  arg )

static

Definition at line 166 of file inifcns.cpp.

real_part_imag_part()

static ex GiNaC::real_part_imag_part ( const ex &  arg )

static

Definition at line 171 of file inifcns.cpp.

real_part_expl_derivative()

static ex GiNaC::real_part_expl_derivative ( const ex &  arg, const symbol &  s  )

static

Definition at line 177 of file inifcns.cpp.

References GiNaC::ex::diff(), GiNaC::basic::hold(), GiNaC::symbol::info(), GiNaC::info_flags::real, and real_part().

REGISTER_FUNCTION() [2/36]

GiNaC::REGISTER_FUNCTION	(	real_part_function	,
		eval_func(real_part_eval). evalf_func(real_part_evalf). expl_derivative_func(real_part_expl_derivative). print_func< print_latex >(real_part_print_latex). conjugate_func(real_part_conjugate). real_part_func(real_part_real_part). imag_part_func(real_part_imag_part). set_name("real_part","real_part")
	)

imag_part_evalf()

static ex GiNaC::imag_part_evalf ( const ex &  arg )

static

Definition at line 201 of file inifcns.cpp.

imag_part_eval()

static ex GiNaC::imag_part_eval ( const ex &  arg )

static

Definition at line 209 of file inifcns.cpp.

References GiNaC::ex::imag_part().

imag_part_print_latex()

static void GiNaC::imag_part_print_latex ( const ex &  arg, const print_context &  c  )

static

Definition at line 214 of file inifcns.cpp.

References c, and GiNaC::ex::print().

imag_part_conjugate()

static ex GiNaC::imag_part_conjugate ( const ex &  arg )

static

Definition at line 219 of file inifcns.cpp.

imag_part_real_part()

static ex GiNaC::imag_part_real_part ( const ex &  arg )

static

Definition at line 224 of file inifcns.cpp.

imag_part_imag_part()

static ex GiNaC::imag_part_imag_part ( const ex &  arg )

static

Definition at line 229 of file inifcns.cpp.

imag_part_expl_derivative()

static ex GiNaC::imag_part_expl_derivative ( const ex &  arg, const symbol &  s  )

static

Definition at line 235 of file inifcns.cpp.

References GiNaC::ex::diff(), GiNaC::basic::hold(), imag_part(), GiNaC::symbol::info(), and GiNaC::info_flags::real.

REGISTER_FUNCTION() [3/36]

GiNaC::REGISTER_FUNCTION	(	imag_part_function	,
		eval_func(imag_part_eval). evalf_func(imag_part_evalf). expl_derivative_func(imag_part_expl_derivative). print_func< print_latex >(imag_part_print_latex). conjugate_func(imag_part_conjugate). real_part_func(imag_part_real_part). imag_part_func(imag_part_imag_part). set_name("imag_part","imag_part")
	)

abs_evalf()

static ex GiNaC::abs_evalf ( const ex &  arg )

static

Definition at line 259 of file inifcns.cpp.

References abs(), and GiNaC::basic::hold().

abs_eval()

static ex GiNaC::abs_eval ( const ex &  arg )

static

Definition at line 267 of file inifcns.cpp.

References abs(), exp(), GiNaC::basic::hold(), GiNaC::ex::info(), is_ex_the_function, GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, GiNaC::ex::op(), GiNaC::info_flags::positive, pow(), GiNaC::info_flags::real, GiNaC::ex::real_part(), and step().

abs_expand()

static ex GiNaC::abs_expand ( const ex &  arg, unsigned  options  )

static

Definition at line 300 of file inifcns.cpp.

References abs(), GiNaC::ex::begin(), GiNaC::ex::end(), GiNaC::ex::expand(), GiNaC::expand_options::expand_function_args, GiNaC::expand_options::expand_transcendental, GiNaC::status_flags::expanded, GiNaC::basic::hold(), GiNaC::ex::nops(), and options.

abs_expl_derivative()

static ex GiNaC::abs_expl_derivative ( const ex &  arg, const symbol &  s  )

static

Definition at line 321 of file inifcns.cpp.

References abs(), GiNaC::ex::conjugate(), and GiNaC::ex::diff().

abs_print_latex()

static void GiNaC::abs_print_latex ( const ex &  arg, const print_context &  c  )

static

Definition at line 327 of file inifcns.cpp.

References c, and GiNaC::ex::print().

abs_print_csrc_float()

static void GiNaC::abs_print_csrc_float ( const ex &  arg, const print_context &  c  )

static

Definition at line 332 of file inifcns.cpp.

References c, and GiNaC::ex::print().

abs_conjugate()

static ex GiNaC::abs_conjugate ( const ex &  arg )

static

Definition at line 337 of file inifcns.cpp.

References abs(), and GiNaC::basic::hold().

abs_real_part()

static ex GiNaC::abs_real_part ( const ex &  arg )

static

Definition at line 342 of file inifcns.cpp.

References abs(), and GiNaC::basic::hold().

abs_imag_part()

static ex GiNaC::abs_imag_part ( const ex &  arg )

static

Definition at line 347 of file inifcns.cpp.

abs_power()

static ex GiNaC::abs_power ( const ex &  arg, const ex &  exp  )

static

Definition at line 352 of file inifcns.cpp.

References abs(), GiNaC::ex::conjugate(), GiNaC::info_flags::even, exp(), GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::numeric::info(), GiNaC::ex::is_equal(), is_even(), pow(), and GiNaC::info_flags::real.

abs_info()

bool GiNaC::abs_info	(	const ex &	arg,
		unsigned	inf
	)

Definition at line 363 of file inifcns.cpp.

References GiNaC::info_flags::even, GiNaC::info_flags::has_indices, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, GiNaC::info_flags::nonnegint, GiNaC::info_flags::odd, GiNaC::info_flags::positive, GiNaC::info_flags::prime, and GiNaC::info_flags::real.

REGISTER_FUNCTION() [4/36]

GiNaC::REGISTER_FUNCTION	(	abs	,
		eval_func(abs_eval). evalf_func(abs_evalf). expand_func(abs_expand). expl_derivative_func(abs_expl_derivative). info_func(abs_info). print_func< print_latex >(abs_print_latex). print_func< print_csrc_float >(abs_print_csrc_float). print_func< print_csrc_double >(abs_print_csrc_float). conjugate_func(abs_conjugate). real_part_func(abs_real_part). imag_part_func(abs_imag_part). power_func(abs_power)
	)

step_evalf()

static ex GiNaC::step_evalf ( const ex &  arg )

static

Definition at line 407 of file inifcns.cpp.

References GiNaC::basic::hold(), and step().

step_eval()

static ex GiNaC::step_eval ( const ex &  arg )

static

Definition at line 415 of file inifcns.cpp.

References GiNaC::basic::hold(), I, GiNaC::numeric::imag(), GiNaC::numeric::is_real(), GiNaC::numeric::is_zero(), GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::numeric::real(), and step().

step_series()

static ex GiNaC::step_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 444 of file inifcns.cpp.

References _ex0, GiNaC::ex::info(), GiNaC::subs_options::no_pattern, GiNaC::info_flags::numeric, options, step(), GiNaC::ex::subs(), and GiNaC::series_options::suppress_branchcut.

step_conjugate()

static ex GiNaC::step_conjugate ( const ex &  arg )

static

Definition at line 459 of file inifcns.cpp.

References GiNaC::basic::hold(), and step().

step_real_part()

static ex GiNaC::step_real_part ( const ex &  arg )

static

Definition at line 464 of file inifcns.cpp.

References GiNaC::basic::hold(), and step().

step_imag_part()

static ex GiNaC::step_imag_part ( const ex &  arg )

static

Definition at line 469 of file inifcns.cpp.

REGISTER_FUNCTION() [5/36]

GiNaC::REGISTER_FUNCTION	(	step	,
		eval_func(step_eval). evalf_func(step_evalf). series_func(step_series). conjugate_func(step_conjugate). real_part_func(step_real_part). imag_part_func(step_imag_part)
	)

csgn_evalf()

static ex GiNaC::csgn_evalf ( const ex &  arg )

static

Definition at line 485 of file inifcns.cpp.

References csgn().

csgn_eval()

static ex GiNaC::csgn_eval ( const ex &  arg )

static

Definition at line 493 of file inifcns.cpp.

References csgn(), I, GiNaC::numeric::imag(), GiNaC::numeric::is_real(), GiNaC::numeric::is_zero(), GiNaC::ex::nops(), GiNaC::ex::op(), and GiNaC::numeric::real().

csgn_series()

static ex GiNaC::csgn_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 522 of file inifcns.cpp.

References _ex0, csgn(), GiNaC::ex::info(), GiNaC::subs_options::no_pattern, GiNaC::info_flags::numeric, options, GiNaC::ex::subs(), and GiNaC::series_options::suppress_branchcut.

csgn_conjugate()

static ex GiNaC::csgn_conjugate ( const ex &  arg )

static

Definition at line 537 of file inifcns.cpp.

References csgn().

csgn_real_part()

static ex GiNaC::csgn_real_part ( const ex &  arg )

static

Definition at line 542 of file inifcns.cpp.

References csgn().

csgn_imag_part()

static ex GiNaC::csgn_imag_part ( const ex &  arg )

static

Definition at line 547 of file inifcns.cpp.

csgn_power()

static ex GiNaC::csgn_power ( const ex &  arg, const ex &  exp  )

static

Definition at line 552 of file inifcns.cpp.

References _ex2, csgn(), exp(), GiNaC::basic::hold(), GiNaC::numeric::info(), is_odd(), and GiNaC::info_flags::positive.

REGISTER_FUNCTION() [6/36]

GiNaC::REGISTER_FUNCTION	(	csgn	,
		eval_func(csgn_eval). evalf_func(csgn_evalf). series_func(csgn_series). conjugate_func(csgn_conjugate). real_part_func(csgn_real_part). imag_part_func(csgn_imag_part). power_func(csgn_power)
	)

eta_evalf()

static ex GiNaC::eta_evalf ( const ex &  x, const ex &  y  )

static

Definition at line 579 of file inifcns.cpp.

References _ex0, csgn(), evalf(), I, imag(), GiNaC::ex::info(), GiNaC::numeric::is_negative(), GiNaC::numeric::is_real(), GiNaC::info_flags::numeric, Pi, GiNaC::info_flags::positive, and x.

eta_eval()

static ex GiNaC::eta_eval ( const ex &  x, const ex &  y  )

static

Definition at line 604 of file inifcns.cpp.

References _ex0, csgn(), I, imag(), GiNaC::ex::info(), GiNaC::numeric::is_negative(), GiNaC::numeric::is_real(), GiNaC::info_flags::numeric, Pi, GiNaC::info_flags::positive, and x.

eta_series()

static ex GiNaC::eta_series ( const ex &  x, const ex &  y, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 629 of file inifcns.cpp.

References _ex0, GiNaC::ex::info(), GiNaC::info_flags::negative, GiNaC::subs_options::no_pattern, GiNaC::info_flags::numeric, GiNaC::ex::subs(), and x.

eta_conjugate()

static ex GiNaC::eta_conjugate ( const ex &  x, const ex &  y  )

static

Definition at line 644 of file inifcns.cpp.

References x.

eta_real_part()

static ex GiNaC::eta_real_part ( const ex &  x, const ex &  y  )

static

Definition at line 649 of file inifcns.cpp.

eta_imag_part()

static ex GiNaC::eta_imag_part ( const ex &  x, const ex &  y  )

static

Definition at line 654 of file inifcns.cpp.

References GiNaC::basic::hold(), I, and x.

REGISTER_FUNCTION() [7/36]

GiNaC::REGISTER_FUNCTION	(	eta	,
		eval_func(eta_eval). evalf_func(eta_evalf). series_func(eta_series). latex_name("\\eta"). set_symmetry(sy_symm(0, 1)). conjugate_func(eta_conjugate). real_part_func(eta_real_part). imag_part_func(eta_imag_part)
	)

Li2_evalf()

static ex GiNaC::Li2_evalf ( const ex &  x )

static

Definition at line 673 of file inifcns.cpp.

References GiNaC::basic::hold(), Li2(), and x.

Li2_eval()

static ex GiNaC::Li2_eval ( const ex &  x )

static

Definition at line 681 of file inifcns.cpp.

References _ex0, _ex1, _ex12, _ex1_2, _ex2, _ex6, _ex_1, _ex_1_2, _ex_48, Catalan, GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), Li2(), log(), GiNaC::info_flags::numeric, Pi, and x.

Li2_deriv()

static ex GiNaC::Li2_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 710 of file inifcns.cpp.

References _ex1, GINAC_ASSERT, log(), and x.

Li2_series() [1/2]

static ex GiNaC::Li2_series ( const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 718 of file inifcns.cpp.

References _ex0, _ex1, _ex2, _num2_p, I, GiNaC::ex::info(), GiNaC::ex::is_equal(), is_real(), GiNaC::ex::is_zero(), GiNaC::relational::lhs(), Li2(), log(), GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::info_flags::numeric, op(), GiNaC::ex::op(), options, order, Pi, pow(), GiNaC::relational::rhs(), GiNaC::ex::series(), series(), subs(), GiNaC::ex::subs(), GiNaC::series_options::suppress_branchcut, x, and zeta().

Referenced by Li2_projection().

Li2_conjugate()

static ex GiNaC::Li2_conjugate ( const ex &  x )

static

Definition at line 798 of file inifcns.cpp.

References _num1_p, GiNaC::ex::conjugate(), GiNaC::basic::hold(), GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::ex::is_zero(), Li2(), GiNaC::info_flags::negative, and x.

REGISTER_FUNCTION() [8/36]

GiNaC::REGISTER_FUNCTION	(	Li2	,
		eval_func(Li2_eval). evalf_func(Li2_evalf). derivative_func(Li2_deriv). series_func(Li2_series). conjugate_func(Li2_conjugate). latex_name("\\mathrm{Li}_2")
	)

Li3_eval()

static ex GiNaC::Li3_eval ( const ex &  x )

static

Definition at line 823 of file inifcns.cpp.

References GiNaC::ex::is_zero(), and x.

REGISTER_FUNCTION() [9/36]

GiNaC::REGISTER_FUNCTION	(	Li3	,
		eval_func(Li3_eval). latex_name("\\mathrm{Li}_3")
	)

zetaderiv_eval()

static ex GiNaC::zetaderiv_eval ( const ex &  n, const ex &  x  )

static

Definition at line 837 of file inifcns.cpp.

References GiNaC::basic::hold(), n, GiNaC::info_flags::numeric, x, and zeta().

zetaderiv_deriv()

static ex GiNaC::zetaderiv_deriv ( const ex &  n, const ex &  x, unsigned  deriv_param  )

static

Definition at line 848 of file inifcns.cpp.

References GINAC_ASSERT, n, and x.

REGISTER_FUNCTION() [10/36]

GiNaC::REGISTER_FUNCTION	(	zetaderiv	,
		eval_func(zetaderiv_eval). derivative_func(zetaderiv_deriv). latex_name("\\zeta^\\prime")
	)

factorial_evalf()

static ex GiNaC::factorial_evalf ( const ex &  x )

static

Definition at line 868 of file inifcns.cpp.

References factorial(), GiNaC::basic::hold(), and x.

factorial_eval()

static ex GiNaC::factorial_eval ( const ex &  x )

static

Definition at line 873 of file inifcns.cpp.

References factorial(), GiNaC::basic::hold(), and x.

factorial_print_dflt_latex()

static void GiNaC::factorial_print_dflt_latex ( const ex &  x, const print_context &  c  )

static

Definition at line 881 of file inifcns.cpp.

References c, GiNaC::ex::print(), and x.

factorial_conjugate()

static ex GiNaC::factorial_conjugate ( const ex &  x )

static

Definition at line 892 of file inifcns.cpp.

References factorial(), GiNaC::basic::hold(), and x.

factorial_real_part()

static ex GiNaC::factorial_real_part ( const ex &  x )

static

Definition at line 897 of file inifcns.cpp.

References factorial(), GiNaC::basic::hold(), and x.

factorial_imag_part()

static ex GiNaC::factorial_imag_part ( const ex &  x )

static

Definition at line 902 of file inifcns.cpp.

REGISTER_FUNCTION() [11/36]

GiNaC::REGISTER_FUNCTION	(	factorial	,
		eval_func(factorial_eval). evalf_func(factorial_evalf). print_func< print_dflt >(factorial_print_dflt_latex). print_func< print_latex >(factorial_print_dflt_latex). conjugate_func(factorial_conjugate). real_part_func(factorial_real_part). imag_part_func(factorial_imag_part)
	)

binomial_evalf()

static ex GiNaC::binomial_evalf ( const ex &  x, const ex &  y  )

static

Definition at line 919 of file inifcns.cpp.

References binomial(), GiNaC::basic::hold(), and x.

binomial_sym()

static ex GiNaC::binomial_sym ( const ex &  x, const numeric &  y  )

static

Definition at line 924 of file inifcns.cpp.

References _ex0, _ex1, binomial(), GiNaC::ex::expand(), GiNaC::basic::hold(), GiNaC::numeric::is_integer(), GiNaC::numeric::is_nonneg_integer(), GiNaC::numeric::to_int(), and x.

Referenced by binomial_eval().

binomial_eval()

static ex GiNaC::binomial_eval ( const ex &  x, const ex &  y  )

static

Definition at line 942 of file inifcns.cpp.

References binomial(), binomial_sym(), GiNaC::basic::hold(), is_integer(), and x.

binomial_conjugate()

static ex GiNaC::binomial_conjugate ( const ex &  x, const ex &  y  )

static

Definition at line 956 of file inifcns.cpp.

References binomial(), GiNaC::basic::hold(), and x.

binomial_real_part()

static ex GiNaC::binomial_real_part ( const ex &  x, const ex &  y  )

static

Definition at line 961 of file inifcns.cpp.

References binomial(), GiNaC::basic::hold(), and x.

binomial_imag_part()

static ex GiNaC::binomial_imag_part ( const ex &  x, const ex &  y  )

static

Definition at line 966 of file inifcns.cpp.

REGISTER_FUNCTION() [12/36]

GiNaC::REGISTER_FUNCTION	(	binomial	,
		eval_func(binomial_eval). evalf_func(binomial_evalf). conjugate_func(binomial_conjugate). real_part_func(binomial_real_part). imag_part_func(binomial_imag_part)
	)

Order_eval()

static ex GiNaC::Order_eval ( const ex &  x )

static

Definition at line 981 of file inifcns.cpp.

References _ex0, _ex1, GiNaC::ex::is_zero(), m, GiNaC::ex::op(), and x.

Order_series()

static ex GiNaC::Order_series ( const ex &  x, const relational &  r, int  order, unsigned  options  )

static

Definition at line 998 of file inifcns.cpp.

References _ex1, GINAC_ASSERT, GiNaC::ex::ldegree(), order, r, and x.

Order_conjugate()

static ex GiNaC::Order_conjugate ( const ex &  x )

static

Definition at line 1007 of file inifcns.cpp.

References x.

Order_real_part()

static ex GiNaC::Order_real_part ( const ex &  x )

static

Definition at line 1012 of file inifcns.cpp.

References x.

Order_imag_part()

static ex GiNaC::Order_imag_part ( const ex &  x )

static

Definition at line 1017 of file inifcns.cpp.

References GiNaC::ex::info(), GiNaC::info_flags::real, and x.

Order_power()

static ex GiNaC::Order_power ( const ex &  x, const ex &  e  )

static

Definition at line 1024 of file inifcns.cpp.

References GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::posint, pow(), and x.

Order_expl_derivative()

static ex GiNaC::Order_expl_derivative ( const ex &  arg, const symbol &  s  )

static

Definition at line 1038 of file inifcns.cpp.

References GiNaC::ex::diff().

REGISTER_FUNCTION() [13/36]

GiNaC::REGISTER_FUNCTION	(	Order	,
		eval_func(Order_eval). series_func(Order_series). latex_name("\\mathcal{O}"). expl_derivative_func(Order_expl_derivative). conjugate_func(Order_conjugate). real_part_func(Order_real_part). imag_part_func(Order_imag_part). power_func(Order_power)
	)

lsolve()

ex GiNaC::lsolve	(	const ex &	eqns,
		const ex &	symbols,
		unsigned	options = solve_algo::automatic
	)

Factorial function.

Binomial function. Order term function (for truncated power series).

Definition at line 1079 of file inifcns.cpp.

References GiNaC::container< C >::append(), c, GiNaC::ex::coeff(), GiNaC::matrix::cols(), GiNaC::ex::expand(), GiNaC::info_flags::exprseq, GINAC_ASSERT, GiNaC::symbolset::has(), GiNaC::ex::info(), GiNaC::info_flags::list, lsolve(), GiNaC::ex::nops(), GiNaC::ex::op(), options, r, GiNaC::info_flags::relation_equal, rhs(), GiNaC::matrix::rows(), GiNaC::matrix::solve(), GiNaC::info_flags::symbol, and syms.

Referenced by lsolve().

fsolve()

const numeric GiNaC::fsolve	(	const ex &	f,
		const symbol &	x,
		const numeric &	x1,
		const numeric &	x2
	)

Find a real root of real-valued function f(x) numerically within a given interval.

The function must change sign across interval. Uses Newton- Raphson method combined with bisection in order to guarantee convergence.

Parameters

f	Function f(x)
x	Symbol f(x)
x1	lower interval limit
x2	upper interval limit

Exceptions

runtime_error

(if interval is invalid).

Definition at line 1166 of file inifcns.cpp.

References GiNaC::ex::diff(), GiNaC::ex::evalf(), GiNaC::numeric::is_real(), is_real(), GiNaC::numeric::is_zero(), GiNaC::ex::lhs(), normal(), GiNaC::ex::rhs(), GiNaC::ex::subs(), and x.

zeta() [1/3]

template<typename T1 >

function GiNaC::zeta ( const T1 &  p1 )

inline

Definition at line 111 of file inifcns.h.

References GiNaC::zeta1_SERIAL::serial.

Referenced by Li2_series(), Li_eval(), psi2_eval(), S_eval(), zeta1_eval(), zeta1_evalf(), zeta2_eval(), zeta2_evalf(), and zetaderiv_eval().

zeta() [2/3]

template<typename T1 , typename T2 >

function GiNaC::zeta ( const T1 &  p1, const T2 &  p2  )

inline

Definition at line 117 of file inifcns.h.

References GiNaC::zeta2_SERIAL::serial.

is_the_function< zeta_SERIAL >()

template<>

bool GiNaC::is_the_function< zeta_SERIAL > ( const ex &  x )

inline

Definition at line 121 of file inifcns.h.

References x.

G() [1/2]

template<typename T1 , typename T2 >

function GiNaC::G ( const T1 &  x, const T2 &  y  )

inline

Definition at line 130 of file inifcns.h.

References GiNaC::G2_SERIAL::serial, and x.

Referenced by G2_eval(), G2_evalf(), G3_eval(), and G3_evalf().

G() [2/2]

template<typename T1 , typename T2 , typename T3 >

function GiNaC::G ( const T1 &  x, const T2 &  s, const T3 &  y  )

inline

Definition at line 136 of file inifcns.h.

References GiNaC::G3_SERIAL::serial, and x.

is_the_function< G_SERIAL >()

template<>

bool GiNaC::is_the_function< G_SERIAL > ( const ex &  x )

inline

Definition at line 140 of file inifcns.h.

References x.

psi() [1/4]

template<typename T1 >

function GiNaC::psi ( const T1 &  p1 )

inline

Definition at line 165 of file inifcns.h.

References GiNaC::psi1_SERIAL::serial.

Referenced by beta_deriv(), lgamma_deriv(), psi1_deriv(), psi1_eval(), psi1_evalf(), psi1_series(), psi2_deriv(), psi2_eval(), psi2_evalf(), psi2_series(), sr_gcd(), and tgamma_deriv().

psi() [2/4]

template<typename T1 , typename T2 >

function GiNaC::psi ( const T1 &  p1, const T2 &  p2  )

inline

Definition at line 171 of file inifcns.h.

References GiNaC::psi2_SERIAL::serial.

is_the_function< psi_SERIAL >()

template<>

bool GiNaC::is_the_function< psi_SERIAL > ( const ex &  x )

inline

Definition at line 175 of file inifcns.h.

References x.

iterated_integral() [1/2]

template<typename T1 , typename T2 >

function GiNaC::iterated_integral ( const T1 &  kernel_lst, const T2 &  lambda  )

inline

Definition at line 190 of file inifcns.h.

References GiNaC::iterated_integral2_SERIAL::serial.

Referenced by iterated_integral2_eval(), iterated_integral3_eval(), and iterated_integral_evalf_impl().

iterated_integral() [2/2]

template<typename T1 , typename T2 , typename T3 >

function GiNaC::iterated_integral ( const T1 &  kernel_lst, const T2 &  lambda, const T3 &  N_trunc  )

inline

Definition at line 196 of file inifcns.h.

References GiNaC::iterated_integral3_SERIAL::serial.

is_the_function< iterated_integral_SERIAL >()

template<>

bool GiNaC::is_the_function< iterated_integral_SERIAL > ( const ex &  x )

inline

Definition at line 200 of file inifcns.h.

References x.

is_order_function()

bool GiNaC::is_order_function ( const ex &  e )

inline

Check whether a function is the Order (O(n)) function.

Definition at line 229 of file inifcns.h.

References is_ex_the_function.

Referenced by GiNaC::pseries::add_series(), GiNaC::pseries::convert_to_poly(), GiNaC::pseries::derivative(), GiNaC::pseries::is_terminating(), GiNaC::pseries::mul_const(), GiNaC::pseries::mul_series(), GiNaC::pseries::op(), GiNaC::pseries::power_const(), GiNaC::pseries::print_series(), GiNaC::pseries::pseries(), GiNaC::pseries::pseries(), and GiNaC::integral::series().

convert_H_to_Li()

ex GiNaC::convert_H_to_Li	(	const ex &	parameterlst,
		const ex &	arg
	)

Converts a given list containing parameters for H in Remiddi/Vermaseren notation into the corresponding GiNaC functions.

Definition at line 3522 of file inifcns_nstdsums.cpp.

References m, and x.

EllipticK_evalf()

static ex GiNaC::EllipticK_evalf ( const ex &  k )

static

Definition at line 166 of file inifcns_elliptic.cpp.

References GiNaC::ex::evalf(), k, GiNaC::info_flags::numeric, Pi, and sqrt().

EllipticK_eval()

static ex GiNaC::EllipticK_eval ( const ex &  k )

static

Definition at line 180 of file inifcns_elliptic.cpp.

References _ex0, GiNaC::info_flags::crational, GiNaC::constant::evalf(), k, GiNaC::info_flags::numeric, and Pi.

EllipticK_deriv()

static ex GiNaC::EllipticK_deriv ( const ex &  k, unsigned  deriv_param  )

static

Definition at line 194 of file inifcns_elliptic.cpp.

References k.

EllipticK_series()

static ex GiNaC::EllipticK_series ( const ex &  k, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 200 of file inifcns_elliptic.cpp.

References _ex0, _ex1, _ex_1, k, GiNaC::subs_options::no_pattern, order, Pi, pow(), GiNaC::ex::series(), GiNaC::symbol::series(), and GiNaC::ex::subs().

EllipticK_print_latex()

static void GiNaC::EllipticK_print_latex ( const ex &  k, const print_context &  c  )

static

Definition at line 229 of file inifcns_elliptic.cpp.

References c, and k.

REGISTER_FUNCTION() [14/36]

GiNaC::REGISTER_FUNCTION	(	EllipticK	,
		evalf_func(EllipticK_evalf). eval_func(EllipticK_eval). derivative_func(EllipticK_deriv). series_func(EllipticK_series). print_func< print_latex >(EllipticK_print_latex). do_not_evalf_params()
	)

EllipticE_evalf()

static ex GiNaC::EllipticE_evalf ( const ex &  k )

static

Definition at line 246 of file inifcns_elliptic.cpp.

References GiNaC::ex::evalf(), k, GiNaC::info_flags::numeric, Pi, and sqrt().

EllipticE_eval()

static ex GiNaC::EllipticE_eval ( const ex &  k )

static

Definition at line 260 of file inifcns_elliptic.cpp.

References _ex0, _ex1, _ex_1, GiNaC::info_flags::crational, GiNaC::constant::evalf(), k, GiNaC::info_flags::numeric, and Pi.

EllipticE_deriv()

static ex GiNaC::EllipticE_deriv ( const ex &  k, unsigned  deriv_param  )

static

Definition at line 278 of file inifcns_elliptic.cpp.

References k.

EllipticE_series()

static ex GiNaC::EllipticE_series ( const ex &  k, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 284 of file inifcns_elliptic.cpp.

References _ex0, _ex1, _ex_1, k, GiNaC::subs_options::no_pattern, order, Pi, pow(), GiNaC::ex::series(), GiNaC::symbol::series(), and GiNaC::ex::subs().

EllipticE_print_latex()

static void GiNaC::EllipticE_print_latex ( const ex &  k, const print_context &  c  )

static

Definition at line 313 of file inifcns_elliptic.cpp.

References c, and k.

REGISTER_FUNCTION() [15/36]

GiNaC::REGISTER_FUNCTION	(	EllipticE	,
		evalf_func(EllipticE_evalf). eval_func(EllipticE_eval). derivative_func(EllipticE_deriv). series_func(EllipticE_series). print_func< print_latex >(EllipticE_print_latex). do_not_evalf_params()
	)

iterated_integral_evalf_impl()

static ex GiNaC::iterated_integral_evalf_impl ( const ex &  kernel_lst, const ex &  lambda, const ex &  N_trunc  )

static

Definition at line 509 of file inifcns_elliptic.cpp.

References coeff(), Digits, GiNaC::ex::evalf(), GiNaC::basic::hold(), GiNaC::ex::info(), iterated_integral(), GiNaC::info_flags::list, GiNaC::info_flags::nonnegint, GiNaC::container< C >::nops(), GiNaC::info_flags::numeric, and one.

Referenced by iterated_integral2_evalf(), and iterated_integral3_evalf().

iterated_integral2_evalf()

static ex GiNaC::iterated_integral2_evalf ( const ex &  kernel_lst, const ex &  lambda  )

static

Definition at line 589 of file inifcns_elliptic.cpp.

References iterated_integral_evalf_impl().

iterated_integral3_evalf()

static ex GiNaC::iterated_integral3_evalf ( const ex &  kernel_lst, const ex &  lambda, const ex &  N_trunc  )

static

Definition at line 594 of file inifcns_elliptic.cpp.

References iterated_integral_evalf_impl().

iterated_integral2_eval()

static ex GiNaC::iterated_integral2_eval ( const ex &  kernel_lst, const ex &  lambda  )

static

Definition at line 599 of file inifcns_elliptic.cpp.

References GiNaC::info_flags::crational, GiNaC::function::evalf(), GiNaC::basic::hold(), GiNaC::ex::info(), iterated_integral(), and GiNaC::info_flags::numeric.

iterated_integral3_eval()

static ex GiNaC::iterated_integral3_eval ( const ex &  kernel_lst, const ex &  lambda, const ex &  N_trunc  )

static

Definition at line 608 of file inifcns_elliptic.cpp.

References GiNaC::info_flags::crational, GiNaC::function::evalf(), GiNaC::basic::hold(), GiNaC::ex::info(), iterated_integral(), and GiNaC::info_flags::numeric.

lgamma_evalf()

static ex GiNaC::lgamma_evalf ( const ex &  x )

static

Definition at line 44 of file inifcns_gamma.cpp.

References lgamma(), and x.

lgamma_eval()

static ex GiNaC::lgamma_eval ( const ex &  x )

static

Evaluation of lgamma(x), the natural logarithm of the Gamma function.

Handles integer arguments as a special case.

Exceptions

GiNaC::pole_error("lgamma_eval()

logarithmic pole",0)

Definition at line 60 of file inifcns_gamma.cpp.

References _ex_1, factorial(), GiNaC::ex::info(), GiNaC::info_flags::integer, is_rational(), lgamma(), log(), GiNaC::info_flags::numeric, GiNaC::info_flags::posint, and x.

lgamma_deriv()

static ex GiNaC::lgamma_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 79 of file inifcns_gamma.cpp.

References GINAC_ASSERT, psi(), and x.

lgamma_series()

static ex GiNaC::lgamma_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 88 of file inifcns_gamma.cpp.

References _ex1, GiNaC::ex::info(), GiNaC::info_flags::integer, lgamma(), log(), m, GiNaC::subs_options::no_pattern, options, order, GiNaC::info_flags::positive, GiNaC::basic::series(), and GiNaC::ex::subs().

lgamma_conjugate()

static ex GiNaC::lgamma_conjugate ( const ex &  x )

static

Definition at line 113 of file inifcns_gamma.cpp.

References GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::ex::is_zero(), lgamma(), GiNaC::info_flags::positive, and x.

REGISTER_FUNCTION() [16/36]

GiNaC::REGISTER_FUNCTION	(	lgamma	,
		eval_func(lgamma_eval). evalf_func(lgamma_evalf). derivative_func(lgamma_deriv). series_func(lgamma_series). conjugate_func(lgamma_conjugate). latex_name("\\log \\Gamma")
	)

tgamma_evalf()

static ex GiNaC::tgamma_evalf ( const ex &  x )

static

Definition at line 140 of file inifcns_gamma.cpp.

References tgamma(), and x.

tgamma_eval()

static ex GiNaC::tgamma_eval ( const ex &  x )

static

Evaluation of tgamma(x), the true Gamma function.

Knows about integer arguments, half-integer arguments and that's it. Somebody ought to provide some good numerical evaluation some day...

Exceptions

pole_error("tgamma_eval()

simple pole",0)

Definition at line 157 of file inifcns_gamma.cpp.

References _num1_2_p, _num1_p, _num2_p, _num_2_p, abs(), GiNaC::numeric::div(), doublefactorial(), factorial(), GiNaC::ex::info(), GiNaC::numeric::is_even(), GiNaC::numeric::is_integer(), GiNaC::numeric::is_positive(), is_rational(), n, GiNaC::info_flags::numeric, Pi, pow(), sqrt(), GiNaC::numeric::sub(), tgamma(), and x.

tgamma_deriv()

static ex GiNaC::tgamma_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 192 of file inifcns_gamma.cpp.

References GINAC_ASSERT, psi(), tgamma(), and x.

tgamma_series()

static ex GiNaC::tgamma_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 201 of file inifcns_gamma.cpp.

References _ex1, GiNaC::ex::info(), GiNaC::info_flags::integer, m, GiNaC::subs_options::no_pattern, options, order, GiNaC::info_flags::positive, GiNaC::ex::series(), GiNaC::ex::subs(), and tgamma().

tgamma_conjugate()

static ex GiNaC::tgamma_conjugate ( const ex &  x )

static

Definition at line 226 of file inifcns_gamma.cpp.

References GiNaC::ex::conjugate(), tgamma(), and x.

REGISTER_FUNCTION() [17/36]

GiNaC::REGISTER_FUNCTION	(	tgamma	,
		eval_func(tgamma_eval). evalf_func(tgamma_evalf). derivative_func(tgamma_deriv). series_func(tgamma_series). conjugate_func(tgamma_conjugate). latex_name("\\Gamma")
	)

beta_evalf()

static ex GiNaC::beta_evalf ( const ex &  x, const ex &  y  )

static

Definition at line 245 of file inifcns_gamma.cpp.

References exp(), lgamma(), and x.

beta_eval()

static ex GiNaC::beta_eval ( const ex &  x, const ex &  y  )

static

Definition at line 257 of file inifcns_gamma.cpp.

References _ex0, _ex1, _num_1_p, evalf(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::numeric::is_integer(), is_integer(), GiNaC::numeric::is_negative(), is_positive(), is_rational(), GiNaC::numeric::is_real(), is_real(), GiNaC::info_flags::numeric, pow(), tgamma(), and x.

beta_deriv()

static ex GiNaC::beta_deriv ( const ex &  x, const ex &  y, unsigned  deriv_param  )

static

Definition at line 298 of file inifcns_gamma.cpp.

References GINAC_ASSERT, psi(), and x.

beta_series()

static ex GiNaC::beta_series ( const ex &  arg1, const ex &  arg2, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 313 of file inifcns_gamma.cpp.

References GINAC_ASSERT, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::relational::lhs(), GiNaC::subs_options::no_pattern, options, order, GiNaC::info_flags::positive, GiNaC::ex::subs(), and tgamma().

REGISTER_FUNCTION() [18/36]

GiNaC::REGISTER_FUNCTION	(	beta	,
		eval_func(beta_eval). evalf_func(beta_evalf). derivative_func(beta_deriv). series_func(beta_series). latex_name("\\mathrm{B}"). set_symmetry(sy_symm(0, 1))
	)

psi1_evalf()

static ex GiNaC::psi1_evalf ( const ex &  x )

static

Definition at line 363 of file inifcns_gamma.cpp.

References GiNaC::basic::hold(), psi(), and x.

psi1_eval()

static ex GiNaC::psi1_eval ( const ex &  x )

static

Evaluation of digamma-function psi(x).

Somebody ought to provide some good numerical evaluation some day...

Definition at line 376 of file inifcns_gamma.cpp.

References _ex1_2, _ex2, _num2_p, _num_1_p, Euler, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::numeric::inverse(), GiNaC::numeric::is_integer(), is_integer(), GiNaC::numeric::is_positive(), log(), GiNaC::info_flags::numeric, pow(), psi(), and x.

psi1_deriv()

static ex GiNaC::psi1_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 419 of file inifcns_gamma.cpp.

References _ex1, GINAC_ASSERT, psi(), and x.

psi1_series()

static ex GiNaC::psi1_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 427 of file inifcns_gamma.cpp.

References _ex1, _ex_1, GiNaC::ex::info(), GiNaC::info_flags::integer, m, GiNaC::subs_options::no_pattern, options, order, GiNaC::info_flags::positive, psi(), GiNaC::power::series(), and GiNaC::ex::subs().

psi2_evalf()

static ex GiNaC::psi2_evalf ( const ex &  n, const ex &  x  )

static

Definition at line 464 of file inifcns_gamma.cpp.

References GiNaC::basic::hold(), n, psi(), and x.

psi2_eval()

static ex GiNaC::psi2_eval ( const ex &  n, const ex &  x  )

static

Evaluation of polygamma-function psi(n,x).

Somebody ought to provide some good numerical evaluation some day...

Definition at line 477 of file inifcns_gamma.cpp.

References _ex1, _ex1_2, _ex_1, _num1_2_p, _num1_p, _num2_p, _num_1_p, factorial(), GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::numeric::is_equal(), GiNaC::numeric::is_integer(), is_integer(), GiNaC::numeric::is_positive(), log(), m, n, GiNaC::info_flags::numeric, GiNaC::info_flags::posint, pow(), psi(), tgamma(), x, and zeta().

psi2_deriv()

static ex GiNaC::psi2_deriv ( const ex &  n, const ex &  x, unsigned  deriv_param  )

static

Definition at line 540 of file inifcns_gamma.cpp.

References _ex1, GINAC_ASSERT, n, psi(), and x.

psi2_series()

static ex GiNaC::psi2_series ( const ex &  n, const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 552 of file inifcns_gamma.cpp.

References _ex1, _ex_1, factorial(), GiNaC::ex::info(), GiNaC::info_flags::integer, m, n, GiNaC::subs_options::no_pattern, options, order, GiNaC::info_flags::positive, psi(), and GiNaC::ex::subs().

G2_evalf()

static ex GiNaC::G2_evalf ( const ex &  x_, const ex &  y  )

static

Definition at line 1266 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, factorial(), G(), GiNaC::basic::hold(), imag(), GiNaC::ex::info(), is_real(), log(), GiNaC::ex::nops(), GiNaC::info_flags::numeric, GiNaC::ex::op(), GiNaC::info_flags::positive, pow(), and x.

G2_eval()

static ex GiNaC::G2_eval ( const ex &  x_, const ex &  y  )

static

Definition at line 1307 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GiNaC::info_flags::crational, factorial(), G(), GiNaC::basic::hold(), imag(), GiNaC::ex::info(), is_real(), log(), GiNaC::ex::nops(), GiNaC::info_flags::numeric, GiNaC::ex::op(), GiNaC::info_flags::positive, pow(), and x.

G3_evalf()

static ex GiNaC::G3_evalf ( const ex &  x_, const ex &  s_, const ex &  y  )

static

Definition at line 1370 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GiNaC::container< C >::begin(), GiNaC::ex::begin(), GiNaC::ex::end(), factorial(), G(), GiNaC::basic::hold(), GiNaC::ex::info(), log(), GiNaC::ex::nops(), GiNaC::container< C >::nops(), GiNaC::info_flags::numeric, GiNaC::ex::op(), GiNaC::info_flags::positive, pow(), GiNaC::info_flags::real, and x.

G3_eval()

static ex GiNaC::G3_eval ( const ex &  x_, const ex &  s_, const ex &  y  )

static

Definition at line 1432 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GiNaC::container< C >::begin(), GiNaC::ex::begin(), GiNaC::info_flags::crational, GiNaC::ex::end(), factorial(), G(), GiNaC::basic::hold(), GiNaC::ex::info(), log(), GiNaC::ex::nops(), GiNaC::container< C >::nops(), GiNaC::info_flags::numeric, GiNaC::ex::op(), GiNaC::info_flags::positive, pow(), GiNaC::info_flags::real, and x.

Li_evalf()

static ex GiNaC::Li_evalf ( const ex &  m_, const ex &  x_  )

static

Definition at line 1527 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GiNaC::ex::begin(), GiNaC::ex::evalf(), GiNaC::ex::info(), m, GiNaC::ex::nops(), GiNaC::info_flags::numeric, GiNaC::ex::op(), GiNaC::info_flags::posint, and x.

Li_eval()

static ex GiNaC::Li_eval ( const ex &  m_, const ex &  x_  )

static

Definition at line 1581 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, _ex2, _ex_1, _ex_48, GiNaC::container< C >::append(), GiNaC::ex::begin(), Catalan, GiNaC::info_flags::crational, GINAC_ASSERT, I, GiNaC::ex::info(), GiNaC::ex::is_equal(), log(), m, GiNaC::ex::nops(), GiNaC::info_flags::numeric, Pi, GiNaC::info_flags::posint, pow(), GiNaC::numeric::to_int(), x, and zeta().

Li_series()

static ex GiNaC::Li_series ( const ex &  m, const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 1677 of file inifcns_nstdsums.cpp.

References _ex1, GiNaC::ex::info(), GiNaC::ex::is_zero(), m, GiNaC::subs_options::no_pattern, GiNaC::info_flags::numeric, order, pow(), GiNaC::ex::series(), GiNaC::ex::subs(), and x.

Li_deriv()

static ex GiNaC::Li_deriv ( const ex &  m_, const ex &  x_, unsigned  deriv_param  )

static

Definition at line 1711 of file inifcns_nstdsums.cpp.

References _ex0, GINAC_ASSERT, m, GiNaC::ex::nops(), GiNaC::ex::op(), and x.

Li_print_latex()

static void GiNaC::Li_print_latex ( const ex &  m_, const ex &  x_, const print_context &  c  )

static

Definition at line 1740 of file inifcns_nstdsums.cpp.

References GiNaC::ex::begin(), c, GiNaC::ex::end(), m, and x.

REGISTER_FUNCTION() [19/36]

GiNaC::REGISTER_FUNCTION	(	Li	,
		evalf_func(Li_evalf). eval_func(Li_eval). series_func(Li_series). derivative_func(Li_deriv). print_func< print_latex >(Li_print_latex). do_not_evalf_params()
	)

S_evalf()

static ex GiNaC::S_evalf ( const ex &  n, const ex &  p, const ex &  x  )

static

Definition at line 2165 of file inifcns_nstdsums.cpp.

References GiNaC::ex::evalf(), GiNaC::ex::info(), n, GiNaC::info_flags::posint, and x.

S_eval()

static ex GiNaC::S_eval ( const ex &  n, const ex &  p, const ex &  x  )

static

Definition at line 2187 of file inifcns_nstdsums.cpp.

References _ex0, GiNaC::container< C >::append(), GiNaC::info_flags::crational, factorial(), GiNaC::ex::info(), log(), m, n, GiNaC::info_flags::numeric, GiNaC::info_flags::posint, pow(), to_int(), x, and zeta().

S_series()

static ex GiNaC::S_series ( const ex &  n, const ex &  p, const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 2219 of file inifcns_nstdsums.cpp.

References _ex1, GiNaC::ex::info(), GiNaC::ex::is_zero(), n, GiNaC::subs_options::no_pattern, GiNaC::info_flags::numeric, options, order, GiNaC::info_flags::posint, pow(), GiNaC::ex::series(), GiNaC::ex::subs(), and x.

S_deriv()

static ex GiNaC::S_deriv ( const ex &  n, const ex &  p, const ex &  x, unsigned  deriv_param  )

static

Definition at line 2265 of file inifcns_nstdsums.cpp.

References _ex0, GINAC_ASSERT, n, and x.

S_print_latex()

static void GiNaC::S_print_latex ( const ex &  n, const ex &  p, const ex &  x, const print_context &  c  )

static

Definition at line 2279 of file inifcns_nstdsums.cpp.

References c, n, GiNaC::ex::print(), and x.

REGISTER_FUNCTION() [20/36]

GiNaC::REGISTER_FUNCTION	(	S	,
		evalf_func(S_evalf). eval_func(S_eval). series_func(S_series). derivative_func(S_deriv). print_func< print_latex >(S_print_latex). do_not_evalf_params()
	)

H_evalf()

static ex GiNaC::H_evalf ( const ex &  x1, const ex &  x2  )

static

Definition at line 3199 of file inifcns_nstdsums.cpp.

References GiNaC::container< C >::append(), GiNaC::container< C >::begin(), GiNaC::container< C >::end(), GiNaC::ex::evalf(), I, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::let_op(), m, GiNaC::ex::nops(), GiNaC::container< C >::nops(), GiNaC::ex::op(), GiNaC::container< C >::op(), Pi, GiNaC::ex::subs(), and x.

H_eval()

static ex GiNaC::H_eval ( const ex &  m_, const ex &  x  )

static

Definition at line 3336 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, _ex_1, GiNaC::ex::begin(), GiNaC::info_flags::crational, GiNaC::ex::evalf(), factorial(), GiNaC::ex::info(), GiNaC::info_flags::integer, log(), m, n, GiNaC::basic::nops(), GiNaC::info_flags::numeric, pow(), step(), and x.

H_series()

static ex GiNaC::H_series ( const ex &  m, const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 3451 of file inifcns_nstdsums.cpp.

References m, and x.

H_deriv()

static ex GiNaC::H_deriv ( const ex &  m_, const ex &  x, unsigned  deriv_param  )

static

Definition at line 3458 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, _ex_1, GiNaC::ex::begin(), GINAC_ASSERT, m, and x.

H_print_latex()

static void GiNaC::H_print_latex ( const ex &  m_, const ex &  x, const print_context &  c  )

static

Definition at line 3490 of file inifcns_nstdsums.cpp.

References GiNaC::ex::begin(), c, m, GiNaC::ex::print(), and x.

REGISTER_FUNCTION() [21/36]

GiNaC::REGISTER_FUNCTION	(	H	,
		evalf_func(H_evalf). eval_func(H_eval). series_func(H_series). derivative_func(H_deriv). print_func< print_latex >(H_print_latex). do_not_evalf_params()
	)

zeta1_evalf()

static ex GiNaC::zeta1_evalf ( const ex &  x )

static

Definition at line 3888 of file inifcns_nstdsums.cpp.

References GiNaC::container< C >::begin(), Digits, GiNaC::basic::hold(), GiNaC::ex::nops(), GiNaC::info_flags::posint, r, x, and zeta().

Referenced by zeta1_eval().

zeta1_eval()

static ex GiNaC::zeta1_eval ( const ex &  m )

static

Definition at line 3943 of file inifcns_nstdsums.cpp.

References _ex0, _ex_1_2, _num1_p, _num2_p, abs(), bernoulli(), GiNaC::info_flags::crational, factorial(), GiNaC::basic::hold(), GiNaC::numeric::info(), GiNaC::numeric::is_equal(), GiNaC::numeric::is_integer(), GiNaC::numeric::is_zero(), m, GiNaC::info_flags::numeric, GiNaC::info_flags::odd, Pi, GiNaC::info_flags::posint, pow(), zeta(), and zeta1_evalf().

zeta1_deriv()

static ex GiNaC::zeta1_deriv ( const ex &  m, unsigned  deriv_param  )

static

Definition at line 3985 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GINAC_ASSERT, and m.

zeta1_print_latex()

static void GiNaC::zeta1_print_latex ( const ex &  m_, const print_context &  c  )

static

Definition at line 3997 of file inifcns_nstdsums.cpp.

References c, m, and GiNaC::ex::print().

zeta2_evalf()

static ex GiNaC::zeta2_evalf ( const ex &  x, const ex &  s  )

static

Definition at line 4034 of file inifcns_nstdsums.cpp.

References GiNaC::container< C >::begin(), evalf(), GiNaC::basic::hold(), GiNaC::ex::nops(), GiNaC::info_flags::posint, x, and zeta().

zeta2_eval()

static ex GiNaC::zeta2_eval ( const ex &  m, const ex &  s_  )

static

Definition at line 4080 of file inifcns_nstdsums.cpp.

References GiNaC::basic::hold(), GiNaC::ex::info(), m, GiNaC::info_flags::positive, and zeta().

zeta2_deriv()

static ex GiNaC::zeta2_deriv ( const ex &  m, const ex &  s, unsigned  deriv_param  )

static

Definition at line 4099 of file inifcns_nstdsums.cpp.

References _ex0, _ex1, GINAC_ASSERT, GiNaC::ex::info(), m, GiNaC::ex::op(), and GiNaC::info_flags::positive.

zeta2_print_latex()

static void GiNaC::zeta2_print_latex ( const ex &  m_, const ex &  s_, const print_context &  c  )

static

Definition at line 4114 of file inifcns_nstdsums.cpp.

References GiNaC::container< C >::begin(), GiNaC::ex::begin(), c, and m.

exp_evalf()

static ex GiNaC::exp_evalf ( const ex &  x )

static

Definition at line 46 of file inifcns_trans.cpp.

References exp(), GiNaC::basic::hold(), and x.

exp_eval()

static ex GiNaC::exp_eval ( const ex &  x )

static

Definition at line 54 of file inifcns_trans.cpp.

References _ex1, _ex2, _ex_1, _num0_p, _num1_p, _num2_p, _num3_p, _num4_p, GiNaC::info_flags::crational, exp(), GiNaC::basic::hold(), I, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::numeric::is_equal(), is_ex_the_function, GiNaC::ex::is_zero(), log(), mod(), GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, and x.

exp_expand()

static ex GiNaC::exp_expand ( const ex &  arg, unsigned  options  )

static

Definition at line 86 of file inifcns_trans.cpp.

References GiNaC::ex::begin(), GiNaC::ex::end(), exp(), GiNaC::ex::expand(), GiNaC::expand_options::expand_function_args, GiNaC::expand_options::expand_transcendental, GiNaC::status_flags::expanded, GiNaC::basic::hold(), GiNaC::ex::nops(), and options.

exp_deriv()

static ex GiNaC::exp_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 107 of file inifcns_trans.cpp.

References exp(), GINAC_ASSERT, and x.

exp_real_part()

static ex GiNaC::exp_real_part ( const ex &  x )

static

Definition at line 115 of file inifcns_trans.cpp.

References cos(), exp(), imag_part(), real_part(), and x.

exp_imag_part()

static ex GiNaC::exp_imag_part ( const ex &  x )

static

Definition at line 120 of file inifcns_trans.cpp.

References exp(), imag_part(), real_part(), sin(), and x.

exp_conjugate()

static ex GiNaC::exp_conjugate ( const ex &  x )

static

Definition at line 125 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), exp(), and x.

exp_power()

static ex GiNaC::exp_power ( const ex &  x, const ex &  a  )

static

Definition at line 131 of file inifcns_trans.cpp.

References _ex_1, exp(), GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, GiNaC::info_flags::real, and x.

exp_info()

static bool GiNaC::exp_info ( const ex &  x, unsigned  inf  )

static

Definition at line 149 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), GiNaC::info_flags::nonnegative, GiNaC::info_flags::positive, GiNaC::info_flags::real, and x.

REGISTER_FUNCTION() [22/36]

GiNaC::REGISTER_FUNCTION	(	exp	,
		eval_func(exp_eval). evalf_func(exp_evalf). info_func(exp_info). expand_func(exp_expand). derivative_func(exp_deriv). real_part_func(exp_real_part). imag_part_func(exp_imag_part). conjugate_func(exp_conjugate). power_func(exp_power). latex_name("\\exp")
	)

log_evalf()

static ex GiNaC::log_evalf ( const ex &  x )

static

Definition at line 178 of file inifcns_trans.cpp.

References GiNaC::basic::hold(), log(), and x.

log_eval()

static ex GiNaC::log_eval ( const ex &  x )

static

Definition at line 186 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex_1_2, GiNaC::info_flags::crational, exp(), GiNaC::basic::hold(), I, GiNaC::ex::info(), GiNaC::ex::is_equal(), is_ex_the_function, GiNaC::ex::is_zero(), log(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, GiNaC::info_flags::rational, GiNaC::info_flags::real, and x.

log_deriv()

static ex GiNaC::log_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 215 of file inifcns_trans.cpp.

References _ex_1, GINAC_ASSERT, and x.

log_series()

static ex GiNaC::log_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 223 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex_1, GiNaC::pseries::add_series(), GiNaC::pseries::coeff(), coeff(), csgn(), GiNaC::ex::diff(), GINAC_ASSERT, I, GiNaC::ex::info(), GiNaC::pseries::is_terminating(), GiNaC::ex::is_zero(), GiNaC::pseries::ldegree(), GiNaC::relational::lhs(), log(), n, GiNaC::info_flags::negative, GiNaC::subs_options::no_pattern, GiNaC::pseries::nops(), options, order, Pi, GiNaC::info_flags::positive, pow(), GiNaC::relational::rhs(), GiNaC::ex::series(), series(), GiNaC::ex::subs(), and GiNaC::series_options::suppress_branchcut.

log_real_part()

static ex GiNaC::log_real_part ( const ex &  x )

static

Definition at line 313 of file inifcns_trans.cpp.

References abs(), GiNaC::basic::hold(), GiNaC::ex::info(), log(), GiNaC::info_flags::nonnegative, and x.

log_imag_part()

static ex GiNaC::log_imag_part ( const ex &  x )

static

Definition at line 320 of file inifcns_trans.cpp.

References imag_part(), GiNaC::ex::info(), GiNaC::info_flags::nonnegative, real_part(), and x.

log_expand()

static ex GiNaC::log_expand ( const ex &  arg, unsigned  options  )

static

Definition at line 327 of file inifcns_trans.cpp.

References _ex1, _ex_1, GiNaC::ex::begin(), GiNaC::ex::end(), expand(), GiNaC::ex::expand(), GiNaC::expand_options::expand_function_args, GiNaC::expand_options::expand_transcendental, GiNaC::basic::hold(), GiNaC::info_flags::indefinite, GiNaC::ex::info(), log(), GiNaC::info_flags::negative, GiNaC::ex::nops(), options, GiNaC::info_flags::positive, GiNaC::status_flags::purely_indefinite, and GiNaC::basic::setflag().

log_conjugate()

static ex GiNaC::log_conjugate ( const ex &  x )

static

Definition at line 374 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::ex::is_zero(), log(), GiNaC::info_flags::positive, and x.

log_info()

static bool GiNaC::log_info ( const ex &  x, unsigned  inf  )

static

Definition at line 388 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), GiNaC::info_flags::positive, GiNaC::info_flags::real, and x.

REGISTER_FUNCTION() [23/36]

GiNaC::REGISTER_FUNCTION	(	log	,
		eval_func(log_eval). evalf_func(log_evalf). info_func(log_info). expand_func(log_expand). derivative_func(log_deriv). series_func(log_series). real_part_func(log_real_part). imag_part_func(log_imag_part). conjugate_func(log_conjugate). latex_name("\\ln")
	)

sin_evalf()

static ex GiNaC::sin_evalf ( const ex &  x )

static

Definition at line 415 of file inifcns_trans.cpp.

References GiNaC::basic::hold(), sin(), and x.

sin_eval()

static ex GiNaC::sin_eval ( const ex &  x )

static

Definition at line 423 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex1_3, _ex1_4, _ex2, _ex3, _ex5, _ex6, _ex60, _ex_1, _ex_1_2, _ex_1_3, _ex_1_4, _num0_p, _num10_p, _num120_p, _num15_p, _num18_p, _num20_p, _num25_p, _num30_p, _num5_p, _num60_p, _num6_p, acos(), asin(), atan(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::numeric::is_equal(), is_ex_the_function, mod(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, sin(), sqrt(), and x.

sin_deriv()

static ex GiNaC::sin_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 486 of file inifcns_trans.cpp.

References cos(), GINAC_ASSERT, and x.

sin_real_part()

static ex GiNaC::sin_real_part ( const ex &  x )

static

Definition at line 494 of file inifcns_trans.cpp.

References cosh(), imag_part(), real_part(), sin(), and x.

sin_imag_part()

static ex GiNaC::sin_imag_part ( const ex &  x )

static

Definition at line 499 of file inifcns_trans.cpp.

References cos(), imag_part(), real_part(), sinh(), and x.

sin_conjugate()

static ex GiNaC::sin_conjugate ( const ex &  x )

static

Definition at line 504 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), sin(), and x.

trig_info()

static bool GiNaC::trig_info ( const ex &  x, unsigned  inf  )

static

Definition at line 510 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), GiNaC::info_flags::real, and x.

REGISTER_FUNCTION() [24/36]

GiNaC::REGISTER_FUNCTION	(	sin	,
		eval_func(sin_eval). evalf_func(sin_evalf). info_func(trig_info). derivative_func(sin_deriv). real_part_func(sin_real_part). imag_part_func(sin_imag_part). conjugate_func(sin_conjugate). latex_name("\\sin")
	)

cos_evalf()

static ex GiNaC::cos_evalf ( const ex &  x )

static

Definition at line 534 of file inifcns_trans.cpp.

References cos(), GiNaC::basic::hold(), and x.

cos_eval()

static ex GiNaC::cos_eval ( const ex &  x )

static

Definition at line 542 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex1_3, _ex1_4, _ex2, _ex3, _ex5, _ex6, _ex60, _ex_1, _ex_1_2, _ex_1_3, _ex_1_4, _num0_p, _num10_p, _num120_p, _num12_p, _num15_p, _num20_p, _num24_p, _num25_p, _num30_p, _num5_p, _num60_p, acos(), asin(), atan(), cos(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::numeric::is_equal(), is_ex_the_function, mod(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, sqrt(), and x.

cos_deriv()

static ex GiNaC::cos_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 605 of file inifcns_trans.cpp.

References GINAC_ASSERT, sin(), and x.

cos_real_part()

static ex GiNaC::cos_real_part ( const ex &  x )

static

Definition at line 613 of file inifcns_trans.cpp.

References cos(), cosh(), imag_part(), real_part(), and x.

cos_imag_part()

static ex GiNaC::cos_imag_part ( const ex &  x )

static

Definition at line 618 of file inifcns_trans.cpp.

References imag_part(), real_part(), sin(), sinh(), and x.

cos_conjugate()

static ex GiNaC::cos_conjugate ( const ex &  x )

static

Definition at line 623 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), cos(), and x.

REGISTER_FUNCTION() [25/36]

GiNaC::REGISTER_FUNCTION	(	cos	,
		eval_func(cos_eval). info_func(trig_info). evalf_func(cos_evalf). derivative_func(cos_deriv). real_part_func(cos_real_part). imag_part_func(cos_imag_part). conjugate_func(cos_conjugate). latex_name("\\cos")
	)

tan_evalf()

static ex GiNaC::tan_evalf ( const ex &  x )

static

Definition at line 642 of file inifcns_trans.cpp.

References GiNaC::basic::hold(), tan(), and x.

tan_eval()

static ex GiNaC::tan_eval ( const ex &  x )

static

Definition at line 650 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_3, _ex2, _ex3, _ex60, _ex_1, _ex_1_2, _num0_p, _num10_p, _num15_p, _num20_p, _num25_p, _num30_p, _num5_p, _num60_p, acos(), asin(), atan(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::numeric::is_equal(), is_ex_the_function, mod(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, sqrt(), tan(), and x.

tan_deriv()

static ex GiNaC::tan_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 710 of file inifcns_trans.cpp.

References _ex1, _ex2, GINAC_ASSERT, tan(), and x.

tan_real_part()

static ex GiNaC::tan_real_part ( const ex &  x )

static

Definition at line 718 of file inifcns_trans.cpp.

References imag_part(), real_part(), tan(), and x.

tan_imag_part()

static ex GiNaC::tan_imag_part ( const ex &  x )

static

Definition at line 725 of file inifcns_trans.cpp.

References imag_part(), real_part(), tan(), tanh(), and x.

tan_series()

static ex GiNaC::tan_series ( const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 732 of file inifcns_trans.cpp.

References cos(), GINAC_ASSERT, GiNaC::relational::lhs(), GiNaC::subs_options::no_pattern, GiNaC::info_flags::odd, options, order, Pi, sin(), GiNaC::ex::subs(), and x.

tan_conjugate()

static ex GiNaC::tan_conjugate ( const ex &  x )

static

Definition at line 748 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), tan(), and x.

REGISTER_FUNCTION() [26/36]

GiNaC::REGISTER_FUNCTION	(	tan	,
		eval_func(tan_eval). evalf_func(tan_evalf). info_func(trig_info). derivative_func(tan_deriv). series_func(tan_series). real_part_func(tan_real_part). imag_part_func(tan_imag_part). conjugate_func(tan_conjugate). latex_name("\\tan")
	)

asin_evalf()

static ex GiNaC::asin_evalf ( const ex &  x )

static

Definition at line 768 of file inifcns_trans.cpp.

References asin(), GiNaC::basic::hold(), and x.

asin_eval()

static ex GiNaC::asin_eval ( const ex &  x )

static

Definition at line 776 of file inifcns_trans.cpp.

References _ex1, _ex1_2, _ex_1, _ex_1_2, asin(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, Pi, and x.

asin_deriv()

static ex GiNaC::asin_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 812 of file inifcns_trans.cpp.

References _ex2, _ex_1_2, GINAC_ASSERT, and x.

asin_conjugate()

static ex GiNaC::asin_conjugate ( const ex &  x )

static

Definition at line 820 of file inifcns_trans.cpp.

References _num1_p, _num_1_p, asin(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), and x.

asin_info()

static bool GiNaC::asin_info ( const ex &  x, unsigned  inf  )

static

Definition at line 831 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), and x.

REGISTER_FUNCTION() [27/36]

GiNaC::REGISTER_FUNCTION	(	asin	,
		eval_func(asin_eval). evalf_func(asin_evalf). info_func(asin_info). derivative_func(asin_deriv). conjugate_func(asin_conjugate). latex_name("\\arcsin")
	)

acos_evalf()

static ex GiNaC::acos_evalf ( const ex &  x )

static

Definition at line 852 of file inifcns_trans.cpp.

References acos(), GiNaC::basic::hold(), and x.

acos_eval()

static ex GiNaC::acos_eval ( const ex &  x )

static

Definition at line 860 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex1_3, _ex_1, _ex_1_2, acos(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, Pi, and x.

acos_deriv()

static ex GiNaC::acos_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 896 of file inifcns_trans.cpp.

References _ex2, _ex_1_2, GINAC_ASSERT, and x.

acos_conjugate()

static ex GiNaC::acos_conjugate ( const ex &  x )

static

Definition at line 904 of file inifcns_trans.cpp.

References _num1_p, _num_1_p, acos(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), and x.

REGISTER_FUNCTION() [28/36]

GiNaC::REGISTER_FUNCTION	(	acos	,
		eval_func(acos_eval). evalf_func(acos_evalf). info_func(asin_info). derivative_func(acos_deriv). conjugate_func(acos_conjugate). latex_name("\\arccos")
	)

atan_evalf()

static ex GiNaC::atan_evalf ( const ex &  x )

static

Definition at line 926 of file inifcns_trans.cpp.

References atan(), GiNaC::basic::hold(), and x.

atan_eval()

static ex GiNaC::atan_eval ( const ex &  x )

static

Definition at line 934 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_4, _ex_1, _ex_1_4, atan(), GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, Pi, and x.

atan_deriv()

static ex GiNaC::atan_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 965 of file inifcns_trans.cpp.

References _ex1, _ex2, _ex_1, GINAC_ASSERT, and x.

atan_series()

static ex GiNaC::atan_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 973 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex_1, _ex_1_2, abs(), atan(), csgn(), GINAC_ASSERT, I, GiNaC::ex::is_equal(), GiNaC::relational::lhs(), log(), GiNaC::subs_options::no_pattern, GiNaC::ex::op(), options, order, Pi, GiNaC::info_flags::real, GiNaC::relational::rhs(), series(), GiNaC::ex::subs(), and GiNaC::series_options::suppress_branchcut.

atan_conjugate()

static ex GiNaC::atan_conjugate ( const ex &  x )

static

Definition at line 1019 of file inifcns_trans.cpp.

References _num1_p, _num_1_p, atan(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::numeric::is_zero(), GiNaC::info_flags::real, GiNaC::ex::real_part(), and x.

atan_info()

static bool GiNaC::atan_info ( const ex &  x, unsigned  inf  )

static

Definition at line 1035 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, GiNaC::info_flags::positive, GiNaC::info_flags::real, and x.

REGISTER_FUNCTION() [29/36]

GiNaC::REGISTER_FUNCTION	(	atan	,
		eval_func(atan_eval). evalf_func(atan_evalf). info_func(atan_info). derivative_func(atan_deriv). series_func(atan_series). conjugate_func(atan_conjugate). latex_name("\\arctan")
	)

atan2_evalf()

static ex GiNaC::atan2_evalf ( const ex &  y, const ex &  x  )

static

Definition at line 1062 of file inifcns_trans.cpp.

References atan(), and x.

atan2_eval()

static ex GiNaC::atan2_eval ( const ex &  y, const ex &  x  )

static

Definition at line 1070 of file inifcns_trans.cpp.

References _ex0, _ex1_2, _ex1_4, _ex_1_2, _ex_1_4, atan(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, Pi, GiNaC::info_flags::positive, GiNaC::info_flags::real, and x.

atan2_deriv()

static ex GiNaC::atan2_deriv ( const ex &  y, const ex &  x, unsigned  deriv_param  )

static

Definition at line 1141 of file inifcns_trans.cpp.

References _ex2, _ex_1, GINAC_ASSERT, and x.

atan2_info()

static bool GiNaC::atan2_info ( const ex &  y, const ex &  x, unsigned  inf  )

static

Definition at line 1153 of file inifcns_trans.cpp.

References GiNaC::info_flags::expanded, GiNaC::ex::info(), GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, GiNaC::info_flags::positive, GiNaC::info_flags::real, and x.

REGISTER_FUNCTION() [30/36]

GiNaC::REGISTER_FUNCTION	(	atan2	,
		eval_func(atan2_eval). evalf_func(atan2_evalf). info_func(atan2_info). evalf_func(atan2_evalf). derivative_func(atan2_deriv)
	)

sinh_evalf()

static ex GiNaC::sinh_evalf ( const ex &  x )

static

Definition at line 1179 of file inifcns_trans.cpp.

References GiNaC::basic::hold(), sinh(), and x.

sinh_eval()

static ex GiNaC::sinh_eval ( const ex &  x )

static

Definition at line 1187 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex2, _ex_1_2, acosh(), asinh(), atanh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), is_ex_the_function, GiNaC::ex::is_zero(), is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, real(), sin(), sinh(), sqrt(), and x.

sinh_deriv()

static ex GiNaC::sinh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1227 of file inifcns_trans.cpp.

References cosh(), GINAC_ASSERT, and x.

sinh_real_part()

static ex GiNaC::sinh_real_part ( const ex &  x )

static

Definition at line 1235 of file inifcns_trans.cpp.

References cos(), imag_part(), real_part(), sinh(), and x.

sinh_imag_part()

static ex GiNaC::sinh_imag_part ( const ex &  x )

static

Definition at line 1240 of file inifcns_trans.cpp.

References cosh(), imag_part(), real_part(), sin(), and x.

sinh_conjugate()

static ex GiNaC::sinh_conjugate ( const ex &  x )

static

Definition at line 1245 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), sinh(), and x.

REGISTER_FUNCTION() [31/36]

GiNaC::REGISTER_FUNCTION	(	sinh	,
		eval_func(sinh_eval). evalf_func(sinh_evalf). info_func(atan_info). derivative_func(sinh_deriv). real_part_func(sinh_real_part). imag_part_func(sinh_imag_part). conjugate_func(sinh_conjugate). latex_name("\\sinh")
	)

cosh_evalf()

static ex GiNaC::cosh_evalf ( const ex &  x )

static

Definition at line 1264 of file inifcns_trans.cpp.

References cosh(), GiNaC::basic::hold(), and x.

cosh_eval()

static ex GiNaC::cosh_eval ( const ex &  x )

static

Definition at line 1272 of file inifcns_trans.cpp.

References _ex1, _ex2, _ex_1_2, acosh(), asinh(), atanh(), cos(), cosh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), is_ex_the_function, GiNaC::ex::is_zero(), is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, real(), sqrt(), and x.

cosh_deriv()

static ex GiNaC::cosh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1312 of file inifcns_trans.cpp.

References GINAC_ASSERT, sinh(), and x.

cosh_real_part()

static ex GiNaC::cosh_real_part ( const ex &  x )

static

Definition at line 1320 of file inifcns_trans.cpp.

References cos(), cosh(), imag_part(), real_part(), and x.

cosh_imag_part()

static ex GiNaC::cosh_imag_part ( const ex &  x )

static

Definition at line 1325 of file inifcns_trans.cpp.

References imag_part(), real_part(), sin(), sinh(), and x.

cosh_conjugate()

static ex GiNaC::cosh_conjugate ( const ex &  x )

static

Definition at line 1330 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), cosh(), and x.

REGISTER_FUNCTION() [32/36]

GiNaC::REGISTER_FUNCTION	(	cosh	,
		eval_func(cosh_eval). evalf_func(cosh_evalf). info_func(exp_info). derivative_func(cosh_deriv). real_part_func(cosh_real_part). imag_part_func(cosh_imag_part). conjugate_func(cosh_conjugate). latex_name("\\cosh")
	)

tanh_evalf()

static ex GiNaC::tanh_evalf ( const ex &  x )

static

Definition at line 1349 of file inifcns_trans.cpp.

References GiNaC::basic::hold(), tanh(), and x.

tanh_eval()

static ex GiNaC::tanh_eval ( const ex &  x )

static

Definition at line 1357 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex2, _ex_1, _ex_1_2, acosh(), asinh(), atanh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), is_ex_the_function, GiNaC::ex::is_zero(), is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, GiNaC::ex::op(), Pi, real(), sqrt(), tan(), tanh(), and x.

tanh_deriv()

static ex GiNaC::tanh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1397 of file inifcns_trans.cpp.

References _ex1, _ex2, GINAC_ASSERT, tanh(), and x.

tanh_series()

static ex GiNaC::tanh_series ( const ex &  x, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 1405 of file inifcns_trans.cpp.

References cosh(), GINAC_ASSERT, I, GiNaC::relational::lhs(), GiNaC::subs_options::no_pattern, GiNaC::info_flags::odd, options, order, Pi, sinh(), GiNaC::ex::subs(), and x.

tanh_real_part()

static ex GiNaC::tanh_real_part ( const ex &  x )

static

Definition at line 1421 of file inifcns_trans.cpp.

References imag_part(), real_part(), tan(), tanh(), and x.

tanh_imag_part()

static ex GiNaC::tanh_imag_part ( const ex &  x )

static

Definition at line 1428 of file inifcns_trans.cpp.

References imag_part(), real_part(), tan(), tanh(), and x.

tanh_conjugate()

static ex GiNaC::tanh_conjugate ( const ex &  x )

static

Definition at line 1435 of file inifcns_trans.cpp.

References GiNaC::ex::conjugate(), tanh(), and x.

REGISTER_FUNCTION() [33/36]

GiNaC::REGISTER_FUNCTION	(	tanh	,
		eval_func(tanh_eval). evalf_func(tanh_evalf). info_func(atan_info). derivative_func(tanh_deriv). series_func(tanh_series). real_part_func(tanh_real_part). imag_part_func(tanh_imag_part). conjugate_func(tanh_conjugate). latex_name("\\tanh")
	)

asinh_evalf()

static ex GiNaC::asinh_evalf ( const ex &  x )

static

Definition at line 1455 of file inifcns_trans.cpp.

References asinh(), GiNaC::basic::hold(), and x.

asinh_eval()

static ex GiNaC::asinh_eval ( const ex &  x )

static

Definition at line 1463 of file inifcns_trans.cpp.

References _ex0, asinh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, and x.

asinh_deriv()

static ex GiNaC::asinh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1483 of file inifcns_trans.cpp.

References _ex1, _ex2, _ex_1_2, GINAC_ASSERT, and x.

asinh_conjugate()

static ex GiNaC::asinh_conjugate ( const ex &  x )

static

Definition at line 1491 of file inifcns_trans.cpp.

References _num1_p, _num_1_p, asinh(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::numeric::is_zero(), GiNaC::info_flags::real, GiNaC::ex::real_part(), and x.

REGISTER_FUNCTION() [34/36]

GiNaC::REGISTER_FUNCTION	(	asinh	,
		eval_func(asinh_eval). evalf_func(asinh_evalf). info_func(atan_info). derivative_func(asinh_deriv). conjugate_func(asinh_conjugate)
	)

acosh_evalf()

static ex GiNaC::acosh_evalf ( const ex &  x )

static

Definition at line 1517 of file inifcns_trans.cpp.

References acosh(), GiNaC::basic::hold(), and x.

acosh_eval()

static ex GiNaC::acosh_eval ( const ex &  x )

static

Definition at line 1525 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex_1, acosh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), I, GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, Pi, and x.

acosh_deriv()

static ex GiNaC::acosh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1553 of file inifcns_trans.cpp.

References _ex1, _ex_1, _ex_1_2, GINAC_ASSERT, and x.

acosh_conjugate()

static ex GiNaC::acosh_conjugate ( const ex &  x )

static

Definition at line 1561 of file inifcns_trans.cpp.

References _num1_p, acosh(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), and x.

REGISTER_FUNCTION() [35/36]

GiNaC::REGISTER_FUNCTION	(	acosh	,
		eval_func(acosh_eval). evalf_func(acosh_evalf). info_func(asin_info). derivative_func(acosh_deriv). conjugate_func(acosh_conjugate)
	)

atanh_evalf()

static ex GiNaC::atanh_evalf ( const ex &  x )

static

Definition at line 1582 of file inifcns_trans.cpp.

References atanh(), GiNaC::basic::hold(), and x.

atanh_eval()

static ex GiNaC::atanh_eval ( const ex &  x )

static

Definition at line 1590 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex_1, atanh(), GiNaC::info_flags::crational, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::info_flags::negative, GiNaC::info_flags::numeric, and x.

atanh_deriv()

static ex GiNaC::atanh_deriv ( const ex &  x, unsigned  deriv_param  )

static

Definition at line 1614 of file inifcns_trans.cpp.

References _ex1, _ex2, _ex_1, GINAC_ASSERT, and x.

atanh_series()

static ex GiNaC::atanh_series ( const ex &  arg, const relational &  rel, int  order, unsigned  options  )

static

Definition at line 1622 of file inifcns_trans.cpp.

References _ex0, _ex1, _ex1_2, _ex_1, _ex_1_2, abs(), atanh(), csgn(), GINAC_ASSERT, I, GiNaC::ex::is_equal(), GiNaC::relational::lhs(), log(), GiNaC::subs_options::no_pattern, GiNaC::ex::op(), options, order, Pi, GiNaC::info_flags::real, GiNaC::relational::rhs(), series(), GiNaC::ex::subs(), and GiNaC::series_options::suppress_branchcut.

atanh_conjugate()

static ex GiNaC::atanh_conjugate ( const ex &  x )

static

Definition at line 1668 of file inifcns_trans.cpp.

References _num1_p, _num_1_p, atanh(), GiNaC::ex::conjugate(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), and x.

REGISTER_FUNCTION() [36/36]

GiNaC::REGISTER_FUNCTION	(	atanh	,
		eval_func(atanh_eval). evalf_func(atanh_evalf). info_func(asin_info). derivative_func(atanh_deriv). series_func(atanh_series). conjugate_func(atanh_conjugate)
	)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [11/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	integral	,
		basic	,
		print_func< print_dflt > &::do_print. print_func< print_python > &::do_print. print_func< print_latex > &::do_print_latex
	)

Definition at line 41 of file integral.cpp.

subsvalue()

ex GiNaC::subsvalue	(	const ex &	var,
		const ex &	value,
		const ex &	fun
	)

Definition at line 181 of file integral.cpp.

References GiNaC::ex::evalf(), GiNaC::ex::subs(), and value.

Referenced by adaptivesimpson().

adaptivesimpson()

GiNaC::ex GiNaC::adaptivesimpson	(	const ex &	x,
		const ex &	a_in,
		const ex &	b_in,
		const ex &	f,
		const ex &	error
	)

Numeric integration routine based upon the "Adaptive Quadrature" one in "Numerical Analysis" by Burden and Faires.

Parameters are integration variable, left boundary, right boundary, function to be integrated and the relative integration error. The function should evalf into a number after substituting the integration variable by a number. Another thing to note is that this implementation is no good at integrating functions with discontinuities.

Definition at line 219 of file integral.cpp.

References abs(), GiNaC::ex::evalf(), GiNaC::integral::max_integration_level, GiNaC::ex::subs(), subsvalue(), and x.

Referenced by GiNaC::integral::evalf().

GINAC_BIND_UNARCHIVER() [21/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

integral

)

GINAC_DECLARE_UNARCHIVER() [22/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

integral

)

ifactor()

ex GiNaC::ifactor

(

const numeric &

n

)

Returns the decomposition of the positive integer n into prime numbers in the form lst( lst(p1,...,pr), lst(a1,...,ar) ) such that n = p1^a1 ... pr^ar.

Definition at line 329 of file integration_kernel.cpp.

References GiNaC::container< C >::append(), irem(), n, and GiNaC::info_flags::prime.

Referenced by is_discriminant_of_quadratic_number_field(), and kronecker_symbol().

is_discriminant_of_quadratic_number_field()

bool GiNaC::is_discriminant_of_quadratic_number_field

(

const numeric &

n

)

Returns true if the integer n is either one or the discriminant of a quadratic number field.

Returns false otherwise.

Ref.: Toshitsune Miyake, Modular Forms, Chapter 3.1

Definition at line 368 of file integration_kernel.cpp.

References abs(), ifactor(), is_discriminant_of_quadratic_number_field(), GiNaC::numeric::is_odd(), mod(), n, GiNaC::container< C >::nops(), and GiNaC::container< C >::op().

Referenced by is_discriminant_of_quadratic_number_field().

kronecker_symbol()

numeric GiNaC::kronecker_symbol	(	const numeric &	a,
		const numeric &	n
	)

Returns the Kronecker symbol a: integer n: integer.

This routine defines kronecker_symbol(1,0) = 1 kronecker_symbol(-1,0) = 1 kronecker_symbol(a,0) = 0, a != 1,-1

In particular kronecker_symbol(-1,0) = 1 (in agreement with Sage)

Ref.: Toshitsune Miyake, Modular Forms, Chapter 3.1

Definition at line 425 of file integration_kernel.cpp.

References GiNaC::container< C >::begin(), GiNaC::container< C >::end(), ifactor(), GiNaC::numeric::is_even(), n, GiNaC::container< C >::op(), pow(), and unit.

Referenced by primitive_dirichlet_character().

primitive_dirichlet_character()

numeric GiNaC::primitive_dirichlet_character	(	const numeric &	n,
		const numeric &	a
	)

Defines a primitive Dirichlet character through the Kronecker symbol.

n: integer a: discriminant of a quadratic field |a|: conductor

The character takes the values -1,0,1.

Definition at line 478 of file integration_kernel.cpp.

References kronecker_symbol(), and n.

Referenced by dirichlet_character(), and generalised_Bernoulli_number().

dirichlet_character()

numeric GiNaC::dirichlet_character	(	const numeric &	n,
		const numeric &	a,
		const numeric &	N
	)

Defines a Dirichlet character through the Kronecker symbol.

n: integer a: discriminant of a quadratic field |a|: conductor N: modulus, needs to be multiple of |a|

The character takes the values -1,0,1.

Definition at line 495 of file integration_kernel.cpp.

References gcd(), n, and primitive_dirichlet_character().

generalised_Bernoulli_number()

numeric GiNaC::generalised_Bernoulli_number	(	const numeric &	k,
		const numeric &	b
	)

The generalised Bernoulli number.

k: index / modular weight

b: discriminant of a quadratic field, defines primitive character psi M=|b|: conductor of primitive character psi

The generalised Bernoulli number is computed from the series expansion of the generating function. The generating function is given in eq.(34), arXiv:1704.08895

Definition at line 517 of file integration_kernel.cpp.

References abs(), GiNaC::ex::coeff(), exp(), factorial(), k, primitive_dirichlet_character(), GiNaC::ex::series(), series_to_poly(), GiNaC::numeric::to_int(), and x.

Bernoulli_polynomial()

ex GiNaC::Bernoulli_polynomial	(	const numeric &	k,
		const ex &	x
	)

The Bernoulli polynomials.

Definition at line 542 of file integration_kernel.cpp.

References GiNaC::ex::coeff(), exp(), factorial(), k, GiNaC::ex::series(), series_to_poly(), and x.

Referenced by GiNaC::Eisenstein_h_kernel::coefficient_a0().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [12/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	integration_kernel	,
		basic	,
		print_func< print_context > &::do_print
	)

Definition at line 559 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [22/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

integration_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [13/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	basic_log_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 784 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [23/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

basic_log_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [14/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	multiple_polylog_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 813 of file integration_kernel.cpp.

References _ex1.

GINAC_BIND_UNARCHIVER() [24/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

multiple_polylog_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [15/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	ELi_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 880 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [25/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

ELi_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [16/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	Ebar_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1009 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [26/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

Ebar_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [17/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	Kronecker_dtau_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1138 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [27/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

Kronecker_dtau_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [18/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	Kronecker_dz_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1309 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [28/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

Kronecker_dz_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [19/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	Eisenstein_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1527 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [29/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

Eisenstein_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [20/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	Eisenstein_h_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1704 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [30/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

Eisenstein_h_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [21/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	modular_form_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 1920 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [31/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

modular_form_kernel

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [22/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	user_defined_kernel	,
		integration_kernel	,
		print_func< print_context > &::do_print
	)

Definition at line 2064 of file integration_kernel.cpp.

GINAC_BIND_UNARCHIVER() [32/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

user_defined_kernel

)

GINAC_DECLARE_UNARCHIVER() [23/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

integration_kernel

)

GINAC_DECLARE_UNARCHIVER() [24/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

basic_log_kernel

)

GINAC_DECLARE_UNARCHIVER() [25/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

multiple_polylog_kernel

)

GINAC_DECLARE_UNARCHIVER() [26/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

ELi_kernel

)

GINAC_DECLARE_UNARCHIVER() [27/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

Ebar_kernel

)

GINAC_DECLARE_UNARCHIVER() [28/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

Kronecker_dtau_kernel

)

GINAC_DECLARE_UNARCHIVER() [29/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

Kronecker_dz_kernel

)

GINAC_DECLARE_UNARCHIVER() [30/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

Eisenstein_kernel

)

GINAC_DECLARE_UNARCHIVER() [31/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

Eisenstein_h_kernel

)

GINAC_DECLARE_UNARCHIVER() [32/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

modular_form_kernel

)

GINAC_DECLARE_UNARCHIVER() [33/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

user_defined_kernel

)

GINAC_DECLARE_UNARCHIVER() [34/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

lst

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [23/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	matrix	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Default ctor.

Initializes to 1 x 1-dimensional zero-matrix.

Definition at line 43 of file matrix.cpp.

References GiNaC::status_flags::not_shareable.

GINAC_BIND_UNARCHIVER() [33/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

matrix

)

lst_to_matrix()

ex GiNaC::lst_to_matrix

(

const lst &

l

)

Convert list of lists to matrix.

Definition at line 1682 of file matrix.cpp.

References cols(), GiNaC::container< C >::nops(), and rows().

diag_matrix() [1/2]

ex GiNaC::diag_matrix

(

const lst &

l

)

Convert list of diagonal elements to matrix.

Definition at line 1709 of file matrix.cpp.

References GiNaC::container< C >::nops().

diag_matrix() [2/2]

ex GiNaC::diag_matrix

(

std::initializer_list< ex >

l

)

Definition at line 1725 of file matrix.cpp.

unit_matrix() [1/2]

ex GiNaC::unit_matrix	(	unsigned	r,
		unsigned	c
	)

Create an r times c unit matrix.

Definition at line 1741 of file matrix.cpp.

References _ex1, c, GiNaC::status_flags::evaluated, r, and GiNaC::basic::setflag().

Referenced by unit_matrix().

symbolic_matrix() [1/2]

ex GiNaC::symbolic_matrix	(	unsigned	r,
		unsigned	c,
		const std::string &	base_name,
		const std::string &	tex_base_name
	)

Create an r times c matrix of newly generated symbols consisting of the given base name plus the numeric row/column position of each element.

The base name for LaTeX output is specified separately.

Definition at line 1751 of file matrix.cpp.

References c, GiNaC::status_flags::evaluated, r, and GiNaC::basic::setflag().

Referenced by symbolic_matrix().

reduced_matrix()

ex GiNaC::reduced_matrix	(	const matrix &	m,
		unsigned	r,
		unsigned	c
	)

Return the reduced matrix that is formed by deleting the rth row and cth column of matrix m.

The determinant of the result is the Minor r, c.

Definition at line 1788 of file matrix.cpp.

References c, cols(), GiNaC::status_flags::evaluated, m, r, rows(), and GiNaC::basic::setflag().

sub_matrix()

ex GiNaC::sub_matrix	(	const matrix &	m,
		unsigned	r,
		unsigned	nr,
		unsigned	c,
		unsigned	nc
	)

Return the nr times nc submatrix starting at position r, c of matrix m.

Definition at line 1819 of file matrix.cpp.

References c, GiNaC::status_flags::evaluated, m, r, and GiNaC::basic::setflag().

GINAC_DECLARE_UNARCHIVER() [35/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

matrix

)

nops() [2/2]

size_t GiNaC::nops ( const matrix &  m )

inline

Definition at line 123 of file matrix.h.

References m.

expand() [2/2]

ex GiNaC::expand ( const matrix &  m, unsigned  options = 0  )

inline

Definition at line 126 of file matrix.h.

References GiNaC::ex::expand(), m, and options.

evalf() [2/2]

ex GiNaC::evalf ( const matrix &  m )

inline

Definition at line 129 of file matrix.h.

References GiNaC::ex::evalf(), and m.

rows()

unsigned GiNaC::rows ( const matrix &  m )

inline

Definition at line 132 of file matrix.h.

References m.

Referenced by lst_to_matrix(), and reduced_matrix().

cols()

unsigned GiNaC::cols ( const matrix &  m )

inline

Definition at line 135 of file matrix.h.

References m.

Referenced by lst_to_matrix(), and reduced_matrix().

transpose()

matrix GiNaC::transpose ( const matrix &  m )

inline

Definition at line 138 of file matrix.h.

References m, and GiNaC::matrix::transpose().

determinant()

ex GiNaC::determinant ( const matrix &  m, unsigned  options = determinant_algo::automatic  )

inline

Definition at line 141 of file matrix.h.

References m, and options.

trace()

ex GiNaC::trace ( const matrix &  m )

inline

Definition at line 144 of file matrix.h.

References m.

charpoly()

ex GiNaC::charpoly ( const matrix &  m, const ex &  lambda  )

inline

Definition at line 147 of file matrix.h.

References m.

inverse() [1/3]

matrix GiNaC::inverse ( const matrix &  m )

inline

Definition at line 150 of file matrix.h.

References GiNaC::solve_algo::automatic, GiNaC::matrix::inverse(), and m.

inverse() [2/3]

matrix GiNaC::inverse ( const matrix &  m, unsigned  algo  )

inline

Definition at line 152 of file matrix.h.

References GiNaC::matrix::inverse(), and m.

rank() [1/2]

unsigned GiNaC::rank ( const matrix &  m )

inline

Definition at line 155 of file matrix.h.

References m, and GiNaC::matrix::rank().

rank() [2/2]

unsigned GiNaC::rank ( const matrix &  m, unsigned  solve_algo  )

inline

Definition at line 157 of file matrix.h.

References m.

unit_matrix() [2/2]

ex GiNaC::unit_matrix ( unsigned  x )

inline

Create a x times x unit matrix.

Definition at line 173 of file matrix.h.

References unit_matrix(), and x.

symbolic_matrix() [2/2]

ex GiNaC::symbolic_matrix ( unsigned  r, unsigned  c, const std::string &  base_name  )

inline

Create an r times c matrix of newly generated symbols consisting of the given base name plus the numeric row/column position of each element.

Definition at line 190 of file matrix.h.

References c, r, and symbolic_matrix().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [24/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	mul	,
		expairseq	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 41 of file mul.cpp.

tryfactsubs()

bool GiNaC::tryfactsubs	(	const ex &	origfactor,
		const ex &	patternfactor,
		int &	nummatches,
		exmap &	repls
	)

Definition at line 671 of file mul.cpp.

References GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::match(), and GiNaC::ex::op().

Referenced by algebraic_match_mul_with_mul(), GiNaC::mul::algebraic_subs_mul(), and GiNaC::power::subs().

algebraic_match_mul_with_mul()

bool GiNaC::algebraic_match_mul_with_mul	(	const mul &	e,
		const ex &	pat,
		exmap &	repls,
		int	factor,
		int &	nummatches,
		const std::vector< bool > &	subsed,
		std::vector< bool > &	matched
	)

Checks whether e matches to the pattern pat and the (possibly to be updated) list of replacements repls.

This matching is in the sense of algebraic substitutions. Matching starts with pat.op(factor) of the pattern because the factors before this one have already been matched. The (possibly updated) number of matches is in nummatches. subsed[i] is true for factors that already have been replaced by previous substitutions and matched[i] is true for factors that have been matched by the current match.

Definition at line 722 of file mul.cpp.

References algebraic_match_mul_with_mul(), factor(), GINAC_ASSERT, GiNaC::ex::nops(), GiNaC::expairseq::nops(), GiNaC::ex::op(), GiNaC::expairseq::op(), and tryfactsubs().

Referenced by algebraic_match_mul_with_mul(), GiNaC::mul::algebraic_subs_mul(), and GiNaC::mul::has().

GINAC_BIND_UNARCHIVER() [34/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

mul

)

GINAC_DECLARE_UNARCHIVER() [36/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

mul

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [25/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	ncmul	,
		exprseq	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree. print_func< print_csrc > &::do_print_csrc. print_func< print_python_repr > &::do_print_csrc
	)

Definition at line 38 of file ncmul.cpp.

reeval_ncmul()

ex GiNaC::reeval_ncmul

(

const exvector &

v

)

Definition at line 608 of file ncmul.cpp.

hold_ncmul()

ex GiNaC::hold_ncmul

(

const exvector &

v

)

Definition at line 613 of file ncmul.cpp.

Referenced by GiNaC::basic::eval_ncmul(), GiNaC::color::eval_ncmul(), and GiNaC::structure< T, ComparisonPolicy >::eval_ncmul().

GINAC_BIND_UNARCHIVER() [35/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

ncmul

)

GINAC_DECLARE_UNARCHIVER() [37/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

ncmul

)

get_first_symbol()

static bool GiNaC::get_first_symbol ( const ex &  e, ex &  x  )

static

Return pointer to first symbol found in expression.

Due to GiNaC's internal ordering of terms, it may not be obvious which symbol this function returns for a given expression.

Parameters

e	expression to search
x	first symbol found (returned)

Returns

"false" if no symbol was found, "true" otherwise

Definition at line 95 of file normal.cpp.

References get_first_symbol(), GiNaC::ex::nops(), GiNaC::ex::op(), and x.

Referenced by divide(), frac_cancel(), get_first_symbol(), and GiNaC::ex::unit().

add_symbol()

static void GiNaC::add_symbol ( const ex &  s, sym_desc_vec &  v  )

static

Definition at line 163 of file normal.cpp.

Referenced by collect_symbols().

collect_symbols()

static void GiNaC::collect_symbols ( const ex &  e, sym_desc_vec &  v  )

static

Definition at line 173 of file normal.cpp.

References add_symbol(), collect_symbols(), GiNaC::ex::nops(), and GiNaC::ex::op().

Referenced by collect_symbols(), and get_symbol_stats().

get_symbol_stats()

static void GiNaC::get_symbol_stats ( const ex &  a, const ex &  b, sym_desc_vec &  v  )

static

Collect statistical information about symbols in polynomials.

This function fills in a vector of "sym_desc" structs which contain information about the highest and lowest degrees of all symbols that appear in two polynomials. The vector is then sorted by minimum degree (lowest to highest). The information gathered by this function is used by the GCD routines to identify trivial factors and to determine which variable to choose as the main variable for GCD computation.

Parameters

a	first multivariate polynomial
b	second multivariate polynomial
v	vector of sym_desc structs (filled in)

Definition at line 197 of file normal.cpp.

References collect_symbols(), GiNaC::ex::degree(), GiNaC::ex::lcoeff(), GiNaC::ex::ldegree(), and GiNaC::ex::nops().

Referenced by divide_in_z(), gcd(), and sqrfree().

lcmcoeff()

static numeric GiNaC::lcmcoeff ( const ex &  e, const numeric &  l  )

static

Definition at line 231 of file normal.cpp.

References _num1_p, c, denom(), GiNaC::ex::info(), lcm(), lcmcoeff(), GiNaC::ex::nops(), GiNaC::ex::op(), pow(), and GiNaC::info_flags::rational.

Referenced by heur_gcd(), lcm_of_coefficients_denominators(), lcmcoeff(), and multiply_lcm().

lcm_of_coefficients_denominators()

static numeric GiNaC::lcm_of_coefficients_denominators ( const ex &  e )

static

Compute LCM of denominators of coefficients of a polynomial.

Given a polynomial with rational coefficients, this function computes the LCM of the denominators of all coefficients. This can be used to bring a polynomial from Q[X] to Z[X].

Parameters

e	multivariate polynomial (need not be expanded)

Returns

LCM of denominators of coefficients

Definition at line 261 of file normal.cpp.

References _num1_p, and lcmcoeff().

Referenced by frac_cancel(), heur_gcd(), and sqrfree().

multiply_lcm()

static ex GiNaC::multiply_lcm ( const ex &  e, const numeric &  lcm  )

static

Bring polynomial from Q[X] to Z[X] by multiplying in the previously determined LCM of the coefficient's denominators.

Parameters

e	multivariate polynomial (need not be expanded)
lcm	LCM to multiply in

Definition at line 271 of file normal.cpp.

References _num1_p, GiNaC::ex::is_equal(), GiNaC::numeric::is_rational(), lcm(), lcmcoeff(), multiply_lcm(), GiNaC::ex::nops(), GiNaC::ex::op(), and pow().

Referenced by frac_cancel(), multiply_lcm(), and sqrfree().

quo()

ex GiNaC::quo	(	const ex &	a,
		const ex &	b,
		const ex &	x,
		bool	check_args
	)

Quotient q(x) of polynomials a(x) and b(x) in Q[x].

It satisfies a(x)=b(x)*q(x)+r(x).

Parameters

a	first polynomial in x (dividend)
b	second polynomial in x (divisor)
x	a and b are polynomials in x
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

quotient of a and b in Q[x]

Definition at line 373 of file normal.cpp.

References _ex1, GiNaC::ex::coeff(), GiNaC::ex::degree(), divide(), expand(), GiNaC::ex::expand(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), pow(), r, GiNaC::info_flags::rational_polynomial, and x.

Referenced by decomp_rational(), GiNaC::ex::primpart(), sqrfree_parfrac(), sqrfree_yun(), and GiNaC::ex::unitcontprim().

rem()

ex GiNaC::rem	(	const ex &	a,
		const ex &	b,
		const ex &	x,
		bool	check_args
	)

Remainder r(x) of polynomials a(x) and b(x) in Q[x].

It satisfies a(x)=b(x)*q(x)+r(x).

Parameters

a	first polynomial in x (dividend)
b	second polynomial in x (divisor)
x	a and b are polynomials in x
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

remainder of a(x) and b(x) in Q[x]

Definition at line 423 of file normal.cpp.

References _ex0, GiNaC::ex::coeff(), GiNaC::ex::degree(), divide(), expand(), GiNaC::ex::expand(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), pow(), r, GiNaC::info_flags::rational_polynomial, and x.

Referenced by decomp_rational(), and sqrfree_parfrac().

decomp_rational()

ex GiNaC::decomp_rational	(	const ex &	a,
		const ex &	x
	)

Decompose rational function a(x)=N(x)/D(x) into P(x)+n(x)/D(x) with degree(n, x) < degree(D, x).

Parameters

a	rational function in x
x	a is a function of x

Returns

decomposed function.

Definition at line 472 of file normal.cpp.

References denom(), numer(), numer_denom(), GiNaC::ex::op(), quo(), rem(), and x.

prem()

ex GiNaC::prem	(	const ex &	a,
		const ex &	b,
		const ex &	x,
		bool	check_args
	)

Pseudo-remainder of polynomials a(x) and b(x) in Q[x].

Parameters

a	first polynomial in x (dividend)
b	second polynomial in x (divisor)
x	a and b are polynomials in x
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

pseudo-remainder of a(x) and b(x) in Q[x]

Definition at line 492 of file normal.cpp.

References _ex0, _ex1, GiNaC::ex::coeff(), GiNaC::ex::degree(), expand(), GiNaC::ex::expand(), GiNaC::ex::info(), GiNaC::ex::is_zero(), pow(), r, GiNaC::info_flags::rational_polynomial, and x.

Referenced by sr_gcd().

sprem()

ex GiNaC::sprem	(	const ex &	a,
		const ex &	b,
		const ex &	x,
		bool	check_args
	)

Sparse pseudo-remainder of polynomials a(x) and b(x) in Q[x].

Parameters

a	first polynomial in x (dividend)
b	second polynomial in x (divisor)
x	a and b are polynomials in x
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

sparse pseudo-remainder of a(x) and b(x) in Q[x]

Definition at line 544 of file normal.cpp.

References _ex0, _ex1, GiNaC::ex::coeff(), GiNaC::ex::degree(), expand(), GiNaC::ex::expand(), GiNaC::ex::info(), GiNaC::ex::is_zero(), pow(), r, GiNaC::info_flags::rational_polynomial, and x.

divide()

bool GiNaC::divide	(	const ex &	a,
		const ex &	b,
		ex &	q,
		bool	check_args
	)

Exact polynomial division of a(X) by b(X) in Q[X].

Parameters

a	first multivariate polynomial (dividend)
b	second multivariate polynomial (divisor)
q	quotient (returned)
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

"true" when exact division succeeds (quotient returned in q), "false" otherwise (q left untouched)

Definition at line 595 of file normal.cpp.

References _ex0, _ex1, GiNaC::ex::coeff(), GiNaC::ex::degree(), divide(), expand(), GiNaC::ex::expand(), get_first_symbol(), GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::ex::nops(), GiNaC::ex::op(), pow(), r, GiNaC::info_flags::rational_polynomial, and x.

Referenced by divide(), find_common_factor(), GiNaC::matrix::fraction_free_elimination(), gcd(), quo(), and rem().

divide_in_z()

static bool GiNaC::divide_in_z ( const ex &  a, const ex &  b, ex &  q, sym_desc_vec::const_iterator  var  )

static

Exact polynomial division of a(X) by b(X) in Z[X].

This functions works like divide() but the input and output polynomials are in Z[X] instead of Q[X] (i.e. they have integer coefficients). Unlike divide(), it doesn't check whether the input polynomials really are integer polynomials, so be careful of what you pass in. Also, you have to run get_symbol_stats() over the input polynomials before calling this function and pass an iterator to the first element of the sym_desc vector. This function is used internally by the heur_gcd().

Parameters

a	first multivariate polynomial (dividend)
b	second multivariate polynomial (divisor)
q	quotient (returned)
var	iterator to first element of vector of sym_desc structs

Returns

"true" when exact division succeeds (the quotient is returned in q), "false" otherwise.

See also

get_symbol_stats, heur_gcd

Definition at line 757 of file normal.cpp.

References _ex0, _ex1, _num0_p, _num1_p, GiNaC::ex::begin(), c, GiNaC::ex::coeff(), GiNaC::ex::degree(), divide_in_z(), expand(), GiNaC::ex::expand(), GiNaC::ex::find(), get_symbol_stats(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::numeric::inverse(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), k, GiNaC::subs_options::no_pattern, GiNaC::ex::op(), pow(), qbar, r, GiNaC::ex::subs(), and x.

Referenced by divide_in_z(), heur_gcd_z(), and sr_gcd().

sr_gcd()

static ex GiNaC::sr_gcd ( const ex &  a, const ex &  b, sym_desc_vec::const_iterator  var  )

static

Compute GCD of multivariate polynomials using the subresultant PRS algorithm.

This function is used internally by gcd().

Parameters

a	first multivariate polynomial
b	second multivariate polynomial
var	iterator to first element of vector of sym_desc structs

Returns

the GCD as a new expression

See also

gcd

Definition at line 1081 of file normal.cpp.

References _ex0, _ex1, c, GiNaC::ex::content(), GiNaC::ex::degree(), divide_in_z(), GiNaC::ex::expand(), gcd(), GiNaC::ex::lcoeff(), pow(), prem(), GiNaC::ex::primpart(), psi(), r, and x.

Referenced by gcd().

interpolate()

static ex GiNaC::interpolate ( const ex &  gamma, const numeric &  xi, const ex &  x, int  degree_hint = 1  )

static

xi-adic polynomial interpolation

Definition at line 1245 of file normal.cpp.

References GiNaC::numeric::inverse(), GiNaC::ex::is_zero(), pow(), GiNaC::ex::smod(), and x.

Referenced by heur_gcd_z().

heur_gcd_z()

static bool GiNaC::heur_gcd_z ( ex &  res, const ex &  a, const ex &  b, ex *  ca, ex *  cb, sym_desc_vec::const_iterator  var  )

static

Compute GCD of multivariate polynomials using the heuristic GCD algorithm.

get_symbol_stats() must have been called previously with the input polynomials and an iterator to the first element of the sym_desc vector passed in. This function is used internally by gcd().

Parameters

a	first integer multivariate polynomial (expanded)
b	second integer multivariate polynomial (expanded)
ca	cofactor of polynomial a (returned), nullptr to suppress calculation of cofactor
cb	cofactor of polynomial b (returned), nullptr to suppress calculation of cofactor
var	iterator to first element of vector of sym_desc structs
res	the GCD (returned)

Returns

true if GCD was computed, false otherwise.

See also

gcd

Exceptions

gcdheu_failed()

Definition at line 1277 of file normal.cpp.

References GiNaC::ex::degree(), divide_in_z(), GiNaC::ex::expand(), gcd(), heur_gcd_z(), GiNaC::numeric::int_length(), GiNaC::ex::integer_content(), interpolate(), GiNaC::numeric::inverse(), iquo(), GiNaC::ex::is_zero(), isqrt(), GiNaC::ex::max_coefficient(), GiNaC::subs_options::no_pattern, GiNaC::ex::subs(), and x.

Referenced by heur_gcd(), and heur_gcd_z().

heur_gcd()

static bool GiNaC::heur_gcd ( ex &  res, const ex &  a, const ex &  b, ex *  ca, ex *  cb, sym_desc_vec::const_iterator  var  )

static

Compute GCD of multivariate polynomials using the heuristic GCD algorithm.

get_symbol_stats() must have been called previously with the input polynomials and an iterator to the first element of the sym_desc vector passed in. This function is used internally by gcd().

Parameters

a	first rational multivariate polynomial (expanded)
b	second rational multivariate polynomial (expanded)
ca	cofactor of polynomial a (returned), nullptr to suppress calculation of cofactor
cb	cofactor of polynomial b (returned), nullptr to suppress calculation of cofactor
var	iterator to first element of vector of sym_desc structs
res	the GCD (returned)

Returns

true if GCD was computed, false otherwise.

See also

heur_gcd_z

gcd

Definition at line 1371 of file normal.cpp.

References heur_gcd_z(), GiNaC::ex::info(), GiNaC::info_flags::integer_polynomial, lcm_of_coefficients_denominators(), and lcmcoeff().

Referenced by gcd().

gcd_pf_pow()

static ex GiNaC::gcd_pf_pow ( const ex &  a, const ex &  b, ex *  ca, ex *  cb  )

static

Definition at line 1694 of file normal.cpp.

References _ex1, expand(), gcd(), gcd_pf_pow(), gcd_pf_pow_pow(), GINAC_ASSERT, GiNaC::ex::is_equal(), GiNaC::ex::ldegree(), GiNaC::ex::op(), and pow().

Referenced by gcd(), and gcd_pf_pow().

gcd_pf_mul()

static ex GiNaC::gcd_pf_mul ( const ex &  a, const ex &  b, ex *  ca, ex *  cb  )

static

Definition at line 1741 of file normal.cpp.

References gcd(), gcd_pf_mul(), GINAC_ASSERT, GiNaC::ex::nops(), and GiNaC::ex::op().

Referenced by gcd(), and gcd_pf_mul().

gcd() [1/2]

ex GiNaC::gcd	(	const ex &	a,
		const ex &	b,
		ex *	ca,
		ex *	cb,
		bool	check_args,
		unsigned	options
	)

Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X) and b(X) in Z[X].

Optionally also compute the cofactors of a and b, defined by a = ca * gcd(a, b) and b = cb * gcd(a, b).

Parameters

a	first multivariate polynomial
b	second multivariate polynomial
ca	pointer to expression that will receive the cofactor of a, or nullptr
cb	pointer to expression that will receive the cofactor of b, or nullptr
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")
options	see GiNaC::gcd_options

Returns

the GCD as a new expression

Definition at line 1433 of file normal.cpp.

References _ex0, _ex1, divide(), expand(), GiNaC::ex::expand(), gcd(), gcd_pf_mul(), gcd_pf_pow(), get_symbol_stats(), heur_gcd(), GiNaC::ex::info(), GiNaC::ex::integer_content(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), GiNaC::numeric::is_zero(), n, GiNaC::gcd_options::no_heur_gcd, GiNaC::gcd_options::no_part_factored, GiNaC::subs_options::no_pattern, options, pow(), GiNaC::info_flags::rational_polynomial, sr_gcd(), GiNaC::ex::subs(), GiNaC::ex::unitcontprim(), GiNaC::gcd_options::use_sr_gcd, and x.

Referenced by GiNaC::ex::content(), dirichlet_character(), find_common_factor(), frac_cancel(), gcd(), gcd_pf_mul(), gcd_pf_pow(), gcd_pf_pow_pow(), heur_gcd_z(), GiNaC::add::integer_content(), lcm(), GiNaC::add::normal(), sqrfree_yun(), and sr_gcd().

gcd_pf_pow_pow()

static ex GiNaC::gcd_pf_pow_pow ( const ex &  a, const ex &  b, ex *  ca, ex *  cb  )

static

Definition at line 1647 of file normal.cpp.

References _ex1, gcd(), GiNaC::ex::is_equal(), GiNaC::ex::op(), and pow().

Referenced by gcd_pf_pow().

lcm() [1/2]

ex GiNaC::lcm	(	const ex &	a,
		const ex &	b,
		bool	check_args
	)

Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].

Parameters

a	first multivariate polynomial
b	second multivariate polynomial
check_args	check whether a and b are polynomials with rational coefficients (defaults to "true")

Returns

the LCM as a new expression

Definition at line 1775 of file normal.cpp.

References gcd(), GiNaC::ex::info(), lcm(), and GiNaC::info_flags::rational_polynomial.

Referenced by GiNaC::add::integer_content(), lcm(), lcmcoeff(), multiply_lcm(), and sqrfree().

sqrfree_yun()

static epvector GiNaC::sqrfree_yun ( const ex &  a, const symbol &  x  )

static

Compute square-free factorization of multivariate polynomial a(x) using Yun's algorithm.

Used internally by sqrfree().

Parameters

a	multivariate polynomial over Z[X], treated here as univariate polynomial in x (needs not be expanded).
x	variable to factor in

Returns

vector of expairs (factor, exponent), sorted by exponents

Definition at line 1799 of file normal.cpp.

References _ex1, GiNaC::ex::diff(), factors, gcd(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), quo(), and x.

Referenced by sqrfree(), and sqrfree_parfrac().

sqrfree()

ex GiNaC::sqrfree	(	const ex &	a,
		const lst &	l
	)

Compute a square-free factorization of a multivariate polynomial in Q[X].

Parameters

a	multivariate polynomial over Q[X] (needs not be expanded)
l	lst of variables to factor in, may be left empty for autodetection

Returns

a square-free factorization of a.

Note

A polynomial is said square-free if, whenever any two polynomials and are such that

we have . This means that has no repeated factors, apart eventually from constants. Given a polynomial , we say that the decomposition

is a square-free factorization of if the following conditions hold:

1. and ;
2. is a positive integer for ;
3. the degree of the polynomial is strictly positive for ;
4. the polynomial is square-free.

Square-free factorizations need not be unique. For example, if is even, we could change the polynomial into . Observe also that the factors need not be irreducible polynomials.

Definition at line 1889 of file normal.cpp.

References _ex0, GiNaC::container< C >::append(), factors, get_symbol_stats(), lcm(), lcm_of_coefficients_denominators(), multiply_lcm(), GiNaC::container< C >::nops(), GiNaC::container< C >::op(), GiNaC::container< C >::remove_first(), sqrfree(), sqrfree_yun(), and x.

Referenced by sqrfree().

sqrfree_parfrac()

ex GiNaC::sqrfree_parfrac	(	const ex &	a,
		const symbol &	x
	)

Compute square-free partial fraction decomposition of rational function a(x).

Parameters

a	rational function over Z[x], treated as univariate polynomial in x
x	variable to factor in

Returns

decomposed rational function

Definition at line 1948 of file normal.cpp.

References _ex1, GiNaC::basic::coeff(), GiNaC::ex::coeff(), coeff(), degree(), denom(), GiNaC::ex::expand(), factor(), GINAC_ASSERT, k, n, numer(), numer_denom(), GiNaC::ex::op(), pow(), quo(), r, rem(), rhs(), GiNaC::matrix::solve(), sqrfree_yun(), to_int(), and x.

replace_with_symbol() [1/2]

static ex GiNaC::replace_with_symbol ( const ex &  e, exmap &  repl, exmap &  rev_lookup, lst &  modifier  )

static

Create a symbol for replacing the expression "e" (or return a previously assigned symbol).

The symbol and expression are appended to repl, for a later application of subs(). An entry in the replacement table repl can be changed in some cases. If it was altered, we need to provide the modifier for the previously build expressions. The modifier is an (ordered) list, because those substitutions need to be done in the incremental order. As an example let us consider a rationalisation of the expression e = exp(2*x)*cos(exp(2*x)+1)*exp(x) The first factor GiNaC denotes by something like symbol1 and will record: e =symbol1*cos(symbol1 + 1)*exp(x) repl = {symbol1 : exp(2*x)} Similarly, the second factor would be denoted as symbol2 and we will have e =symbol1*symbol2*exp(x) repl = {symbol1 : exp(2*x), symbol2 : cos(symbol1 + 1)} Denoting the third term as symbol3 GiNaC is willing to re-think exp(2*x) as symbol3^2 rather than just symbol1. Here are two issues: 1) The replacement "symbol1 -> symbol3^2" in the previous part of the expression needs to be done outside of the present routine; 2) The pair "symbol1 : exp(2*x)" shall be deleted from the replacement table repl. However, this will create illegal substitution "symbol2 : cos(symbol1 + 1)" with undefined symbol1. These both problems are mitigated through the additions of the record "symbol1==symbol3^2" to the list modifier. Changed length of the modifier signals to the calling code that the previous portion of the expression needs to be altered (it solves 1). Thus GiNaC can record now e =symbol3^2*symbol2*symbol3 repl = {symbol2 : cos(symbol1 + 1), symbol3 : exp(x)} modifier = {symbol1==symbol3^2} Then, doing the backward substitutions the list modifier will be used to restore such iterative substitutions in the right way (this solves 2).

See also

ex::normal

Definition at line 2078 of file normal.cpp.

References _ex_1, GiNaC::container< C >::append(), degree(), denom(), exp(), GiNaC::ex::find(), GiNaC::ex::is_equal(), is_ex_the_function, is_integer(), is_rational(), GiNaC::subs_options::no_pattern, normal(), numer(), GiNaC::ex::op(), pow(), and GiNaC::ex::subs().

Referenced by GiNaC::basic::normal(), GiNaC::numeric::normal(), GiNaC::power::normal(), GiNaC::pseries::normal(), GiNaC::basic::to_polynomial(), GiNaC::numeric::to_polynomial(), GiNaC::power::to_polynomial(), GiNaC::basic::to_rational(), GiNaC::numeric::to_rational(), and GiNaC::power::to_rational().

replace_with_symbol() [2/2]

static ex GiNaC::replace_with_symbol ( const ex &  e, exmap &  repl  )

static

Create a symbol for replacing the expression "e" (or return a previously assigned symbol).

The symbol and expression are appended to repl, and the symbol is returned.

See also

basic::to_rational

basic::to_polynomial

Definition at line 2191 of file normal.cpp.

References GiNaC::subs_options::no_pattern, and GiNaC::ex::subs().

frac_cancel()

static ex GiNaC::frac_cancel ( const ex &  n, const ex &  d  )

static

Fraction cancellation.

Parameters

n	numerator
d	denominator

Returns

cancelled fraction {n, d} as a list

Definition at line 2276 of file normal.cpp.

References _ex1, _ex_1, _num1_p, GiNaC::numeric::denom(), GiNaC::ex::expand(), gcd(), get_first_symbol(), GINAC_ASSERT, GiNaC::ex::is_equal(), is_negative(), GiNaC::ex::is_zero(), lcm_of_coefficients_denominators(), multiply_lcm(), n, GiNaC::numeric::numer(), GiNaC::ex::unit(), and x.

Referenced by GiNaC::add::normal(), and GiNaC::mul::normal().

find_common_factor()

static ex GiNaC::find_common_factor ( const ex &  e, ex &  factor, exmap &  repl  )

static

Remove the common factor in the terms of a sum 'e' by calculating the GCD, and multiply it into the expression 'factor' (which needs to be initialized to 1, unless you're accumulating factors).

Definition at line 2770 of file normal.cpp.

References _ex0, _ex1, divide(), factor(), find_common_factor(), gcd(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), k, GiNaC::ex::nops(), GiNaC::ex::op(), pow(), GiNaC::ex::to_polynomial(), and x.

Referenced by collect_common_factors(), and find_common_factor().

collect_common_factors()

ex GiNaC::collect_common_factors

(

const ex &

e

)

Collect common factors in sums.

This converts expressions like 'a*(b*x+b*y)' to 'a*b*(x+y)'.

Definition at line 2862 of file normal.cpp.

References factor(), find_common_factor(), GiNaC::subs_options::no_pattern, r, and GiNaC::ex::subs().

Referenced by GiNaC::power::to_polynomial().

resultant()

ex GiNaC::resultant	(	const ex &	e1,
		const ex &	e2,
		const ex &	s
	)

Resultant of two expressions e1,e2 with respect to symbol s.

Method: Compute determinant of Sylvester matrix of e1,e2,s.

Definition at line 2878 of file normal.cpp.

References GiNaC::ex::coeff(), GiNaC::ex::degree(), GiNaC::ex::expand(), GiNaC::ex::info(), k, GiNaC::ex::ldegree(), m, and GiNaC::info_flags::polynomial.

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [26/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	numeric	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_csrc_cl_N > &::do_print_csrc_cl_N. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

default ctor.

Numerically it initializes to an integer zero.

Definition at line 60 of file numeric.cpp.

References GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, GiNaC::basic::setflag(), and GiNaC::numeric::value.

make_real_float()

static const cln::cl_F GiNaC::make_real_float ( const cln::cl_idecoded_float &  dec )

static

Construct a floating point number from sign, mantissa, and exponent.

Definition at line 269 of file numeric.cpp.

References x.

Referenced by read_real_float().

read_real_float()

static const cln::cl_F GiNaC::read_real_float ( std::istream &  s )

static

Read serialized floating point number.

Definition at line 281 of file numeric.cpp.

References make_real_float(), and x.

Referenced by GiNaC::numeric::read_archive().

GINAC_BIND_UNARCHIVER() [36/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

numeric

)

write_real_float()

static void GiNaC::write_real_float ( std::ostream &  s, const cln::cl_R &  n  )

static

Definition at line 338 of file numeric.cpp.

References n.

Referenced by GiNaC::numeric::archive().

print_real_number()

static void GiNaC::print_real_number ( const print_context &  c, const cln::cl_R &  x  )

static

Helper function to print a real number in a nicer way than is CLN's default.

Instead of printing 42.0L0 this just prints 42.0 to ostream os and instead of 3.99168L7 it prints 3.99168E7. This is fine in GiNaC as long as it only uses cl_LF and no other floating point types that we might want to visibly distinguish from cl_LF.

See also

numeric::print()

Definition at line 397 of file numeric.cpp.

References c, and x.

Referenced by GiNaC::numeric::print_numeric(), and print_real_cl_N().

print_integer_csrc()

static void GiNaC::print_integer_csrc ( const print_context &  c, const cln::cl_I &  x  )

static

Helper function to print integer number in C++ source format.

See also

numeric::print()

Definition at line 426 of file numeric.cpp.

References c, and x.

Referenced by print_real_csrc().

print_real_csrc()

static void GiNaC::print_real_csrc ( const print_context &  c, const cln::cl_R &  x  )

static

Helper function to print real number in C++ source format.

See also

numeric::print()

Definition at line 440 of file numeric.cpp.

References c, denom(), numer(), print_integer_csrc(), and x.

Referenced by GiNaC::numeric::do_print_csrc().

coerce()

template<typename T1 , typename T2 >

static bool GiNaC::coerce ( T1 &  dst, const T2 &  arg  )

inlinestatic

Referenced by print_real_cl_N().

coerce< int, cln::cl_I >()

template<>

bool GiNaC::coerce< int, cln::cl_I > ( int &  dst, const cln::cl_I &  arg  )

inline

Check if CLN integer can be converted into int.

See also

https://www.ginac.de/pipermail/cln-list/2006-October/000248.html

Definition at line 479 of file numeric.cpp.

coerce< unsigned int, cln::cl_I >()

template<>

bool GiNaC::coerce< unsigned int, cln::cl_I > ( unsigned int &  dst, const cln::cl_I &  arg  )

inline

Definition at line 493 of file numeric.cpp.

print_real_cl_N()

static void GiNaC::print_real_cl_N ( const print_context &  c, const cln::cl_R &  x  )

static

Helper function to print real number in C++ source format using cl_N types.

See also

numeric::print()

Definition at line 507 of file numeric.cpp.

References c, coerce(), Digits, print_real_number(), and x.

Referenced by GiNaC::numeric::do_print_csrc_cl_N().

exp()

const numeric GiNaC::exp

(

const numeric &

x

)

Exponential function.

Returns

arbitrary precision numerical exp(x).

Definition at line 1439 of file numeric.cpp.

References x.

Referenced by abs_eval(), abs_power(), Bernoulli_polynomial(), beta_evalf(), GiNaC::Eisenstein_h_kernel::coefficient_an(), csgn_power(), GiNaC::power::do_print_csrc(), exp_conjugate(), exp_deriv(), exp_eval(), exp_evalf(), exp_expand(), exp_imag_part(), exp_power(), exp_real_part(), generalised_Bernoulli_number(), GiNaC::Kronecker_dtau_kernel::get_numerical_value(), GiNaC::power::imag_part(), log_eval(), print_sym_pow(), GiNaC::power::real_part(), replace_with_symbol(), GiNaC::power::series(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), and tgamma().

log()

const numeric GiNaC::log

(

const numeric &

x

)

Natural logarithm.

Parameters

x	complex number

Returns

arbitrary precision numerical log(x).

Exceptions

pole_error("log()

logarithmic pole",0)

Definition at line 1450 of file numeric.cpp.

References GiNaC::ex::is_zero(), and x.

Referenced by atan_series(), atanh_series(), GiNaC::power::derivative(), GiNaC::integral::eval_integ(), exp_eval(), G2_eval(), G2_evalf(), G3_eval(), G3_evalf(), H_eval(), GiNaC::power::imag_part(), lgamma(), lgamma_eval(), lgamma_series(), Li2_deriv(), Li2_eval(), Li2_series(), Li_eval(), log_conjugate(), log_eval(), log_evalf(), log_expand(), log_real_part(), log_series(), psi1_eval(), psi2_eval(), GiNaC::power::real_part(), S_eval(), and GiNaC::power::series().

sin()

const numeric GiNaC::sin

(

const numeric &

x

)

Numeric sine (trigonometric function).

Returns

arbitrary precision numerical sin(x).

Definition at line 1461 of file numeric.cpp.

References x.

Referenced by GiNaC::Eisenstein_h_kernel::coefficient_a0(), cos_deriv(), cos_imag_part(), cosh_imag_part(), exp_imag_part(), GiNaC::power::imag_part(), lgamma(), sin_conjugate(), sin_eval(), sin_evalf(), sin_real_part(), sinh_eval(), sinh_imag_part(), and tan_series().

cos()

const numeric GiNaC::cos

(

const numeric &

x

)

Numeric cosine (trigonometric function).

Returns

arbitrary precision numerical cos(x).

Definition at line 1470 of file numeric.cpp.

References x.

Referenced by GiNaC::Eisenstein_h_kernel::coefficient_a0(), cos_conjugate(), cos_eval(), cos_evalf(), cos_real_part(), cosh_eval(), cosh_real_part(), exp_real_part(), GiNaC::power::real_part(), sin_deriv(), sin_imag_part(), sinh_real_part(), and tan_series().

tan()

const numeric GiNaC::tan

(

const numeric &

x

)

Numeric tangent (trigonometric function).

Returns

arbitrary precision numerical tan(x).

Definition at line 1479 of file numeric.cpp.

References x.

Referenced by tan_conjugate(), tan_deriv(), tan_eval(), tan_evalf(), tan_imag_part(), tan_real_part(), tanh_eval(), tanh_imag_part(), and tanh_real_part().

asin()

const numeric GiNaC::asin

(

const numeric &

x

)

Numeric inverse sine (trigonometric function).

Returns

arbitrary precision numerical asin(x).

Definition at line 1488 of file numeric.cpp.

References x.

Referenced by asin_conjugate(), asin_eval(), asin_evalf(), cos_eval(), sin_eval(), and tan_eval().

acos()

const numeric GiNaC::acos

(

const numeric &

x

)

Numeric inverse cosine (trigonometric function).

Returns

arbitrary precision numerical acos(x).

Definition at line 1497 of file numeric.cpp.

References x.

Referenced by acos_conjugate(), acos_eval(), acos_evalf(), cos_eval(), sin_eval(), and tan_eval().

atan() [1/2]

const numeric GiNaC::atan

(

const numeric &

x

)

Numeric arcustangent.

Parameters

x	complex number

Returns

atan(x)

Exceptions

pole_error("atan()

logarithmic pole",0) if x==I or x==-I.

Definition at line 1508 of file numeric.cpp.

References _num1_p, abs(), GiNaC::numeric::is_equal(), GiNaC::ex::is_zero(), and x.

Referenced by atan2_eval(), atan2_evalf(), atan_conjugate(), atan_eval(), atan_evalf(), atan_series(), cos_eval(), sin_eval(), and tan_eval().

atan() [2/2]

const numeric GiNaC::atan	(	const numeric &	y,
		const numeric &	x
	)

Numeric arcustangent of two arguments, analytically continued in a suitable way.

Parameters

y	complex number
x	complex number

Returns

-I*log((x+I*y)/sqrt(x^2+y^2)), which is equal to atan(y/x) if y and x are both real.

Exceptions

pole_error("atan()

logarithmic pole",0) if y/x==+I or y/x==-I.

Definition at line 1525 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_real(), GiNaC::ex::is_zero(), GiNaC::numeric::is_zero(), GiNaC::numeric::to_cl_N(), and x.

sinh()

const numeric GiNaC::sinh

(

const numeric &

x

)

Numeric hyperbolic sine (trigonometric function).

Returns

arbitrary precision numerical sinh(x).

Definition at line 1554 of file numeric.cpp.

References x.

Referenced by cos_imag_part(), cosh_deriv(), cosh_imag_part(), sin_imag_part(), sinh_conjugate(), sinh_eval(), sinh_evalf(), sinh_real_part(), and tanh_series().

cosh()

const numeric GiNaC::cosh

(

const numeric &

x

)

Numeric hyperbolic cosine (trigonometric function).

Returns

arbitrary precision numerical cosh(x).

Definition at line 1563 of file numeric.cpp.

References x.

Referenced by cos_real_part(), cosh_conjugate(), cosh_eval(), cosh_evalf(), cosh_real_part(), sin_real_part(), sinh_deriv(), sinh_imag_part(), and tanh_series().

tanh()

const numeric GiNaC::tanh

(

const numeric &

x

)

Numeric hyperbolic tangent (trigonometric function).

Returns

arbitrary precision numerical tanh(x).

Definition at line 1572 of file numeric.cpp.

References x.

Referenced by tan_imag_part(), tanh_conjugate(), tanh_deriv(), tanh_eval(), tanh_evalf(), tanh_imag_part(), and tanh_real_part().

asinh()

const numeric GiNaC::asinh

(

const numeric &

x

)

Numeric inverse hyperbolic sine (trigonometric function).

Returns

arbitrary precision numerical asinh(x).

Definition at line 1581 of file numeric.cpp.

References x.

Referenced by asinh_conjugate(), asinh_eval(), asinh_evalf(), cosh_eval(), sinh_eval(), and tanh_eval().

acosh()

const numeric GiNaC::acosh

(

const numeric &

x

)

Numeric inverse hyperbolic cosine (trigonometric function).

Returns

arbitrary precision numerical acosh(x).

Definition at line 1590 of file numeric.cpp.

References x.

Referenced by acosh_conjugate(), acosh_eval(), acosh_evalf(), cosh_eval(), sinh_eval(), and tanh_eval().

atanh()

const numeric GiNaC::atanh

(

const numeric &

x

)

Numeric inverse hyperbolic tangent (trigonometric function).

Returns

arbitrary precision numerical atanh(x).

Definition at line 1599 of file numeric.cpp.

References x.

Referenced by atanh_conjugate(), atanh_eval(), atanh_evalf(), atanh_series(), cosh_eval(), sinh_eval(), and tanh_eval().

Li2_series() [2/2]

static cln::cl_N GiNaC::Li2_series ( const cln::cl_N &  x, const cln::float_format_t &  prec  )

static

Numeric evaluation of Dilogarithm within circle of convergence (unit circle) using a power series.

Definition at line 1633 of file numeric.cpp.

References x.

Li2_projection()

static cln::cl_N GiNaC::Li2_projection ( const cln::cl_N &  x, const cln::float_format_t &  prec  )

static

Folds Li2's argument inside a small rectangle to enhance convergence.

Definition at line 1652 of file numeric.cpp.

References Li2_projection(), Li2_series(), and x.

Referenced by Li2_(), and Li2_projection().

Li2_()

const cln::cl_N GiNaC::Li2_

(

const cln::cl_N &

value

)

Numeric evaluation of Dilogarithm.

The domain is the entire complex plane, the branch cut lies along the positive real axis, starting at 1 and continuous with quadrant IV.

Returns

arbitrary precision numerical Li2(x).

Definition at line 1679 of file numeric.cpp.

References Li2_projection(), and value.

Referenced by Li2().

Li2()

const numeric GiNaC::Li2

(

const numeric &

x

)

Definition at line 1705 of file numeric.cpp.

References _num0_p, Li2_(), and x.

Referenced by Li2_conjugate(), Li2_eval(), Li2_evalf(), and Li2_series().

zeta() [3/3]

const numeric GiNaC::zeta

(

const numeric &

x

)

Numeric evaluation of Riemann's Zeta function.

Currently works only for integer arguments.

Definition at line 1717 of file numeric.cpp.

References x.

guess_precision()

static cln::float_format_t GiNaC::guess_precision ( const cln::cl_N &  x )

static

Definition at line 2024 of file numeric.cpp.

References x.

Referenced by lgamma(), and tgamma().

lgamma() [1/2]

const cln::cl_N GiNaC::lgamma

(

const cln::cl_N &

x

)

The Gamma function.

Use the Lanczos approximation. If the coefficients used here are not sufficiently many or sufficiently accurate, more can be calculated using the program doc/examples/lanczos.cpp. In that case, be sure to read the comments in that file.

Definition at line 2039 of file numeric.cpp.

References GiNaC::lanczos_coeffs::calc_lanczos_A(), GiNaC::lanczos_coeffs::get_order(), guess_precision(), lgamma(), log(), sin(), GiNaC::lanczos_coeffs::sufficiently_accurate(), and x.

Referenced by beta_evalf(), lgamma(), lgamma(), lgamma_conjugate(), lgamma_eval(), lgamma_evalf(), and lgamma_series().

lgamma() [2/2]

const numeric GiNaC::lgamma

(

const numeric &

x

)

Definition at line 2060 of file numeric.cpp.

References lgamma(), and x.

tgamma() [1/2]

const cln::cl_N GiNaC::tgamma

(

const cln::cl_N &

x

)

Definition at line 2067 of file numeric.cpp.

References GiNaC::lanczos_coeffs::calc_lanczos_A(), exp(), GiNaC::lanczos_coeffs::get_order(), guess_precision(), sqrt(), GiNaC::lanczos_coeffs::sufficiently_accurate(), tgamma(), and x.

Referenced by beta_eval(), beta_series(), psi2_eval(), tgamma(), tgamma(), tgamma_conjugate(), tgamma_deriv(), tgamma_eval(), tgamma_evalf(), and tgamma_series().

tgamma() [2/2]

const numeric GiNaC::tgamma

(

const numeric &

x

)

Definition at line 2086 of file numeric.cpp.

References tgamma(), and x.

psi() [3/4]

const numeric GiNaC::psi

(

const numeric &

x

)

The psi function (aka polygamma function).

This is only a stub!

Definition at line 2095 of file numeric.cpp.

psi() [4/4]

const numeric GiNaC::psi	(	const numeric &	n,
		const numeric &	x
	)

The psi functions (aka polygamma functions).

This is only a stub!

Definition at line 2103 of file numeric.cpp.

factorial()

const numeric GiNaC::factorial

(

const numeric &

n

)

Factorial combinatorial function.

Parameters

n	integer argument >= 0

Exceptions

range_error

(argument must be integer >= 0)

Definition at line 2113 of file numeric.cpp.

References n.

Referenced by Bernoulli_polynomial(), factorial_conjugate(), factorial_eval(), factorial_evalf(), factorial_real_part(), G2_eval(), G2_evalf(), G3_eval(), G3_evalf(), generalised_Bernoulli_number(), H_eval(), lgamma_eval(), multinomial_coefficient(), psi2_eval(), psi2_series(), S_eval(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), symm(), tgamma_eval(), and zeta1_eval().

doublefactorial()

const numeric GiNaC::doublefactorial

(

const numeric &

n

)

The double factorial combinatorial function.

(Scarcely used, but still useful in cases, like for exact results of tgamma(n+1/2) for instance.)

Parameters

n	integer argument >= -1

Returns

n!! == n * (n-2) * (n-4) * ... * ({1|2}) with 0!! == (-1)!! == 1

Exceptions

range_error

(argument must be integer >= -1)

Definition at line 2127 of file numeric.cpp.

References _num1_p, _num_1_p, and n.

Referenced by tgamma_eval().

binomial()

const numeric GiNaC::binomial	(	const numeric &	n,
		const numeric &	k
	)

The Binomial coefficients.

It computes the binomial coefficients. For integer n and k and positive n this is the number of ways of choosing k objects from n distinct objects. If n is a negative integer, the formula binomial(n,k) == (-1)^k*binomial(k-n-1,k) (if k>=0) binomial(n,k) == (-1)^(n-k)*binomial(-k-1,n-k) (otherwise) is used to compute the result.

Definition at line 2145 of file numeric.cpp.

References _num0_p, _num1_p, _num_1_p, binomial(), k, n, and GiNaC::numeric::power().

Referenced by binomial(), binomial_conjugate(), binomial_eval(), binomial_evalf(), binomial_real_part(), binomial_sym(), GiNaC::power::expand_add(), GiNaC::power::imag_part(), and GiNaC::power::real_part().

bernoulli()

const numeric GiNaC::bernoulli

(

const numeric &

nn

)

Bernoulli number.

The nth Bernoulli number is the coefficient of x^n/n! in the expansion of the function x/(e^x-1).

Returns

the nth Bernoulli number (a rational number).

Exceptions

range_error

(argument must be integer >= 0)

Definition at line 2171 of file numeric.cpp.

References _num1_p, c, GiNaC::numeric::is_integer(), GiNaC::numeric::is_negative(), k, n, and GiNaC::numeric::to_int().

Referenced by GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), and zeta1_eval().

fibonacci()

const numeric GiNaC::fibonacci

(

const numeric &

n

)

Fibonacci number.

The nth Fibonacci number F(n) is defined by the recurrence formula F(n)==F(n-1)+F(n-2) with F(0)==0 and F(1)==1.

Parameters

n	an integer

Returns

the nth Fibonacci number F(n) (an integer number)

Exceptions

range_error

(argument must be an integer)

Definition at line 2263 of file numeric.cpp.

References _num0_p, fibonacci(), m, and n.

Referenced by fibonacci().

abs()

const numeric GiNaC::abs

(

const numeric &

x

)

Absolute value.

Definition at line 2320 of file numeric.cpp.

References x.

Referenced by abs_conjugate(), abs_eval(), abs_evalf(), abs_expand(), abs_expl_derivative(), abs_power(), abs_real_part(), adaptivesimpson(), atan(), atan_series(), atanh_series(), GiNaC::power::eval(), generalised_Bernoulli_number(), GiNaC::power::imag_part(), GiNaC::mul::integer_content(), GiNaC::numeric::integer_content(), is_discriminant_of_quadratic_number_field(), log_real_part(), GiNaC::add::max_coefficient(), GiNaC::mul::max_coefficient(), GiNaC::numeric::max_coefficient(), GiNaC::matrix::pivot(), GiNaC::power::real_part(), tgamma_eval(), GiNaC::ex::unitcontprim(), and zeta1_eval().

mod()

const numeric GiNaC::mod	(	const numeric &	a,
		const numeric &	b
	)

Modulus (in positive representation).

In general, mod(a,b) has the sign of b or is zero, and rem(a,b) has the sign of a or is zero. This is different from Maple's modp, where the sign of b is ignored. It is in agreement with Mathematica's Mod.

Returns

a mod b in the range [0,abs(b)-1] with sign of b if both are integer, 0 otherwise.

Definition at line 2333 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), and GiNaC::numeric::to_cl_N().

Referenced by GiNaC::Eisenstein_h_kernel::coefficient_a0(), GiNaC::Eisenstein_h_kernel::coefficient_an(), cos_eval(), exp_eval(), is_discriminant_of_quadratic_number_field(), sin_eval(), and tan_eval().

smod()

const numeric GiNaC::smod	(	const numeric &	a_,
		const numeric &	b_
	)

Modulus (in symmetric representation).

Returns

a mod b in the range [-iquo(abs(b),2), iquo(abs(b),2)].

Definition at line 2346 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), m, and GiNaC::numeric::to_cl_N().

Referenced by GiNaC::add::smod(), GiNaC::mul::smod(), and GiNaC::numeric::smod().

irem() [1/2]

const numeric GiNaC::irem	(	const numeric &	a,
		const numeric &	b
	)

Numeric integer remainder.

Equivalent to Maple's irem(a,b) as far as sign conventions are concerned. In general, mod(a,b) has the sign of b or is zero, and irem(a,b) has the sign of a or is zero.

Returns

remainder of a/b if both are integer, 0 otherwise.

Exceptions

overflow_error

(division by zero) if b is zero.

Definition at line 2368 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), GiNaC::numeric::is_zero(), and GiNaC::numeric::to_cl_N().

Referenced by GiNaC::Eisenstein_h_kernel::coefficient_a0(), GiNaC::Eisenstein_h_kernel::coefficient_an(), and ifactor().

irem() [2/2]

const numeric GiNaC::irem	(	const numeric &	a,
		const numeric &	b,
		numeric &	q
	)

Numeric integer remainder.

Equivalent to Maple's irem(a,b,'q') it obeyes the relation irem(a,b,q) == a - q*b. In general, mod(a,b) has the sign of b or is zero, and irem(a,b) has the sign of a or is zero.

Returns

remainder of a/b and quotient stored in q if both are integer, 0 otherwise.

Exceptions

overflow_error

(division by zero) if b is zero.

Definition at line 2388 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), GiNaC::numeric::is_zero(), and GiNaC::numeric::to_cl_N().

iquo() [1/2]

const numeric GiNaC::iquo	(	const numeric &	a,
		const numeric &	b
	)

Numeric integer quotient.

Equivalent to Maple's iquo as far as sign conventions are concerned.

Returns

truncated quotient of a/b if both are integer, 0 otherwise.

Exceptions

overflow_error

(division by zero) if b is zero.

Definition at line 2409 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), GiNaC::numeric::is_zero(), and GiNaC::numeric::to_cl_N().

Referenced by GiNaC::power::eval(), and heur_gcd_z().

iquo() [2/2]

const numeric GiNaC::iquo	(	const numeric &	a,
		const numeric &	b,
		numeric &	r
	)

Numeric integer quotient.

Equivalent to Maple's iquo(a,b,'r') it obeyes the relation r == a - iquo(a,b,r)*b.

Returns

truncated quotient of a/b and remainder stored in r if both are integer, 0 otherwise.

Exceptions

overflow_error

(division by zero) if b is zero.

Definition at line 2428 of file numeric.cpp.

References _num0_p, GiNaC::numeric::is_integer(), GiNaC::numeric::is_zero(), r, and GiNaC::numeric::to_cl_N().

gcd() [2/2]

const numeric GiNaC::gcd	(	const numeric &	a,
		const numeric &	b
	)

Greatest Common Divisor.

Returns

The GCD of two numbers if both are integer, a numerical 1 if they are not.

Definition at line 2448 of file numeric.cpp.

References _num1_p, GiNaC::numeric::is_integer(), and GiNaC::numeric::to_cl_N().

lcm() [2/2]

const numeric GiNaC::lcm	(	const numeric &	a,
		const numeric &	b
	)

Least Common Multiple.

Returns

The LCM of two numbers if both are integer, the product of those two numbers if they are not.

Definition at line 2462 of file numeric.cpp.

References GiNaC::numeric::is_integer(), GiNaC::numeric::mul(), and GiNaC::numeric::to_cl_N().

sqrt() [1/2]

const numeric GiNaC::sqrt

(

const numeric &

x

)

Numeric square root.

If possible, sqrt(x) should respect squares of exact numbers, i.e. sqrt(4) should return integer 2.

Parameters

x	numeric argument

Returns

square root of x. Branch cut along negative real axis, the negative real axis itself where imag(x)==0 and real(x)<0 belongs to the upper part where imag(x)>0.

Definition at line 2480 of file numeric.cpp.

References x.

Referenced by cos_eval(), cosh_eval(), EllipticE_evalf(), EllipticK_evalf(), GiNaC::su3f::eval_indexed(), GiNaC::su3d::eval_indexed(), sin_eval(), sinh_eval(), tan_eval(), tanh_eval(), tgamma(), and tgamma_eval().

isqrt()

const numeric GiNaC::isqrt

(

const numeric &

x

)

Integer numeric square root.

Definition at line 2487 of file numeric.cpp.

References _num0_p, and x.

Referenced by heur_gcd_z().

PiEvalf()

ex GiNaC::PiEvalf

(

)

Floating point evaluation of Archimedes' constant Pi.

Definition at line 2499 of file numeric.cpp.

EulerEvalf()

ex GiNaC::EulerEvalf

(

)

Floating point evaluation of Euler's constant gamma.

Definition at line 2506 of file numeric.cpp.

CatalanEvalf()

ex GiNaC::CatalanEvalf

(

)

Floating point evaluation of Catalan's constant.

Definition at line 2513 of file numeric.cpp.

operator<<() [6/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const _numeric_digits &	e
	)

Definition at line 2574 of file numeric.cpp.

References GiNaC::_numeric_digits::print().

GINAC_DECLARE_UNARCHIVER() [38/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

numeric

)

pow() [1/3]

const numeric GiNaC::pow ( const numeric &  x, const numeric &  y  )

inline

Definition at line 251 of file numeric.h.

References x.

Referenced by abs_eval(), abs_power(), GiNaC::mul::algebraic_subs_mul(), beta_eval(), GiNaC::Eisenstein_h_kernel::coefficient_an(), GiNaC::basic::collect(), GiNaC::mul::combine_ex_with_coeff_to_pair(), GiNaC::mul::combine_pair_with_coeff_to_pair(), GiNaC::pseries::convert_to_poly(), GiNaC::mul::derivative(), GiNaC::power::derivative(), divide(), divide_in_z(), EllipticE_series(), EllipticK_series(), GiNaC::power::eval(), GiNaC::power::evalm(), GiNaC::power::expand(), GiNaC::power::expand_add(), factor(), find_common_factor(), G2_eval(), G2_evalf(), G3_eval(), G3_evalf(), gcd(), gcd_pf_pow(), gcd_pf_pow_pow(), GiNaC::Kronecker_dtau_kernel::get_numerical_value(), GiNaC::Kronecker_dz_kernel::get_numerical_value(), H_eval(), GiNaC::power::imag_part(), interpolate(), kronecker_symbol(), GiNaC::integration_kernel::Laurent_series(), lcmcoeff(), Li2_series(), Li_eval(), Li_series(), log_series(), multiply_lcm(), GiNaC::power::normal(), GiNaC::pseries::op(), Order_power(), GiNaC::pseries::power_const(), prem(), GiNaC::pseries::print_series(), psi1_eval(), psi2_eval(), GiNaC::Eisenstein_h_kernel::q_expansion_modular_form(), quo(), GiNaC::power::real_part(), rem(), replace_with_symbol(), S_eval(), S_series(), GiNaC::modular_form_kernel::series(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), sprem(), sqrfree_parfrac(), sr_gcd(), GiNaC::power::subs(), tgamma_eval(), GiNaC::power::to_polynomial(), GiNaC::power::to_rational(), and zeta1_eval().

inverse() [3/3]

const numeric GiNaC::inverse ( const numeric &  x )

inline

Definition at line 254 of file numeric.h.

References x.

step()

numeric GiNaC::step ( const numeric &  x )

inline

Definition at line 257 of file numeric.h.

References x.

Referenced by abs_eval(), H_eval(), step_conjugate(), step_eval(), step_evalf(), step_real_part(), and step_series().

csgn()

int GiNaC::csgn ( const numeric &  x )

inline

Definition at line 260 of file numeric.h.

References x.

Referenced by atan_series(), atanh_series(), csgn_conjugate(), csgn_eval(), csgn_evalf(), csgn_power(), csgn_real_part(), csgn_series(), eta_eval(), eta_evalf(), and log_series().

is_zero() [2/2]

bool GiNaC::is_zero ( const numeric &  x )

inline

Definition at line 263 of file numeric.h.

References GiNaC::ex::is_zero(), and x.

is_positive()

bool GiNaC::is_positive ( const numeric &  x )

inline

Definition at line 266 of file numeric.h.

References x.

Referenced by beta_eval().

is_negative()

bool GiNaC::is_negative ( const numeric &  x )

inline

Definition at line 269 of file numeric.h.

References x.

Referenced by GiNaC::power::do_print_latex(), GiNaC::power::eval(), and frac_cancel().

is_integer()

bool GiNaC::is_integer ( const numeric &  x )

inline

Definition at line 272 of file numeric.h.

References x.

Referenced by beta_eval(), binomial_eval(), GiNaC::power::coeff(), GiNaC::power::degree(), GiNaC::power::expand(), GiNaC::power::ldegree(), GiNaC::pseries::power_const(), psi1_eval(), psi2_eval(), replace_with_symbol(), and GiNaC::power::series().

is_pos_integer()

bool GiNaC::is_pos_integer ( const numeric &  x )

inline

Definition at line 275 of file numeric.h.

References x.

Referenced by GiNaC::power::expand_add(), and GiNaC::power::expand_add_2().

is_nonneg_integer()

bool GiNaC::is_nonneg_integer ( const numeric &  x )

inline

Definition at line 278 of file numeric.h.

References x.

is_even()

bool GiNaC::is_even ( const numeric &  x )

inline

Definition at line 281 of file numeric.h.

References x.

Referenced by abs_power(), and GiNaC::Kronecker_dz_kernel::series_coeff_impl().

is_odd()

bool GiNaC::is_odd ( const numeric &  x )

inline

Definition at line 284 of file numeric.h.

References x.

Referenced by csgn_power().

is_prime()

bool GiNaC::is_prime ( const numeric &  x )

inline

Definition at line 287 of file numeric.h.

References x.

is_rational()

bool GiNaC::is_rational ( const numeric &  x )

inline

Definition at line 290 of file numeric.h.

References x.

Referenced by beta_eval(), lgamma_eval(), replace_with_symbol(), and tgamma_eval().

is_real()

bool GiNaC::is_real ( const numeric &  x )

inline

Definition at line 293 of file numeric.h.

References x.

Referenced by beta_eval(), fsolve(), G2_eval(), G2_evalf(), and Li2_series().

is_cinteger()

bool GiNaC::is_cinteger ( const numeric &  x )

inline

Definition at line 296 of file numeric.h.

References x.

is_crational()

bool GiNaC::is_crational ( const numeric &  x )

inline

Definition at line 299 of file numeric.h.

References x.

to_int()

int GiNaC::to_int ( const numeric &  x )

inline

Definition at line 302 of file numeric.h.

References x.

Referenced by GiNaC::basic::operator[](), GiNaC::basic::operator[](), GiNaC::pseries::power_const(), S_eval(), GiNaC::power::series(), and sqrfree_parfrac().

to_long()

long GiNaC::to_long ( const numeric &  x )

inline

Definition at line 305 of file numeric.h.

References x.

to_double()

double GiNaC::to_double ( const numeric &  x )

inline

Definition at line 308 of file numeric.h.

References x.

real()

const numeric GiNaC::real ( const numeric &  x )

inline

Definition at line 311 of file numeric.h.

References x.

Referenced by cosh_eval(), sinh_eval(), and tanh_eval().

imag()

const numeric GiNaC::imag ( const numeric &  x )

inline

Definition at line 314 of file numeric.h.

References x.

Referenced by eta_eval(), eta_evalf(), G2_eval(), and G2_evalf().

numer() [2/2]

const numeric GiNaC::numer ( const numeric &  x )

inline

Definition at line 317 of file numeric.h.

References GiNaC::ex::numer(), and x.

denom() [2/2]

const numeric GiNaC::denom ( const numeric &  x )

inline

Definition at line 320 of file numeric.h.

References GiNaC::ex::denom(), and x.

exadd()

static const ex GiNaC::exadd ( const ex &  lh, const ex &  rh  )

inlinestatic

Used internally by operator+() to add two ex objects.

Definition at line 36 of file operators.cpp.

Referenced by operator+(), operator++(), operator++(), operator+=(), operator-(), operator--(), operator--(), and operator-=().

exmul()

static const ex GiNaC::exmul ( const ex &  lh, const ex &  rh  )

inlinestatic

Used internally by operator*() to multiply two ex objects.

Definition at line 42 of file operators.cpp.

References GiNaC::return_types::commutative, and GiNaC::ex::return_type().

Referenced by operator*(), operator*=(), operator/(), and operator/=().

exminus()

static const ex GiNaC::exminus ( const ex &  lh )

inlinestatic

Used internally by operator-() and friends to change the sign of an argument.

Definition at line 56 of file operators.cpp.

References _ex_1.

Referenced by operator-(), operator-(), and operator-=().

operator+() [1/4]

const ex GiNaC::operator+	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 63 of file operators.cpp.

References exadd().

operator-() [1/4]

const ex GiNaC::operator-	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 68 of file operators.cpp.

References exadd(), and exminus().

operator*() [1/2]

const ex GiNaC::operator*	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 73 of file operators.cpp.

References exmul().

operator/() [1/2]

const ex GiNaC::operator/	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 78 of file operators.cpp.

References _ex_1, and exmul().

operator+() [2/4]

const numeric GiNaC::operator+	(	const numeric &	lh,
		const numeric &	rh
	)

Definition at line 86 of file operators.cpp.

References GiNaC::numeric::add().

operator-() [2/4]

const numeric GiNaC::operator-	(	const numeric &	lh,
		const numeric &	rh
	)

Definition at line 91 of file operators.cpp.

References GiNaC::numeric::sub().

operator*() [2/2]

const numeric GiNaC::operator*	(	const numeric &	lh,
		const numeric &	rh
	)

Definition at line 96 of file operators.cpp.

References GiNaC::numeric::mul().

operator/() [2/2]

const numeric GiNaC::operator/	(	const numeric &	lh,
		const numeric &	rh
	)

Definition at line 101 of file operators.cpp.

References GiNaC::numeric::div().

operator+=() [1/2]

ex & GiNaC::operator+=	(	ex &	lh,
		const ex &	rh
	)

Definition at line 109 of file operators.cpp.

References exadd().

operator-=() [1/2]

ex & GiNaC::operator-=	(	ex &	lh,
		const ex &	rh
	)

Definition at line 114 of file operators.cpp.

References exadd(), and exminus().

operator*=() [1/2]

ex & GiNaC::operator*=	(	ex &	lh,
		const ex &	rh
	)

Definition at line 119 of file operators.cpp.

References exmul().

operator/=() [1/2]

ex & GiNaC::operator/=	(	ex &	lh,
		const ex &	rh
	)

Definition at line 124 of file operators.cpp.

References _ex_1, and exmul().

operator+=() [2/2]

numeric & GiNaC::operator+=	(	numeric &	lh,
		const numeric &	rh
	)

Definition at line 132 of file operators.cpp.

References GiNaC::numeric::add().

operator-=() [2/2]

numeric & GiNaC::operator-=	(	numeric &	lh,
		const numeric &	rh
	)

Definition at line 138 of file operators.cpp.

References GiNaC::numeric::sub().

operator*=() [2/2]

numeric & GiNaC::operator*=	(	numeric &	lh,
		const numeric &	rh
	)

Definition at line 144 of file operators.cpp.

References GiNaC::numeric::mul().

operator/=() [2/2]

numeric & GiNaC::operator/=	(	numeric &	lh,
		const numeric &	rh
	)

Definition at line 150 of file operators.cpp.

References GiNaC::numeric::div().

operator+() [3/4]

const ex GiNaC::operator+

(

const ex &

lh

)

Definition at line 159 of file operators.cpp.

operator-() [3/4]

const ex GiNaC::operator-

(

const ex &

lh

)

Definition at line 164 of file operators.cpp.

References exminus().

operator+() [4/4]

const numeric GiNaC::operator+

(

const numeric &

lh

)

Definition at line 169 of file operators.cpp.

operator-() [4/4]

const numeric GiNaC::operator-

(

const numeric &

lh

)

Definition at line 174 of file operators.cpp.

References _num_1_p, and GiNaC::numeric::mul().

operator++() [1/4]

ex & GiNaC::operator++

(

ex &

rh

)

Expression prefix increment.

Adds 1 and returns incremented ex.

Definition at line 183 of file operators.cpp.

References _ex1, and exadd().

operator--() [1/4]

ex & GiNaC::operator--

(

ex &

rh

)

Expression prefix decrement.

Subtracts 1 and returns decremented ex.

Definition at line 189 of file operators.cpp.

References _ex_1, and exadd().

operator++() [2/4]

const ex GiNaC::operator++	(	ex &	lh,
		int
	)

Expression postfix increment.

Returns the ex and leaves the original incremented by 1.

Definition at line 196 of file operators.cpp.

References _ex1, and exadd().

operator--() [2/4]

const ex GiNaC::operator--	(	ex &	lh,
		int
	)

Expression postfix decrement.

Returns the ex and leaves the original decremented by 1.

Definition at line 205 of file operators.cpp.

References _ex_1, and exadd().

operator++() [3/4]

numeric & GiNaC::operator++

(

numeric &

rh

)

Numeric prefix increment.

Adds 1 and returns incremented number.

Definition at line 213 of file operators.cpp.

References _num1_p, and GiNaC::numeric::add().

operator--() [3/4]

numeric & GiNaC::operator--

(

numeric &

rh

)

Numeric prefix decrement.

Subtracts 1 and returns decremented number.

Definition at line 220 of file operators.cpp.

References _num_1_p, and GiNaC::numeric::add().

operator++() [4/4]

const numeric GiNaC::operator++	(	numeric &	lh,
		int
	)

Numeric postfix increment.

Returns the number and leaves the original incremented by 1.

Definition at line 228 of file operators.cpp.

References _num1_p, and GiNaC::numeric::add().

operator--() [4/4]

const numeric GiNaC::operator--	(	numeric &	lh,
		int
	)

Numeric postfix decrement.

Returns the number and leaves the original decremented by 1.

Definition at line 237 of file operators.cpp.

References _num_1_p, and GiNaC::numeric::add().

operator==()

const relational GiNaC::operator==	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 246 of file operators.cpp.

References GiNaC::relational::equal.

operator!=()

const relational GiNaC::operator!=	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 251 of file operators.cpp.

References GiNaC::relational::not_equal.

operator<()

const relational GiNaC::operator<	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 256 of file operators.cpp.

References GiNaC::relational::less.

operator<=()

const relational GiNaC::operator<=	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 261 of file operators.cpp.

References GiNaC::relational::less_or_equal.

operator>()

const relational GiNaC::operator>	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 266 of file operators.cpp.

References GiNaC::relational::greater.

operator>=()

const relational GiNaC::operator>=	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 271 of file operators.cpp.

References GiNaC::relational::greater_or_equal.

my_ios_index()

static int GiNaC::my_ios_index ( )

static

Definition at line 278 of file operators.cpp.

Referenced by get_print_context(), and set_print_context().

my_ios_callback()

static void GiNaC::my_ios_callback ( std::ios_base::event  ev, std::ios_base &  s, int  i  )

static

Definition at line 285 of file operators.cpp.

Referenced by set_print_context().

get_print_context()

static print_context * GiNaC::get_print_context ( std::ios_base &  s )

inlinestatic

Definition at line 301 of file operators.cpp.

References my_ios_index().

Referenced by get_print_options(), operator<<(), operator<<(), operator<<(), operator<<(), and set_print_options().

set_print_context()

static void GiNaC::set_print_context ( std::ios_base &  s, const print_context &  c  )

static

Definition at line 307 of file operators.cpp.

References c, callback_registered, my_ios_callback(), my_ios_index(), options, and GiNaC::print_context::options.

Referenced by csrc(), csrc_cl_N(), csrc_double(), csrc_float(), dflt(), latex(), python(), python_repr(), set_print_options(), and tree().

get_print_options()

static unsigned GiNaC::get_print_options ( std::ios_base &  s )

inlinestatic

Definition at line 324 of file operators.cpp.

References get_print_context(), and GiNaC::print_context::options.

Referenced by index_dimensions(), and no_index_dimensions().

set_print_options()

static void GiNaC::set_print_options ( std::ostream &  s, unsigned  options  )

static

Definition at line 331 of file operators.cpp.

References get_print_context(), options, GiNaC::print_context::options, and set_print_context().

Referenced by dflt(), index_dimensions(), and no_index_dimensions().

operator<<() [7/16]

std::ostream & GiNaC::operator<<	(	std::ostream &	os,
		const ex &	e
	)

Definition at line 340 of file operators.cpp.

References get_print_context(), and GiNaC::ex::print().

operator>>() [3/3]

std::istream & GiNaC::operator>>	(	std::istream &	is,
		ex &	e
	)

Definition at line 436 of file operators.cpp.

dflt()

std::ostream & GiNaC::dflt

(

std::ostream &

os

)

Definition at line 441 of file operators.cpp.

References set_print_context(), and set_print_options().

latex()

std::ostream & GiNaC::latex

(

std::ostream &

os

)

Definition at line 448 of file operators.cpp.

References set_print_context().

python()

std::ostream & GiNaC::python

(

std::ostream &

os

)

Definition at line 454 of file operators.cpp.

References set_print_context().

python_repr()

std::ostream & GiNaC::python_repr

(

std::ostream &

os

)

Definition at line 460 of file operators.cpp.

References set_print_context().

tree()

std::ostream & GiNaC::tree

(

std::ostream &

os

)

Definition at line 466 of file operators.cpp.

References set_print_context().

Referenced by GiNaC::class_info< OPT >::dump_hierarchy().

csrc()

std::ostream & GiNaC::csrc

(

std::ostream &

os

)

Definition at line 472 of file operators.cpp.

References set_print_context().

csrc_float()

std::ostream & GiNaC::csrc_float

(

std::ostream &

os

)

Definition at line 478 of file operators.cpp.

References set_print_context().

csrc_double()

std::ostream & GiNaC::csrc_double

(

std::ostream &

os

)

Definition at line 484 of file operators.cpp.

References set_print_context().

csrc_cl_N()

std::ostream & GiNaC::csrc_cl_N

(

std::ostream &

os

)

Definition at line 490 of file operators.cpp.

References set_print_context().

index_dimensions()

std::ostream & GiNaC::index_dimensions

(

std::ostream &

os

)

Definition at line 496 of file operators.cpp.

References get_print_options(), GiNaC::print_options::print_index_dimensions, and set_print_options().

no_index_dimensions()

std::ostream & GiNaC::no_index_dimensions

(

std::ostream &

os

)

Definition at line 502 of file operators.cpp.

References get_print_options(), GiNaC::print_options::print_index_dimensions, and set_print_options().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [27/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	power	,
		basic	,
		print_func< print_dflt > &::do_print_dflt. print_func< print_latex > &::do_print_latex. print_func< print_csrc > &::do_print_csrc. print_func< print_python > &::do_print_python. print_func< print_python_repr > &::do_print_python_repr. print_func< print_csrc_cl_N > &::do_print_csrc_cl_N
	)

Definition at line 48 of file power.cpp.

print_sym_pow()

static void GiNaC::print_sym_pow ( const print_context &  c, const symbol &  x, int  exp  )

static

Definition at line 139 of file power.cpp.

References c, exp(), GiNaC::ex::print(), print_sym_pow(), and x.

Referenced by GiNaC::power::do_print_csrc(), and print_sym_pow().

GINAC_BIND_UNARCHIVER() [37/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

power

)

GINAC_DECLARE_UNARCHIVER() [39/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

power

)

pow() [2/3]

ex GiNaC::pow ( const ex &  b, const ex &  e  )

inline

Symbolic exponentiation.

Returns a power-object as a new expression.

Parameters

b	the basis expression
e	the exponent expression

Definition at line 116 of file power.h.

pow() [3/3]

template<typename T1 , typename T2 >

ex GiNaC::pow ( const T1 &  b, const T2 &  e  )

inline

Definition at line 121 of file power.h.

sqrt() [2/2]

ex GiNaC::sqrt ( const ex &  a )

inline

Square root expression.

Returns a power-object with exponent 1/2.

Definition at line 127 of file power.h.

References _ex1_2.

is_a() [3/3]

template<class T >

bool GiNaC::is_a ( const print_context &  obj )

inline

Check if obj is a T, including base classes.

Definition at line 189 of file print.h.

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [28/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	pseries	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree. print_func< print_python > &::do_print_python. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 43 of file pseries.cpp.

GINAC_BIND_UNARCHIVER() [38/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

pseries

)

GINAC_DECLARE_UNARCHIVER() [40/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

pseries

)

series_to_poly()

ex GiNaC::series_to_poly ( const ex &  e )

inline

Convert the pseries object embedded in an expression to an ordinary polynomial in the expansion variable.

The result is undefined if the expression does not contain a pseries object at its top level.

Parameters

e	expression

Returns

polynomial expression

See also

is_a<>

pseries::convert_to_poly

Definition at line 136 of file pseries.h.

Referenced by Bernoulli_polynomial(), generalised_Bernoulli_number(), GiNaC::modular_form_kernel::is_numeric(), and GiNaC::modular_form_kernel::Laurent_series().

is_terminating()

bool GiNaC::is_terminating ( const pseries &  s )

inline

Definition at line 141 of file pseries.h.

References GiNaC::pseries::is_terminating().

make_return_type_t()

template<typename T >

return_type_t GiNaC::make_return_type_t ( const unsigned  rl = 0 )

inline

Definition at line 70 of file registrar.h.

References GiNaC::return_type_t::rl, and GiNaC::return_type_t::tinfo.

set_print_func() [1/2]

template<class Alg , class Ctx , class T , class C >

void GiNaC::set_print_func ( void   fconst T &, const C &c, unsigned )

extern

Add or replace a print method.

Definition at line 195 of file registrar.h.

References GiNaC::class_info< OPT >::options, and options.

set_print_func() [2/2]

template<class Alg , class Ctx , class T , class C >

void GiNaC::set_print_func ( void(T::*)(const C &, unsigned)  f )

extern

Add or replace a print method.

Definition at line 202 of file registrar.h.

References options.

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [29/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	relational	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 34 of file relational.cpp.

GINAC_BIND_UNARCHIVER() [39/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

relational

)

print_operator()

static void GiNaC::print_operator ( const print_context &  c, relational::operators  o  )

static

Definition at line 84 of file relational.cpp.

References c, GiNaC::relational::equal, GiNaC::relational::greater, GiNaC::relational::greater_or_equal, GiNaC::relational::less, GiNaC::relational::less_or_equal, and GiNaC::relational::not_equal.

Referenced by GiNaC::relational::do_print(), and GiNaC::relational::do_print_python_repr().

GINAC_DECLARE_UNARCHIVER() [41/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

relational

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [30/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	symbol	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_latex > &::do_print_latex. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 36 of file symbol.cpp.

References GiNaC::status_flags::evaluated, and GiNaC::status_flags::expanded.

get_default_TeX_name()

static const std::string & GiNaC::get_default_TeX_name ( const std::string &  name )

static

Return default TeX name for symbol.

This recognizes some greek letters.

Definition at line 297 of file symbol.cpp.

Referenced by GiNaC::symbol::do_print_latex(), and GiNaC::symbol::get_TeX_name().

GINAC_BIND_UNARCHIVER() [40/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

symbol

)

GINAC_BIND_UNARCHIVER() [41/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

realsymbol

)

GINAC_BIND_UNARCHIVER() [42/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

possymbol

)

GINAC_DECLARE_UNARCHIVER() [42/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

symbol

)

GINAC_DECLARE_UNARCHIVER() [43/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

realsymbol

)

GINAC_DECLARE_UNARCHIVER() [44/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

possymbol

)

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [31/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	symmetry	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree
	)

Definition at line 38 of file symmetry.cpp.

References GiNaC::status_flags::evaluated, and GiNaC::status_flags::expanded.

GINAC_BIND_UNARCHIVER() [43/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

symmetry

)

index0()

static const symmetry & GiNaC::index0 ( )

static

Definition at line 325 of file symmetry.cpp.

Referenced by antisymmetric2(), antisymmetric3(), antisymmetric4(), symmetric2(), symmetric3(), and symmetric4().

index1()

static const symmetry & GiNaC::index1 ( )

static

Definition at line 331 of file symmetry.cpp.

Referenced by antisymmetric2(), antisymmetric3(), antisymmetric4(), symmetric2(), symmetric3(), and symmetric4().

index2()

static const symmetry & GiNaC::index2 ( )

static

Definition at line 337 of file symmetry.cpp.

Referenced by antisymmetric3(), antisymmetric4(), symmetric3(), and symmetric4().

index3()

static const symmetry & GiNaC::index3 ( )

static

Definition at line 343 of file symmetry.cpp.

Referenced by antisymmetric4(), and symmetric4().

not_symmetric()

const symmetry & GiNaC::not_symmetric

(

)

Definition at line 349 of file symmetry.cpp.

Referenced by GiNaC::indexed::indexed(), and GiNaC::indexed::read_archive().

symmetric2()

const symmetry & GiNaC::symmetric2

(

)

Definition at line 355 of file symmetry.cpp.

References index0(), index1(), and GiNaC::symmetry::symmetric.

Referenced by delta_tensor(), GiNaC::clifford::get_metric(), lorentz_g(), and metric_tensor().

symmetric3()

const symmetry & GiNaC::symmetric3

(

)

Definition at line 361 of file symmetry.cpp.

References index0(), index1(), index2(), and GiNaC::symmetry::symmetric.

Referenced by color_d().

symmetric4()

const symmetry & GiNaC::symmetric4

(

)

Definition at line 367 of file symmetry.cpp.

References index0(), index1(), index2(), index3(), and GiNaC::symmetry::symmetric.

antisymmetric2()

const symmetry & GiNaC::antisymmetric2

(

)

Definition at line 373 of file symmetry.cpp.

References GiNaC::symmetry::antisymmetric, index0(), and index1().

Referenced by epsilon_tensor(), and spinor_metric().

antisymmetric3()

const symmetry & GiNaC::antisymmetric3

(

)

Definition at line 379 of file symmetry.cpp.

References GiNaC::symmetry::antisymmetric, index0(), index1(), and index2().

Referenced by color_f(), and epsilon_tensor().

antisymmetric4()

const symmetry & GiNaC::antisymmetric4

(

)

Definition at line 385 of file symmetry.cpp.

References GiNaC::symmetry::antisymmetric, index0(), index1(), index2(), and index3().

Referenced by lorentz_eps().

canonicalize()

int GiNaC::canonicalize	(	exvector::iterator	v,
		const symmetry &	symm
	)

Canonicalize the order of elements of an expression vector, according to the symmetry properties defined in a symmetry tree.

Parameters

v	Start of expression vector
symm	Root node of symmetry tree

Returns

the overall sign introduced by the reordering (+1, -1 or 0) or numeric_limits<int>::max() if nothing changed

Definition at line 437 of file symmetry.cpp.

Referenced by GiNaC::function::eval(), and GiNaC::indexed::eval().

symm()

static ex GiNaC::symm ( const ex &  e, exvector::const_iterator  first, exvector::const_iterator  last, bool  asymmetric  )

static

Definition at line 484 of file symmetry.cpp.

References GiNaC::container< C >::append(), factorial(), last, GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, GiNaC::container< C >::op(), permutation_sign(), and GiNaC::ex::subs().

Referenced by antisymmetrize(), GiNaC::ex::antisymmetrize(), GiNaC::indexed::read_archive(), symmetrize(), and GiNaC::ex::symmetrize().

symmetrize() [3/4]

ex GiNaC::symmetrize	(	const ex &	e,
		exvector::const_iterator	first,
		exvector::const_iterator	last
	)

Symmetrize expression over a set of objects (symbols, indices).

Definition at line 523 of file symmetry.cpp.

References last, and symm().

antisymmetrize() [3/4]

ex GiNaC::antisymmetrize	(	const ex &	e,
		exvector::const_iterator	first,
		exvector::const_iterator	last
	)

Antisymmetrize expression over a set of objects (symbols, indices).

Definition at line 528 of file symmetry.cpp.

References last, and symm().

symmetrize_cyclic() [3/4]

ex GiNaC::symmetrize_cyclic	(	const ex &	e,
		exvector::const_iterator	first,
		exvector::const_iterator	last
	)

Symmetrize expression by cyclic permutation over a set of objects (symbols, indices).

Definition at line 533 of file symmetry.cpp.

References GiNaC::container< C >::append(), last, GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, GiNaC::container< C >::op(), GiNaC::container< C >::remove_first(), and GiNaC::ex::subs().

GINAC_DECLARE_UNARCHIVER() [45/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

symmetry

)

sy_none() [1/4]

symmetry GiNaC::sy_none ( )

inline

Definition at line 116 of file symmetry.h.

sy_none() [2/4]

symmetry GiNaC::sy_none ( const symmetry &  c1, const symmetry &  c2  )

inline

Definition at line 117 of file symmetry.h.

References GiNaC::symmetry::none.

sy_none() [3/4]

symmetry GiNaC::sy_none ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3  )

inline

Definition at line 118 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::none.

sy_none() [4/4]

symmetry GiNaC::sy_none ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3, const symmetry &  c4  )

inline

Definition at line 119 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::none.

sy_symm() [1/4]

symmetry GiNaC::sy_symm ( )

inline

Definition at line 121 of file symmetry.h.

References GiNaC::symmetry::set_type(), and GiNaC::symmetry::symmetric.

Referenced by GiNaC::indexed::read_archive().

sy_symm() [2/4]

symmetry GiNaC::sy_symm ( const symmetry &  c1, const symmetry &  c2  )

inline

Definition at line 122 of file symmetry.h.

References GiNaC::symmetry::symmetric.

sy_symm() [3/4]

symmetry GiNaC::sy_symm ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3  )

inline

Definition at line 123 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::symmetric.

sy_symm() [4/4]

symmetry GiNaC::sy_symm ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3, const symmetry &  c4  )

inline

Definition at line 124 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::symmetric.

sy_anti() [1/4]

symmetry GiNaC::sy_anti ( )

inline

Definition at line 126 of file symmetry.h.

References GiNaC::symmetry::antisymmetric, and GiNaC::symmetry::set_type().

Referenced by GiNaC::indexed::read_archive().

sy_anti() [2/4]

symmetry GiNaC::sy_anti ( const symmetry &  c1, const symmetry &  c2  )

inline

Definition at line 127 of file symmetry.h.

References GiNaC::symmetry::antisymmetric.

sy_anti() [3/4]

symmetry GiNaC::sy_anti ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3  )

inline

Definition at line 128 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::antisymmetric.

sy_anti() [4/4]

symmetry GiNaC::sy_anti ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3, const symmetry &  c4  )

inline

Definition at line 129 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::antisymmetric.

sy_cycl() [1/4]

symmetry GiNaC::sy_cycl ( )

inline

Definition at line 131 of file symmetry.h.

References GiNaC::symmetry::cyclic, and GiNaC::symmetry::set_type().

sy_cycl() [2/4]

symmetry GiNaC::sy_cycl ( const symmetry &  c1, const symmetry &  c2  )

inline

Definition at line 132 of file symmetry.h.

References GiNaC::symmetry::cyclic.

sy_cycl() [3/4]

symmetry GiNaC::sy_cycl ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3  )

inline

Definition at line 133 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::cyclic.

sy_cycl() [4/4]

symmetry GiNaC::sy_cycl ( const symmetry &  c1, const symmetry &  c2, const symmetry &  c3, const symmetry &  c4  )

inline

Definition at line 134 of file symmetry.h.

References GiNaC::symmetry::add(), and GiNaC::symmetry::cyclic.

symmetrize() [4/4]

ex GiNaC::symmetrize ( const ex &  e, const exvector &  v  )

inline

Symmetrize expression over a set of objects (symbols, indices).

Definition at line 159 of file symmetry.h.

References GiNaC::ex::begin(), and symmetrize().

antisymmetrize() [4/4]

ex GiNaC::antisymmetrize ( const ex &  e, const exvector &  v  )

inline

Antisymmetrize expression over a set of objects (symbols, indices).

Definition at line 168 of file symmetry.h.

References antisymmetrize(), and GiNaC::ex::begin().

symmetrize_cyclic() [4/4]

ex GiNaC::symmetrize_cyclic ( const ex &  e, const exvector &  v  )

inline

Symmetrize expression by cyclic permutation over a set of objects (symbols, indices).

Definition at line 179 of file symmetry.h.

References GiNaC::ex::begin(), and symmetrize().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [32/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	tensdelta	,
		tensor	,
		print_func< print_dflt > &::do_print. print_func< print_latex > &::do_print_latex
	)

print_func< print_dflt >() [3/3]

GiNaC::print_func< print_dflt >

(

&tensmetric::do_print

)

&

Definition at line 46 of file tensor.cpp.

References GiNaC::status_flags::evaluated, and GiNaC::status_flags::expanded.

GINAC_BIND_UNARCHIVER() [44/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

minkmetric

)

GINAC_BIND_UNARCHIVER() [45/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

tensepsilon

)

GINAC_BIND_UNARCHIVER() [46/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

tensdelta

)

GINAC_BIND_UNARCHIVER() [47/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

tensmetric

)

GINAC_BIND_UNARCHIVER() [48/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

spinmetric

)

delta_tensor()

ex GiNaC::delta_tensor	(	const ex &	i1,
		const ex &	i2
	)

Create a delta tensor with specified indices.

The indices must be of class idx or a subclass. The delta tensor is always symmetric and its trace is the dimension of the index space.

Parameters

i1	First index
i2	Second index

Returns

newly constructed delta tensor

Definition at line 576 of file tensor.cpp.

References symmetric2().

Referenced by color_trace(), GiNaC::su3f::contract_with(), GiNaC::su3d::contract_with(), GiNaC::spinmetric::contract_with(), GiNaC::tensepsilon::contract_with(), and GiNaC::tensmetric::eval_indexed().

metric_tensor()

ex GiNaC::metric_tensor	(	const ex &	i1,
		const ex &	i2
	)

Create a symmetric metric tensor with specified indices.

The indices must be of class varidx or a subclass. A metric tensor with one covariant and one contravariant index is equivalent to the delta tensor.

Parameters

i1	First index
i2	Second index

Returns

newly constructed metric tensor

Definition at line 586 of file tensor.cpp.

References symmetric2().

Referenced by GiNaC::tensepsilon::contract_with().

lorentz_g()

ex GiNaC::lorentz_g	(	const ex &	i1,
		const ex &	i2,
		bool	pos_sig = false
	)

Create a Minkowski metric tensor with specified indices.

The indices must be of class varidx or a subclass. The Lorentz metric is a symmetric tensor with a matrix representation of diag(1,-1,-1,...) (negative signature, the default) or diag(-1,1,1,...) (positive signature).

Parameters

i1	First index
i2	Second index
pos_sig	Whether the signature is positive

Returns

newly constructed Lorentz metric tensor

Definition at line 596 of file tensor.cpp.

References symmetric2().

Referenced by GiNaC::tensepsilon::contract_with().

spinor_metric()

ex GiNaC::spinor_metric	(	const ex &	i1,
		const ex &	i2
	)

Create a spinor metric tensor with specified indices.

The indices must be of class spinidx or a subclass and have a dimension of 2. The spinor metric is an antisymmetric tensor with a matrix representation of [[ [[ 0, 1 ]], [[ -1, 0 ]] ]].

Parameters

i1	First index
i2	Second index

Returns

newly constructed spinor metric tensor

Definition at line 607 of file tensor.cpp.

References antisymmetric2().

epsilon_tensor() [1/2]

ex GiNaC::epsilon_tensor	(	const ex &	i1,
		const ex &	i2
	)

Create an epsilon tensor in a Euclidean space with two indices.

The indices must be of class idx or a subclass, and have a dimension of 2.

Parameters

i1	First index
i2	Second index

Returns

newly constructed epsilon tensor

Definition at line 619 of file tensor.cpp.

References _ex2, antisymmetric2(), GiNaC::basic::hold(), GiNaC::ex::is_equal(), and GiNaC::ex::op().

epsilon_tensor() [2/2]

ex GiNaC::epsilon_tensor	(	const ex &	i1,
		const ex &	i2,
		const ex &	i3
	)

Create an epsilon tensor in a Euclidean space with three indices.

The indices must be of class idx or a subclass, and have a dimension of 3.

Parameters

i1	First index
i2	Second index
i3	Third index

Returns

newly constructed epsilon tensor

Definition at line 638 of file tensor.cpp.

References _ex3, antisymmetric3(), GiNaC::basic::hold(), GiNaC::ex::is_equal(), and GiNaC::ex::op().

lorentz_eps()

ex GiNaC::lorentz_eps	(	const ex &	i1,
		const ex &	i2,
		const ex &	i3,
		const ex &	i4,
		bool	pos_sig = false
	)

Create an epsilon tensor in a Minkowski space with four indices.

The indices must be of class varidx or a subclass, and have a dimension of 4.

Parameters

i1	First index
i2	Second index
i3	Third index
i4	Fourth index
pos_sig	Whether the signature of the metric is positive

Returns

newly constructed epsilon tensor

Definition at line 657 of file tensor.cpp.

References _ex4, antisymmetric4(), GiNaC::ex::is_equal(), and GiNaC::ex::op().

GINAC_DECLARE_UNARCHIVER() [46/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

tensdelta

)

GINAC_DECLARE_UNARCHIVER() [47/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

tensmetric

)

GINAC_DECLARE_UNARCHIVER() [48/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

minkmetric

)

GINAC_DECLARE_UNARCHIVER() [49/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

spinmetric

)

GINAC_DECLARE_UNARCHIVER() [50/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

tensepsilon

)

log2()

unsigned GiNaC::log2

(

unsigned

n

)

Integer binary logarithm.

Definition at line 48 of file utils.cpp.

References k, and n.

Referenced by GiNaC::remember_table::remember_table().

multinomial_coefficient()

const numeric GiNaC::multinomial_coefficient

(

const std::vector< unsigned > &

p

)

Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where n = p1+p2+...+pk, i.e.

p is a partition of n.

Definition at line 60 of file utils.cpp.

References GiNaC::numeric::add(), GiNaC::numeric::div(), factorial(), GiNaC::numeric::mul(), and n.

Referenced by GiNaC::power::expand_add().

rotate_left()

unsigned GiNaC::rotate_left ( unsigned  n )

inline

Rotate bits of unsigned value by one bit to the left.

This can be necessary if the user wants to define its own hashes.

Definition at line 48 of file utils.h.

References n.

Referenced by GiNaC::basic::calchash(), GiNaC::expairseq::calchash(), GiNaC::function::calchash(), GiNaC::idx::calchash(), GiNaC::relational::calchash(), and GiNaC::symmetry::calchash().

compare_pointers()

template<class T >

int GiNaC::compare_pointers ( const T *  a, const T *  b  )

inline

Compare two pointers (just to establish some sort of canonical order).

Returns

-1, 0, or 1

Definition at line 56 of file utils.h.

Referenced by GiNaC::basic::compare_same_type().

golden_ratio_hash()

unsigned GiNaC::golden_ratio_hash ( uintptr_t  n )

inline

Truncated multiplication with golden ratio, for computing hash values.

Definition at line 68 of file utils.h.

References n.

Referenced by GiNaC::constant::calchash(), GiNaC::function::calchash(), GiNaC::numeric::calchash(), GiNaC::symbol::calchash(), GiNaC::wildcard::calchash(), and make_hash_seed().

permutation_sign() [1/2]

template<class It >

int GiNaC::permutation_sign	(	It	first,
		It	last
	)

Definition at line 77 of file utils.h.

References last, swap(), and std::swap().

Referenced by GiNaC::matrix::determinant(), GiNaC::tensepsilon::eval_indexed(), and symm().

permutation_sign() [2/2]

template<class It , class Cmp , class Swap >

int GiNaC::permutation_sign	(	It	first,
		It	last,
		Cmp	comp,
		Swap	swapit
	)

Definition at line 135 of file utils.h.

References last.

shaker_sort()

template<class It , class Cmp , class Swap >

void GiNaC::shaker_sort	(	It	first,
		It	last,
		Cmp	comp,
		Swap	swapit
	)

Definition at line 193 of file utils.h.

References last.

Referenced by find_free_and_dummy(), and rename_dummy_indices().

cyclic_permutation()

template<class It , class Swap >

void GiNaC::cyclic_permutation	(	It	first,
		It	last,
		It	new_first,
		Swap	swapit
	)

Definition at line 244 of file utils.h.

References last.

format_index_value() [1/2]

template<typename T >

std::enable_if< has_distance< T >::value, typenamestd::iterator_traits< T >::difference_type >::type GiNaC::format_index_value	(	const T &	a,
		const T &	b
	)

For printing a multi-index: If the templates are used, where T is an iterator, printing the address where the iterator points to is not meaningful.

However, we may print the difference to the starting point.

Definition at line 57 of file utils_multi_iterator.h.

Referenced by operator<<(), operator<<(), operator<<(), operator<<(), operator<<(), operator<<(), operator<<(), operator<<(), and operator<<().

format_index_value() [2/2]

template<typename T >

std::enable_if<!has_distance< T >::value, T >::type GiNaC::format_index_value	(	const T &	a,
		const T &	b
	)

For all other cases we simply print the value.

Definition at line 66 of file utils_multi_iterator.h.

operator<<() [8/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const basic_multi_iterator< T > &  v  )

inline

Output operator.

A multi_iterator prints out as basic_multi_iterator( ).

Definition at line 543 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [9/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_ordered< T > &  v  )

inline

Output operator.

A multi_iterator_ordered prints out as multi_iterator_ordered( ).

Definition at line 657 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [10/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_ordered_eq< T > &  v  )

inline

Output operator.

A multi_iterator_ordered_eq prints out as multi_iterator_ordered_eq( ).

Definition at line 768 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [11/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_ordered_eq_indv< T > &  v  )

inline

Output operator.

A multi_iterator_ordered_eq_indv prints out as multi_iterator_ordered_eq_indv( ).

Definition at line 880 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [12/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_counter< T > &  v  )

inline

Output operator.

A multi_iterator_counter prints out as multi_iterator_counter( ).

Definition at line 988 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [13/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_counter_indv< T > &  v  )

inline

Output operator.

A multi_iterator_counter_indv prints out as multi_iterator_counter_indv( ).

Definition at line 1096 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [14/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_permutation< T > &  v  )

inline

Output operator.

A multi_iterator_permutation prints out as multi_iterator_permutation( ).

Definition at line 1268 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [15/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_shuffle< T > &  v  )

inline

Output operator.

A multi_iterator_shuffle prints out as multi_iterator_shuffle( ).

Definition at line 1409 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

operator<<() [16/16]

template<class T >

std::ostream & GiNaC::operator<< ( std::ostream &  os, const multi_iterator_shuffle_prime< T > &  v  )

inline

Output operator.

A multi_iterator_shuffle_prime prints out as multi_iterator_shuffle_prime( ).

Definition at line 1473 of file utils_multi_iterator.h.

References GiNaC::basic_multi_iterator< T >::B, format_index_value(), and GiNaC::basic_multi_iterator< T >::size().

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT() [33/33]

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT	(	wildcard	,
		basic	,
		print_func< print_context > &::do_print. print_func< print_tree > &::do_print_tree. print_func< print_python_repr > &::do_print_python_repr
	)

Definition at line 30 of file wildcard.cpp.

References GiNaC::status_flags::evaluated, and GiNaC::status_flags::expanded.

GINAC_BIND_UNARCHIVER() [49/49]

GiNaC::GINAC_BIND_UNARCHIVER

(

wildcard

)

haswild()

bool GiNaC::haswild

(

const ex &

x

)

Check whether x has a wildcard anywhere as a subexpression.

Definition at line 122 of file wildcard.cpp.

References haswild(), GiNaC::ex::nops(), GiNaC::ex::op(), and x.

Referenced by GiNaC::integral::eval(), and haswild().

GINAC_DECLARE_UNARCHIVER() [51/51]

GiNaC::GINAC_DECLARE_UNARCHIVER

(

wildcard

)

wild()

ex GiNaC::wild ( unsigned  label = 0 )

inline

Create a wildcard object with the specified label.

Definition at line 72 of file wildcard.h.

Variable Documentation

unarch_table_instance

unarchive_table_t GiNaC::unarch_table_instance

static

Definition at line 179 of file archive.h.

map_evalm

GiNaC::evalm_map_function GiNaC::map_evalm

Referenced by GiNaC::basic::evalm().

map_eval_integ

GiNaC::eval_integ_map_function GiNaC::map_eval_integ

Referenced by GiNaC::basic::eval_integ().

tensor

GiNaC::tensor

Definition at line 51 of file clifford.cpp.

Pi

const constant GiNaC::Pi	(	"Pi"	,
		PiEvalf	,
		"\\pi"	,
		domain::positive
	)

Pi.

(3.14159...) Diverts straight into CLN for evalf().

Definition at line 82 of file constant.h.

Referenced by acos_eval(), acosh_eval(), asin_eval(), atan2_eval(), atan_eval(), atan_series(), atanh_series(), GiNaC::Eisenstein_h_kernel::coefficient_a0(), GiNaC::Eisenstein_h_kernel::coefficient_an(), cos_eval(), cosh_eval(), EllipticE_eval(), EllipticE_evalf(), EllipticE_series(), EllipticK_eval(), EllipticK_evalf(), EllipticK_series(), eta_eval(), eta_evalf(), exp_eval(), GiNaC::Kronecker_dtau_kernel::get_numerical_value(), GiNaC::Kronecker_dz_kernel::get_numerical_value(), H_evalf(), Li2_eval(), Li2_series(), Li_eval(), log_eval(), log_series(), GiNaC::constant::read_archive(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), sin_eval(), sinh_eval(), tan_eval(), tan_series(), tanh_eval(), tanh_series(), tgamma_eval(), and zeta1_eval().

Euler

const constant GiNaC::Euler	(	"Euler"	,
		EulerEvalf	,
		"\\gamma_E"	,
		domain::positive
	)

Euler's constant.

(0.57721...) Sometimes called Euler-Mascheroni constant. Diverts straight into CLN for evalf().

Definition at line 84 of file constant.h.

Referenced by psi1_eval(), and GiNaC::constant::read_archive().

Catalan

const constant GiNaC::Catalan	(	"Catalan"	,
		CatalanEvalf	,
		"G"	,
		domain::positive
	)

Catalan's constant.

(0.91597...) Diverts straight into CLN for evalf().

Definition at line 83 of file constant.h.

Referenced by Li2_eval(), Li_eval(), and GiNaC::constant::read_archive().

crctab

unsigned const GiNaC::crctab[256]

static

Definition at line 10 of file crc32.h.

Referenced by crc32().

library_initializer

library_init GiNaC::library_initializer

static

For construction of flyweights, etc.

Definition at line 60 of file ex.h.

_num0_bp

const basic * GiNaC::_num0_bp

Definition at line 368 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

idx

GiNaC::idx

Definition at line 43 of file idx.cpp.

force_include_tgamma

unsigned GiNaC::force_include_tgamma = tgamma_SERIAL::serial

Definition at line 1289 of file inifcns.cpp.

force_include_zeta1

unsigned GiNaC::force_include_zeta1 = zeta1_SERIAL::serial

Definition at line 1290 of file inifcns.cpp.

GINAC_BIND_UNARCHIVER

template<>

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT_T(lst, basic, print_func< print_context >(&lst::do_print). print_func< print_tree >(&lst::do_print_tree)) template<> bool lst GiNaC::GINAC_BIND_UNARCHIVER(lst)

(

lst

)

Specialization of container::info() for lst.

Definition at line 42 of file lst.cpp.

I

const numeric GiNaC::I = numeric(cln::complex(cln::cl_I(0),cln::cl_I(1)))

Imaginary unit.

This is not a constant but a numeric since we are natively handing complex numbers anyways, so in each expression containing an I it is automatically eval'ed away anyhow.

Definition at line 1433 of file numeric.cpp.

Referenced by acosh_eval(), atan_eval(), atan_series(), atanh_series(), GiNaC::Eisenstein_h_kernel::coefficient_a0(), GiNaC::Eisenstein_h_kernel::coefficient_an(), color_h(), GiNaC::su3f::contract_with(), cosh_eval(), csgn_eval(), eta_eval(), eta_evalf(), eta_imag_part(), exp_eval(), GiNaC::Kronecker_dtau_kernel::get_numerical_value(), GiNaC::Kronecker_dz_kernel::get_numerical_value(), H_evalf(), GiNaC::numeric::has(), Li2_eval(), Li2_series(), Li_eval(), log_eval(), log_series(), GiNaC::numeric::normal(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), GiNaC::Kronecker_dz_kernel::series_coeff_impl(), sinh_eval(), step_eval(), tanh_eval(), tanh_series(), GiNaC::numeric::to_polynomial(), and GiNaC::numeric::to_rational().

Digits

_numeric_digits GiNaC::Digits

Accuracy in decimal digits.

Only object of this type! Can be set using assignment from C++ unsigned ints and evaluated like any built-in type.

Definition at line 2591 of file numeric.cpp.

Referenced by GiNaC::integration_kernel::get_numerical_value_impl(), iterated_integral_evalf_impl(), GiNaC::numeric::numeric(), print_real_cl_N(), and zeta1_evalf().

next_print_context_id

unsigned GiNaC::next_print_context_id = 0

Next free ID for print_context types.

Definition at line 30 of file print.cpp.

version_major

const int GiNaC::version_major = GINACLIB_MAJOR_VERSION

Definition at line 32 of file utils.cpp.

version_minor

const int GiNaC::version_minor = GINACLIB_MINOR_VERSION

Definition at line 33 of file utils.cpp.

version_micro

const int GiNaC::version_micro = GINACLIB_MICRO_VERSION

Definition at line 34 of file utils.cpp.

_num_120_p

const numeric * GiNaC::_num_120_p

Definition at line 271 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_120

const ex GiNaC::_ex_120 = ex(*_num_120_p)

Definition at line 272 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_60_p

const numeric * GiNaC::_num_60_p

Definition at line 275 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_60

const ex GiNaC::_ex_60 = ex(*_num_60_p)

Definition at line 276 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_48_p

const numeric * GiNaC::_num_48_p

Definition at line 279 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_48

const ex GiNaC::_ex_48 = ex(*_num_48_p)

Definition at line 280 of file utils.cpp.

Referenced by Li2_eval(), Li_eval(), GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_30_p

const numeric * GiNaC::_num_30_p

Definition at line 283 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_30

const ex GiNaC::_ex_30 = ex(*_num_30_p)

Definition at line 284 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_25_p

const numeric * GiNaC::_num_25_p

Definition at line 287 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_25

const ex GiNaC::_ex_25 = ex(*_num_25_p)

Definition at line 288 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_24_p

const numeric * GiNaC::_num_24_p

Definition at line 291 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_24

const ex GiNaC::_ex_24 = ex(*_num_24_p)

Definition at line 292 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_20_p

const numeric * GiNaC::_num_20_p

Definition at line 295 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_20

const ex GiNaC::_ex_20 = ex(*_num_20_p)

Definition at line 296 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_18_p

const numeric * GiNaC::_num_18_p

Definition at line 299 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_18

const ex GiNaC::_ex_18 = ex(*_num_18_p)

Definition at line 300 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_15_p

const numeric * GiNaC::_num_15_p

Definition at line 303 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_15

const ex GiNaC::_ex_15 = ex(*_num_15_p)

Definition at line 304 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_12_p

const numeric * GiNaC::_num_12_p

Definition at line 307 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_12

const ex GiNaC::_ex_12 = ex(*_num_12_p)

Definition at line 308 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_11_p

const numeric * GiNaC::_num_11_p

Definition at line 311 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_11

const ex GiNaC::_ex_11 = ex(*_num_11_p)

Definition at line 312 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_10_p

const numeric * GiNaC::_num_10_p

Definition at line 315 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_10

const ex GiNaC::_ex_10 = ex(*_num_10_p)

Definition at line 316 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_9_p

const numeric * GiNaC::_num_9_p

Definition at line 319 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_9

const ex GiNaC::_ex_9 = ex(*_num_9_p)

Definition at line 320 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_8_p

const numeric * GiNaC::_num_8_p

Definition at line 323 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_8

const ex GiNaC::_ex_8 = ex(*_num_8_p)

Definition at line 324 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_7_p

const numeric * GiNaC::_num_7_p

Definition at line 327 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_7

const ex GiNaC::_ex_7 = ex(*_num_7_p)

Definition at line 328 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_6_p

const numeric * GiNaC::_num_6_p

Definition at line 331 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_6

const ex GiNaC::_ex_6 = ex(*_num_6_p)

Definition at line 332 of file utils.cpp.

Referenced by GiNaC::su3d::eval_indexed(), GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_5_p

const numeric * GiNaC::_num_5_p

Definition at line 335 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_5

const ex GiNaC::_ex_5 = ex(*_num_5_p)

Definition at line 336 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_4_p

const numeric * GiNaC::_num_4_p

Definition at line 339 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_4

const ex GiNaC::_ex_4 = ex(*_num_4_p)

Definition at line 340 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_3_p

const numeric * GiNaC::_num_3_p

Definition at line 343 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), and GiNaC::library_init::library_init().

_ex_3

const ex GiNaC::_ex_3 = ex(*_num_3_p)

Definition at line 344 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_2_p

const numeric * GiNaC::_num_2_p

Definition at line 347 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::library_init::library_init(), and tgamma_eval().

_ex_2

const ex GiNaC::_ex_2 = ex(*_num_2_p)

Definition at line 348 of file utils.cpp.

Referenced by GiNaC::spinmetric::contract_with(), GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num_1_p

const numeric * GiNaC::_num_1_p

Definition at line 351 of file utils.cpp.

Referenced by acos_conjugate(), asin_conjugate(), asinh_conjugate(), atan_conjugate(), atanh_conjugate(), beta_eval(), binomial(), GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::add::do_print_csrc(), doublefactorial(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::library_init::library_init(), operator-(), operator--(), operator--(), GiNaC::add::print_add(), GiNaC::mul::print_overall_coeff(), psi1_eval(), and psi2_eval().

_ex_1

const ex GiNaC::_ex_1 = ex(*_num_1_p)

Definition at line 352 of file utils.cpp.

Referenced by acos_eval(), acosh_deriv(), acosh_eval(), asin_eval(), atan2_deriv(), atan_deriv(), atan_eval(), atan_series(), atanh_deriv(), atanh_eval(), atanh_series(), cos_eval(), GiNaC::power::derivative(), GiNaC::add::do_print_csrc(), GiNaC::mul::do_print_csrc(), GiNaC::power::do_print_csrc(), GiNaC::power::do_print_csrc_cl_N(), EllipticE_eval(), EllipticE_series(), EllipticK_series(), GiNaC::power::eval(), GiNaC::minkmetric::eval_indexed(), GiNaC::spinmetric::eval_indexed(), exminus(), exp_eval(), exp_power(), GiNaC::power::expand(), frac_cancel(), H_deriv(), H_eval(), lgamma_eval(), Li2_eval(), Li_eval(), GiNaC::library_init::library_init(), log_deriv(), log_expand(), log_series(), operator--(), operator--(), operator/(), operator/=(), psi1_series(), psi2_eval(), psi2_series(), replace_with_symbol(), sin_eval(), tan_eval(), tanh_eval(), GiNaC::power::to_polynomial(), GiNaC::ex::unit(), GiNaC::ex::unitcontprim(), and GiNaC::library_init::~library_init().

_num_1_2_p

const numeric * GiNaC::_num_1_2_p

Definition at line 355 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_1_2

const ex GiNaC::_ex_1_2 = ex(*_num_1_2_p)

Definition at line 356 of file utils.cpp.

Referenced by acos_deriv(), acos_eval(), acosh_deriv(), asin_deriv(), asin_eval(), asinh_deriv(), atan2_eval(), atan_series(), atanh_series(), cos_eval(), cosh_eval(), GiNaC::su3f::eval_indexed(), GiNaC::su3d::eval_indexed(), Li2_eval(), GiNaC::library_init::library_init(), log_eval(), sin_eval(), sinh_eval(), tan_eval(), tanh_eval(), zeta1_eval(), and GiNaC::library_init::~library_init().

_num_1_3_p

const numeric * GiNaC::_num_1_3_p

Definition at line 359 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_1_3

const ex GiNaC::_ex_1_3 = ex(*_num_1_3_p)

Definition at line 360 of file utils.cpp.

Referenced by cos_eval(), GiNaC::su3d::eval_indexed(), GiNaC::library_init::library_init(), sin_eval(), and GiNaC::library_init::~library_init().

_num_1_4_p

const numeric * GiNaC::_num_1_4_p

Definition at line 363 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex_1_4

const ex GiNaC::_ex_1_4 = ex(*_num_1_4_p)

Definition at line 364 of file utils.cpp.

Referenced by atan2_eval(), atan_eval(), cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and GiNaC::library_init::~library_init().

_num0_p

const numeric * GiNaC::_num0_p

Definition at line 367 of file utils.cpp.

Referenced by GiNaC::numeric::add_dyn(), atan(), binomial(), GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), cos_eval(), divide_in_z(), GiNaC::power::eval(), exp_eval(), GiNaC::mul::expand(), fibonacci(), GiNaC::numeric::has(), GiNaC::add::integer_content(), iquo(), iquo(), irem(), irem(), isqrt(), Li2(), GiNaC::library_init::library_init(), mod(), GiNaC::relational::operator safe_bool(), GiNaC::numeric::power(), GiNaC::numeric::power_dyn(), sin_eval(), smod(), GiNaC::numeric::sub_dyn(), and tan_eval().

_ex0

const ex GiNaC::_ex0 = ex(*_num0_p)

Definition at line 369 of file utils.cpp.

Referenced by acos_eval(), acosh_eval(), GiNaC::add::add(), GiNaC::add::add(), GiNaC::add::add(), GiNaC::add::add(), GiNaC::pseries::add_series(), asinh_eval(), atan2_eval(), atan_eval(), atan_series(), atanh_eval(), atanh_series(), beta_eval(), binomial_sym(), GiNaC::relational::canonical(), GiNaC::basic::coeff(), GiNaC::add::coeff(), GiNaC::mul::coeff(), GiNaC::ncmul::coeff(), GiNaC::numeric::coeff(), GiNaC::power::coeff(), GiNaC::pseries::coeff(), GiNaC::basic::collect(), color_trace(), GiNaC::ex::content(), cos_eval(), csgn_series(), GiNaC::expairseq::default_overall_coeff(), GiNaC::basic::derivative(), GiNaC::constant::derivative(), GiNaC::idx::derivative(), GiNaC::indexed::derivative(), GiNaC::symbol::derivative(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), divide(), divide_in_z(), GiNaC::matrix::division_free_elimination(), EllipticE_eval(), EllipticE_series(), EllipticK_eval(), EllipticK_series(), eta_eval(), eta_evalf(), eta_series(), GiNaC::function::eval(), GiNaC::indexed::eval(), GiNaC::integral::eval(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::su3f::eval_indexed(), GiNaC::su3d::eval_indexed(), GiNaC::tensdelta::eval_indexed(), GiNaC::minkmetric::eval_indexed(), GiNaC::spinmetric::eval_indexed(), GiNaC::tensepsilon::eval_indexed(), GiNaC::indexed::expand(), find_common_factor(), GiNaC::matrix::fraction_free_elimination(), G2_eval(), G2_evalf(), G3_eval(), G3_evalf(), GiNaC::matrix::gauss_elimination(), gcd(), H_deriv(), H_eval(), GiNaC::ex::is_zero(), Li2_eval(), Li2_series(), Li_deriv(), Li_eval(), Li_evalf(), GiNaC::library_init::library_init(), log_eval(), log_series(), GiNaC::matrix::markowitz_elimination(), GiNaC::matrix::matrix(), GiNaC::pseries::mul_series(), Order_eval(), GiNaC::pseries::power_const(), prem(), GiNaC::ex::primpart(), rem(), S_deriv(), S_eval(), GiNaC::ex::series(), GiNaC::basic::series(), GiNaC::symbol::series(), sin_eval(), sinh_eval(), sprem(), sqrfree(), sr_gcd(), step_series(), tan_eval(), tanh_eval(), GiNaC::ex::unitcontprim(), zeta1_deriv(), zeta1_eval(), zeta2_deriv(), and GiNaC::library_init::~library_init().

_num1_4_p

const numeric * GiNaC::_num1_4_p

Definition at line 372 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex1_4

const ex GiNaC::_ex1_4 = ex(*_num1_4_p)

Definition at line 373 of file utils.cpp.

Referenced by atan2_eval(), atan_eval(), cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and GiNaC::library_init::~library_init().

_num1_3_p

const numeric * GiNaC::_num1_3_p

Definition at line 376 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex1_3

const ex GiNaC::_ex1_3 = ex(*_num1_3_p)

Definition at line 377 of file utils.cpp.

Referenced by acos_eval(), cos_eval(), GiNaC::su3d::eval_indexed(), GiNaC::library_init::library_init(), sin_eval(), tan_eval(), and GiNaC::library_init::~library_init().

_num1_2_p

const numeric * GiNaC::_num1_2_p

Definition at line 380 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), psi2_eval(), and tgamma_eval().

_ex1_2

const ex GiNaC::_ex1_2 = ex(*_num1_2_p)

Definition at line 381 of file utils.cpp.

Referenced by acos_eval(), asin_eval(), atan2_eval(), atan_series(), atanh_series(), cos_eval(), GiNaC::power::do_print_dflt(), GiNaC::power::do_print_latex(), GiNaC::su3f::eval_indexed(), GiNaC::su3d::eval_indexed(), GiNaC::clifford::get_metric(), Li2_eval(), GiNaC::library_init::library_init(), log_eval(), psi1_eval(), psi2_eval(), sin_eval(), sqrt(), and GiNaC::library_init::~library_init().

_num1_p

const numeric * GiNaC::_num1_p

Definition at line 384 of file utils.cpp.

Referenced by acos_conjugate(), acosh_conjugate(), asin_conjugate(), asinh_conjugate(), atan(), atan_conjugate(), atanh_conjugate(), bernoulli(), binomial(), GiNaC::add::combine_pair_with_coeff_to_pair(), GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), GiNaC::numeric::denom(), GiNaC::numeric::div_dyn(), divide_in_z(), GiNaC::add::do_print_csrc(), doublefactorial(), GiNaC::mul::eval(), GiNaC::power::eval(), exp_eval(), GiNaC::power::expand_add(), frac_cancel(), gcd(), GiNaC::mul::info(), GiNaC::basic::integer_content(), GiNaC::add::integer_content(), lcm_of_coefficients_denominators(), lcmcoeff(), Li2_conjugate(), GiNaC::library_init::library_init(), GiNaC::basic::max_coefficient(), GiNaC::numeric::mul_dyn(), multiply_lcm(), operator++(), operator++(), GiNaC::matrix::pow(), GiNaC::numeric::power(), GiNaC::numeric::power_dyn(), GiNaC::add::print_add(), GiNaC::mul::print_overall_coeff(), psi2_eval(), GiNaC::add::recombine_pair_to_ex(), tgamma_eval(), and zeta1_eval().

_ex1

const ex GiNaC::_ex1 = ex(*_num1_p)

Definition at line 385 of file utils.cpp.

Referenced by acos_eval(), acosh_deriv(), acosh_eval(), GiNaC::pseries::add_series(), asin_eval(), asinh_deriv(), atan_deriv(), atan_eval(), atan_series(), atanh_deriv(), atanh_eval(), atanh_series(), beta_eval(), binomial_sym(), GiNaC::basic::coeff(), GiNaC::ncmul::coeff(), GiNaC::power::coeff(), GiNaC::basic::collect(), color_trace(), GiNaC::add::combine_ex_with_coeff_to_pair(), GiNaC::mul::combine_ex_with_coeff_to_pair(), GiNaC::add::combine_pair_with_coeff_to_pair(), GiNaC::mul::combine_pair_with_coeff_to_pair(), GiNaC::su3t::contract_with(), GiNaC::su3f::contract_with(), GiNaC::su3d::contract_with(), GiNaC::matrix::contract_with(), GiNaC::spinmetric::contract_with(), GiNaC::tensepsilon::contract_with(), cos_eval(), cosh_eval(), GiNaC::mul::default_overall_coeff(), GiNaC::mul::derivative(), GiNaC::power::derivative(), GiNaC::symbol::derivative(), GiNaC::matrix::determinant_minor(), divide(), divide_in_z(), GiNaC::add::do_print_csrc(), GiNaC::mul::do_print_csrc(), EllipticE_eval(), EllipticE_series(), EllipticK_series(), GiNaC::mul::eval(), GiNaC::ncmul::eval(), GiNaC::power::eval(), GiNaC::tensdelta::eval_indexed(), GiNaC::minkmetric::eval_indexed(), GiNaC::spinmetric::eval_indexed(), GiNaC::mul::evalm(), exp_eval(), GiNaC::expairseq::expair_needs_further_processing(), GiNaC::mul::expair_needs_further_processing(), GiNaC::mul::expand(), GiNaC::ncmul::expand(), GiNaC::power::expand(), GiNaC::power::expand_add(), GiNaC::power::expand_add_2(), GiNaC::power::expand_mul(), find_common_factor(), frac_cancel(), GiNaC::matrix::fraction_free_elimination(), G2_eval(), G2_evalf(), G3_eval(), G3_evalf(), gcd(), gcd_pf_pow(), gcd_pf_pow_pow(), GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(), H_deriv(), H_eval(), GiNaC::power::imag_part(), GiNaC::matrix::inverse(), lgamma_series(), Li2_deriv(), Li2_eval(), Li2_series(), Li_eval(), Li_evalf(), Li_series(), GiNaC::library_init::library_init(), log_eval(), log_expand(), log_series(), GiNaC::expairseq::make_flat(), GiNaC::expairseq::make_flat(), GiNaC::mul::mul(), GiNaC::mul::mul(), GiNaC::mul::mul(), GiNaC::mul::mul(), GiNaC::mul::mul(), GiNaC::pseries::mul_series(), GiNaC::basic::normal(), GiNaC::power::normal(), GiNaC::pseries::normal(), GiNaC::symbol::normal(), operator++(), operator++(), Order_eval(), Order_series(), GiNaC::matrix::pow(), GiNaC::pseries::power_const(), prem(), GiNaC::ex::primpart(), GiNaC::pseries::print_series(), psi1_deriv(), psi1_series(), psi2_deriv(), psi2_eval(), psi2_series(), quo(), GiNaC::power::real_part(), GiNaC::mul::recombine_pair_to_ex(), GiNaC::tensor::replace_contr_index(), S_series(), GiNaC::basic::series(), GiNaC::add::series(), GiNaC::integral::series(), GiNaC::pseries::series(), GiNaC::mul::series(), GiNaC::power::series(), GiNaC::symbol::series(), sin_eval(), sinh_eval(), GiNaC::expairseq::split_ex_to_pair(), GiNaC::add::split_ex_to_pair(), GiNaC::mul::split_ex_to_pair(), sprem(), sqrfree_parfrac(), sqrfree_yun(), sr_gcd(), tan_deriv(), tan_eval(), tanh_deriv(), tanh_eval(), tgamma_series(), GiNaC::expairseq::to_polynomial(), GiNaC::expairseq::to_rational(), GiNaC::ex::unit(), unit_matrix(), GiNaC::ex::unitcontprim(), zeta1_deriv(), zeta2_deriv(), and GiNaC::library_init::~library_init().

_num2_p

const numeric * GiNaC::_num2_p

Definition at line 388 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), exp_eval(), GiNaC::power::expand_add_2(), Li2_series(), GiNaC::library_init::library_init(), GiNaC::matrix::pow(), psi1_eval(), psi2_eval(), tgamma_eval(), and zeta1_eval().

_ex2

const ex GiNaC::_ex2 = ex(*_num2_p)

Definition at line 389 of file utils.cpp.

Referenced by acos_deriv(), asin_deriv(), asinh_deriv(), atan2_deriv(), atan_deriv(), atanh_deriv(), GiNaC::spinmetric::contract_with(), cos_eval(), cosh_eval(), csgn_power(), epsilon_tensor(), exp_eval(), GiNaC::power::expand_add_2(), Li2_eval(), Li2_series(), Li_eval(), GiNaC::library_init::library_init(), product_to_exvector(), psi1_eval(), sin_eval(), sinh_eval(), tan_deriv(), tan_eval(), tanh_deriv(), tanh_eval(), and GiNaC::library_init::~library_init().

_num3_p

const numeric * GiNaC::_num3_p

Definition at line 392 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), exp_eval(), and GiNaC::library_init::library_init().

_ex3

const ex GiNaC::_ex3 = ex(*_num3_p)

Definition at line 393 of file utils.cpp.

Referenced by color_trace(), cos_eval(), epsilon_tensor(), GiNaC::su3f::eval_indexed(), GiNaC::su3d::eval_indexed(), GiNaC::library_init::library_init(), sin_eval(), tan_eval(), and GiNaC::library_init::~library_init().

_num4_p

const numeric * GiNaC::_num4_p

Definition at line 396 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), exp_eval(), and GiNaC::library_init::library_init().

_ex4

const ex GiNaC::_ex4 = ex(*_num4_p)

Definition at line 397 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), lorentz_eps(), and GiNaC::library_init::~library_init().

_num5_p

const numeric * GiNaC::_num5_p

Definition at line 400 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex5

const ex GiNaC::_ex5 = ex(*_num5_p)

Definition at line 401 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and GiNaC::library_init::~library_init().

_num6_p

const numeric * GiNaC::_num6_p

Definition at line 404 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), GiNaC::library_init::library_init(), and sin_eval().

_ex6

const ex GiNaC::_ex6 = ex(*_num6_p)

Definition at line 405 of file utils.cpp.

Referenced by cos_eval(), Li2_eval(), GiNaC::library_init::library_init(), sin_eval(), and GiNaC::library_init::~library_init().

_num7_p

const numeric * GiNaC::_num7_p

Definition at line 408 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), and GiNaC::library_init::library_init().

_ex7

const ex GiNaC::_ex7 = ex(*_num7_p)

Definition at line 409 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num8_p

const numeric * GiNaC::_num8_p

Definition at line 412 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), and GiNaC::library_init::library_init().

_ex8

const ex GiNaC::_ex8 = ex(*_num8_p)

Definition at line 413 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num9_p

const numeric * GiNaC::_num9_p

Definition at line 416 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), and GiNaC::library_init::library_init().

_ex9

const ex GiNaC::_ex9 = ex(*_num9_p)

Definition at line 417 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num10_p

const numeric * GiNaC::_num10_p

Definition at line 420 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex10

const ex GiNaC::_ex10 = ex(*_num10_p)

Definition at line 421 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num11_p

const numeric * GiNaC::_num11_p

Definition at line 424 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), and GiNaC::library_init::library_init().

_ex11

const ex GiNaC::_ex11 = ex(*_num11_p)

Definition at line 425 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num12_p

const numeric * GiNaC::_num12_p

Definition at line 428 of file utils.cpp.

Referenced by GiNaC::ex::construct_from_int(), GiNaC::ex::construct_from_long(), GiNaC::ex::construct_from_uint(), GiNaC::ex::construct_from_ulong(), cos_eval(), and GiNaC::library_init::library_init().

_ex12

const ex GiNaC::_ex12 = ex(*_num12_p)

Definition at line 429 of file utils.cpp.

Referenced by Li2_eval(), GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num15_p

const numeric * GiNaC::_num15_p

Definition at line 432 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex15

const ex GiNaC::_ex15 = ex(*_num15_p)

Definition at line 433 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num18_p

const numeric * GiNaC::_num18_p

Definition at line 436 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and sin_eval().

_ex18

const ex GiNaC::_ex18 = ex(*_num18_p)

Definition at line 437 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num20_p

const numeric * GiNaC::_num20_p

Definition at line 440 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex20

const ex GiNaC::_ex20 = ex(*_num20_p)

Definition at line 441 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num24_p

const numeric * GiNaC::_num24_p

Definition at line 444 of file utils.cpp.

Referenced by cos_eval(), and GiNaC::library_init::library_init().

_ex24

const ex GiNaC::_ex24 = ex(*_num24_p)

Definition at line 445 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num25_p

const numeric * GiNaC::_num25_p

Definition at line 448 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex25

const ex GiNaC::_ex25 = ex(*_num25_p)

Definition at line 449 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num30_p

const numeric * GiNaC::_num30_p

Definition at line 452 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex30

const ex GiNaC::_ex30 = ex(*_num30_p)

Definition at line 453 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num48_p

const numeric * GiNaC::_num48_p

Definition at line 456 of file utils.cpp.

Referenced by GiNaC::library_init::library_init().

_ex48

const ex GiNaC::_ex48 = ex(*_num48_p)

Definition at line 457 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().

_num60_p

const numeric * GiNaC::_num60_p

Definition at line 460 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), and tan_eval().

_ex60

const ex GiNaC::_ex60 = ex(*_num60_p)

Definition at line 461 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), sin_eval(), tan_eval(), and GiNaC::library_init::~library_init().

_num120_p

const numeric * GiNaC::_num120_p

Definition at line 464 of file utils.cpp.

Referenced by cos_eval(), GiNaC::library_init::library_init(), and sin_eval().

_ex120

const ex GiNaC::_ex120 = ex(*_num120_p)

Definition at line 465 of file utils.cpp.

Referenced by GiNaC::library_init::library_init(), and GiNaC::library_init::~library_init().