GiNaC Namespace Reference

CRC32 hash function. More...

Namespaces
namespace	internal
Classes
class	add
	Sum of expressions. 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	unarchive_table_t
class	archive
	This class holds archived versions of GiNaC expressions (class ex). 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...
struct	eval_integ_map_function
	Function object to be applied by basic::eval_integ(). More...
struct	derivative_map_function
	Function object to be applied by basic::derivative(). More...
struct	expand_map_function
	Function object to be applied by basic::expand(). More...
struct	map_function
	Function object for map(). More...
class	visitor
	Degenerate base class for visitors. More...
class	basic
	This class is the ABC (abstract base class) of GiNaC's class hierarchy. More...
class	class_info
struct	is_not_a_clifford
	Predicate for finding non-clifford objects. More...
class	clifford
	This class holds an object representing an element of the Clifford algebra (the Dirac gamma matrices). More...
class	diracone
	This class represents the Clifford algebra unity element. More...
class	cliffordunit
	This class represents the Clifford algebra generators (units). 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	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	su3one
	This class represents the su(3) unity element. More...
class	su3t
	This class represents an su(3) generator. More...
class	su3f
	This class represents the tensor of antisymmetric su(3) structure constants. More...
class	su3d
	This class represents the tensor of symmetric su(3) structure constants. More...
class	constant
	This class holds constants, symbols with specific numerical value. More...
class	container_storage
	Helper template for encapsulating the reserve() mechanics of STL containers. More...
class	container_init
	Helper template to allow initialization of containers via an overloaded comma operator (idea stolen from Blitz++). More...
class	container
	Wrapper template for making GiNaC classes out of STL containers. More...
class	library_init
	Helper class to initialize the library. More...
class	ex
	Lightweight wrapper for GiNaC's symbolic objects. More...
class	const_iterator
class	const_preorder_iterator
class	const_postorder_iterator
struct	ex_is_less
struct	ex_is_equal
struct	op0_is_equal
struct	ex_swap
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	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...
class	make_flat_inserter
	Class to handle the renaming of dummy indices. More...
class	fail
class	fderivative
	This class represents the (abstract) derivative of a symbolic function. More...
class	expand_options
	Flags to control the behavior of expand(). More...
class	has_options
	Flags to control the behavior of has(). More...
class	subs_options
	Flags to control the behavior of subs(). More...
class	domain
	Domain of an object. More...
class	series_options
	Flags to control series expansion. More...
class	determinant_algo
	Switch to control algorithm for determinant computation. More...
class	solve_algo
	Switch to control algorithm for linear system solving. More...
class	status_flags
	Flags to store information about the state of an object. More...
class	info_flags
	Possible attributes an object can have. More...
class	return_types
class	remember_strategies
	Strategies how to clean up the function remember cache. More...
class	factor_options
	Flags to control the polynomial factorization. More...
class	function_options
class	do_taylor
	Exception class thrown by classes which provide their own series expansion to signal that ordinary Taylor expansion is safe. More...
class	function
	The class function is used to implement builtin functions like sin, cos... More...
class	exhashmap
	Pair Associative Container with 'ex' objects as keys, that is implemented with a hash table and can be used as a replacement for map<> in many cases. More...
class	idx
	This class holds one index of an indexed object. More...
class	varidx
	This class holds an index with a variance (co- or contravariant). More...
class	spinidx
	This class holds a spinor index that can be dotted or undotted and that also has a variance. More...
struct	idx_is_not
struct	idx_is_equal_ignore_dim
struct	is_summation_idx
struct	ex_base_is_less
class	terminfo
	This structure stores the original and symmetrized versions of terms obtained during the simplification of sums. More...
class	terminfo_is_less
class	symminfo
	This structure stores the individual symmetrized terms obtained during the simplification of sums. More...
class	symminfo_is_less_by_symmterm
class	symminfo_is_less_by_orig
class	indexed
	This class holds an indexed expression. More...
class	spmapkey
class	scalar_products
	Helper class for storing information about known scalar products which are to be automatically replaced by simplify_indexed(). More...
class	zeta1_SERIAL
	Complex conjugate. More...
class	zeta2_SERIAL
	Alternating Euler sum or colored MZV. More...
class	G2_SERIAL
	Generalized multiple polylogarithm. More...
class	G3_SERIAL
	Generalized multiple polylogarithm with explicit imaginary parts. More...
class	psi1_SERIAL
	Polylogarithm and multiple polylogarithm. More...
class	psi2_SERIAL
	Derivatives of Psi-function (aka polygamma-functions). More...
struct	error_and_integral
struct	error_and_integral_is_less
class	integral
	Symbolic integral. More...
class	matrix_init
	Helper template to allow initialization of matrices via an overloaded comma operator (idea stolen from Blitz++). More...
class	matrix
	Symbolic matrices. More...
class	mul
	Product of expressions. More...
class	ncmul
	Non-commutative product of expressions. More...
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	gcdheu_failed
	Exception thrown by heur_gcd() to signal failure. More...
struct	normal_map_function
	Function object to be applied by basic::normal(). More...
struct	gcd_options
	Flags to control the behaviour of gcd() and friends. More...
class	lanczos_coeffs
class	_numeric_digits
	This class is used to instantiate a global singleton object Digits which behaves just like Maple's Digits. More...
class	pole_error
	Exception class thrown when a singularity is encountered. More...
class	numeric
	This class is a wrapper around CLN-numbers within the GiNaC class hierarchy. More...
class	power
	This class holds a two-component object, a basis and and exponent representing exponentiation. More...
class	print_context_options
	This class stores information about a registered print_context class. More...
class	print_options
	Flags to control the behavior of a print_context. More...
class	print_context
	Base class for print_contexts. More...
class	print_dflt
	Context for default (ginsh-parsable) output. More...
class	print_latex
	Context for latex-parsable output. 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	print_csrc
	Base context for C source output. More...
class	print_csrc_float
	Context for C source output using float precision. More...
class	print_csrc_double
	Context for C source output using double precision. More...
class	print_csrc_cl_N
	Context for C source output using CLN numbers. More...
class	print_functor_impl
	Base class for print_functor handlers. More...
class	print_ptrfun_handler
	print_functor handler for pointer-to-functions of class T, context type C More...
class	print_memfun_handler
	print_functor handler for member functions of class T, context type C More...
class	print_functor
	This class represents a print method for a certain algebraic class and print_context type. More...
class	pseries
	This class holds a extended truncated power series (positive and negative integer powers). More...
class	refcounted
	Base class for reference-counted objects. More...
class	ptr
	Class of (intrusively) reference-counted pointers that support copy-on-write semantics. More...
struct	return_type_t
	To distinguish between different kinds of non-commutative 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_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...
class	remember_table
	The remember table is organized like an n-fold associative cache in a microprocessor. More...
class	compare_all_equal
	Comparison policy: all structures of one type are equal. More...
class	compare_std_less
	Comparison policy: use std::equal_to/std::less (defaults to operators == and <) to compare structures. More...
class	compare_bitwise
	Comparison policy: use bit-wise comparison to compare structures. More...
class	structure
	Wrapper template for making GiNaC classes out of C++ structures. More...
class	symbol
	Basic CAS symbol. More...
class	realsymbol
	Specialization of symbol to real domain. More...
class	possymbol
	Specialization of symbol to real positive domain. More...
class	sy_is_less
class	sy_swap
class	symmetry
	This class describes the symmetry of a group of indices. More...
class	tensor
	This class holds one of GiNaC's predefined special tensors such as the delta and the metric tensors. More...
class	tensdelta
	This class represents the delta tensor. More...
class	tensmetric
	This class represents a general metric tensor which can be used to raise/lower indices. More...
class	minkmetric
	This class represents a Minkowski metric tensor. 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	tensepsilon
	This class represents the totally antisymmetric epsilon tensor. More...
class	dunno
	Exception class thrown by functions to signal unimplemented functionality so the expression may just be .hold() More...
class	wildcard
	This class acts as a wildcard for subs(), match(), has() and find(). 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 std::list< epp >	epplist
	list of expair-vector pointers
typedef std::vector< epplist >	epplistvector
	vector of epplist
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(*	derivative_funcp )()
typedef ex(*	power_funcp )()
typedef ex(*	series_funcp )()
typedef void(*	print_funcp )()
typedef ex(*	eval_funcp_1 )(const ex &)
typedef ex(*	eval_funcp_2 )(const ex &, const ex &)
typedef ex(*	eval_funcp_3 )(const ex &, const ex &, const ex &)
typedef ex(*	eval_funcp_4 )(const ex &, const ex &, const ex &, const ex &)
typedef ex(*	eval_funcp_5 )(const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	eval_funcp_6 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	eval_funcp_7 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	eval_funcp_8 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
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(*	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(*	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(*	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(*	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(*	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_1 )(const ex &)
typedef ex(*	evalf_funcp_2 )(const ex &, const ex &)
typedef ex(*	evalf_funcp_3 )(const ex &, const ex &, const ex &)
typedef ex(*	evalf_funcp_4 )(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(*	evalf_funcp_6 )(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(*	evalf_funcp_8 )(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(*	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(*	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(*	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(*	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(*	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_1 )(const ex &)
typedef ex(*	conjugate_funcp_2 )(const ex &, const ex &)
typedef ex(*	conjugate_funcp_3 )(const ex &, const ex &, const ex &)
typedef ex(*	conjugate_funcp_4 )(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(*	conjugate_funcp_6 )(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(*	conjugate_funcp_8 )(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(*	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(*	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(*	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(*	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(*	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_1 )(const ex &)
typedef ex(*	real_part_funcp_2 )(const ex &, const ex &)
typedef ex(*	real_part_funcp_3 )(const ex &, const ex &, const ex &)
typedef ex(*	real_part_funcp_4 )(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(*	real_part_funcp_6 )(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(*	real_part_funcp_8 )(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(*	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(*	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(*	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(*	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(*	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_1 )(const ex &)
typedef ex(*	imag_part_funcp_2 )(const ex &, const ex &)
typedef ex(*	imag_part_funcp_3 )(const ex &, const ex &, const ex &)
typedef ex(*	imag_part_funcp_4 )(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(*	imag_part_funcp_6 )(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(*	imag_part_funcp_8 )(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(*	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(*	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(*	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(*	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(*	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(*	derivative_funcp_1 )(const ex &, unsigned)
typedef ex(*	derivative_funcp_2 )(const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_3 )(const ex &, const ex &, const ex &, unsigned)
typedef ex(*	derivative_funcp_4 )(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(*	derivative_funcp_6 )(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(*	derivative_funcp_8 )(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(*	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(*	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(*	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(*	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(*	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(*	power_funcp_1 )(const ex &, const ex &)
typedef ex(*	power_funcp_2 )(const ex &, const ex &, const ex &)
typedef ex(*	power_funcp_3 )(const ex &, const ex &, const ex &, const ex &)
typedef ex(*	power_funcp_4 )(const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	power_funcp_5 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	power_funcp_6 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
typedef ex(*	power_funcp_7 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &)
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(*	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(*	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(*	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(*	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(*	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(*	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_1 )(const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_2 )(const ex &, const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_3 )(const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_4 )(const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_5 )(const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_6 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
typedef ex(*	series_funcp_7 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const relational &, int, unsigned)
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 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 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 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 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 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 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_1 )(const ex &, const print_context &)
typedef void(*	print_funcp_2 )(const ex &, const ex &, const print_context &)
typedef void(*	print_funcp_3 )(const ex &, const ex &, const ex &, const print_context &)
typedef void(*	print_funcp_4 )(const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef void(*	print_funcp_5 )(const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef void(*	print_funcp_6 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
typedef void(*	print_funcp_7 )(const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const ex &, const print_context &)
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 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 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 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 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 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 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 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(*	derivative_funcp_exvector )(const exvector &, unsigned)
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 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
typedef unsigned long	p_int
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.
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (clifford, indexed, print_func< print_dflt >(&clifford::do_print_dflt).print_func< print_latex >(&clifford::do_print_latex)) 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 (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_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)
static ex	get_clifford_comp (const ex &e, const ex &c)
	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 (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, coincides with the conjugate().
	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).
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, int level=0)
ex	to_rational (const ex &thisex, lst &repl_lst)
ex	to_rational (const ex &thisex, exmap &repl)
ex	to_polynomial (const ex &thisex, exmap &repl)
ex	to_polynomial (const ex &thisex, lst &repl_lst)
ex	collect (const ex &thisex, const ex &s, bool distributed=false)
ex	eval (const ex &thisex, int level=0)
ex	evalf (const ex &thisex, int level=0)
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 >
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)
void	iter_swap (std::vector< expair >::iterator i1, std::vector< expair >::iterator i2)
	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.
template<>
	GINAC_IMPLEMENT_REGISTERED_CLASS_OPT_T (exprseq, basic, print_func< print_context >(&exprseq::do_print).print_func< print_tree >(&exprseq::do_print_tree)) template<> bool exprseq
	Specialization of container::info() for exprseq.
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_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)
	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_real_part (const ex &arg)
static ex	conjugate_imag_part (const ex &arg)
	REGISTER_FUNCTION (conjugate_function, eval_func(conjugate_eval).evalf_func(conjugate_evalf).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)
	REGISTER_FUNCTION (real_part_function, eval_func(real_part_eval).evalf_func(real_part_evalf).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)
	REGISTER_FUNCTION (imag_part_function, eval_func(imag_part_eval).evalf_func(imag_part_evalf).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 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)
	REGISTER_FUNCTION (abs, eval_func(abs_eval).evalf_func(abs_evalf).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)
	REGISTER_FUNCTION (Order, eval_func(Order_eval).series_func(Order_series).latex_name("\\mathcal{O}").conjugate_func(Order_conjugate).real_part_func(Order_real_part).imag_part_func(Order_imag_part))
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)
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	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_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)
	REGISTER_FUNCTION (exp, eval_func(exp_eval).evalf_func(exp_evalf).derivative_func(exp_deriv).real_part_func(exp_real_part).imag_part_func(exp_imag_part).conjugate_func(exp_conjugate).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_conjugate (const ex &x)
	REGISTER_FUNCTION (log, eval_func(log_eval).evalf_func(log_evalf).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)
	REGISTER_FUNCTION (sin, eval_func(sin_eval).evalf_func(sin_evalf).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).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).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)
	REGISTER_FUNCTION (asin, eval_func(asin_eval).evalf_func(asin_evalf).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).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)
	REGISTER_FUNCTION (atan, eval_func(atan_eval).evalf_func(atan_evalf).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)
	REGISTER_FUNCTION (atan2, eval_func(atan2_eval).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).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).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).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).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).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).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_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)
	GINAC_BIND_UNARCHIVER (lst)
	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	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	eval (const matrix &m, int level=0)
ex	evalf (const matrix &m, int level=0)
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)
unsigned	rank (const matrix &m)
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 wheter 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 exvector	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)
	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 const 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 together.
static const ex	exmul (const ex &lh, const ex &rh)
	Used internally by operator*() to multiply two ex objects together.
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)
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 permuation 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)
template<class T >
std::string	ToString (const T &t)
unsigned	log2 (unsigned n)
	Integer binary logarithm.
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 (p_int 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)
	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
int	max_recursion_level = 1024
	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
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_120
const numeric *	_num_60_p
const ex	_ex_60 = _ex_60
const numeric *	_num_48_p
const ex	_ex_48 = _ex_48
const numeric *	_num_30_p
const ex	_ex_30 = _ex_30
const numeric *	_num_25_p
const ex	_ex_25 = _ex_25
const numeric *	_num_24_p
const ex	_ex_24 = _ex_24
const numeric *	_num_20_p
const ex	_ex_20 = _ex_20
const numeric *	_num_18_p
const ex	_ex_18 = _ex_18
const numeric *	_num_15_p
const ex	_ex_15 = _ex_15
const numeric *	_num_12_p
const ex	_ex_12 = _ex_12
const numeric *	_num_11_p
const ex	_ex_11 = _ex_11
const numeric *	_num_10_p
const ex	_ex_10 = _ex_10
const numeric *	_num_9_p
const ex	_ex_9 = _ex_9
const numeric *	_num_8_p
const ex	_ex_8 = _ex_8
const numeric *	_num_7_p
const ex	_ex_7 = _ex_7
const numeric *	_num_6_p
const ex	_ex_6 = _ex_6
const numeric *	_num_5_p
const ex	_ex_5 = _ex_5
const numeric *	_num_4_p
const ex	_ex_4 = _ex_4
const numeric *	_num_3_p
const ex	_ex_3 = _ex_3
const numeric *	_num_2_p
const ex	_ex_2 = _ex_2
const numeric *	_num_1_p
const ex	_ex_1 = _ex_1
const numeric *	_num_1_2_p
const ex	_ex_1_2 = _ex_1_2
const numeric *	_num_1_3_p
const ex	_ex_1_3 = _ex_1_3
const numeric *	_num_1_4_p
const ex	_ex_1_4 = _ex_1_4
const numeric *	_num0_p
const ex	_ex0 = _ex0
const numeric *	_num1_4_p
const ex	_ex1_4 = _ex1_4
const numeric *	_num1_3_p
const ex	_ex1_3 = _ex1_3
const numeric *	_num1_2_p
const ex	_ex1_2 = _ex1_2
const numeric *	_num1_p
const ex	_ex1 = _ex1
const numeric *	_num2_p
const ex	_ex2 = _ex2
const numeric *	_num3_p
const ex	_ex3 = _ex3
const numeric *	_num4_p
const ex	_ex4 = _ex4
const numeric *	_num5_p
const ex	_ex5 = _ex5
const numeric *	_num6_p
const ex	_ex6 = _ex6
const numeric *	_num7_p
const ex	_ex7 = _ex7
const numeric *	_num8_p
const ex	_ex8 = _ex8
const numeric *	_num9_p
const ex	_ex9 = _ex9
const numeric *	_num10_p
const ex	_ex10 = _ex10
const numeric *	_num11_p
const ex	_ex11 = _ex11
const numeric *	_num12_p
const ex	_ex12 = _ex12
const numeric *	_num15_p
const ex	_ex15 = _ex15
const numeric *	_num18_p
const ex	_ex18 = _ex18
const numeric *	_num20_p
const ex	_ex20 = _ex20
const numeric *	_num24_p
const ex	_ex24 = _ex24
const numeric *	_num25_p
const ex	_ex25 = _ex25
const numeric *	_num30_p
const ex	_ex30 = _ex30
const numeric *	_num48_p
const ex	_ex48 = _ex48
const numeric *	_num60_p
const ex	_ex60 = _ex60
const numeric *	_num120_p
const ex	_ex120 = _ex120

---

Detailed Description

CRC32 hash function.

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

Shamelessly stolen from GNU coreutils (cksum.c)

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 got more hash collisions (and slower evaluation as a result), but being a bit slower is much better than being wrong.

---

Typedef Documentation

typedef unsigned GiNaC::archive_node_id

Numerical ID value to refer to an archive_node.

Definition at line 35 of file archive.h.

typedef unsigned GiNaC::archive_atom

Numerical ID value to refer to a string.

Definition at line 42 of file archive.h.

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

Definition at line 161 of file archive.h.

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

Definition at line 162 of file archive.h.

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

Definition at line 47 of file basic.h.

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

Definition at line 50 of file basic.h.

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

Definition at line 51 of file basic.h.

typedef ex(* GiNaC::evalffunctype)()

Definition at line 34 of file constant.h.

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

Function pointer with one function parameter.

Definition at line 39 of file excompiler.h.

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

Function pointer with two function parameters.

Definition at line 44 of file excompiler.h.

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.

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

expair-vector

Definition at line 48 of file expairseq.h.

typedef epvector::iterator GiNaC::epp

expair-vector pointer

Definition at line 49 of file expairseq.h.

typedef std::list<epp> GiNaC::epplist

list of expair-vector pointers

Definition at line 50 of file expairseq.h.

typedef std::vector<epplist> GiNaC::epplistvector

vector of epplist

Definition at line 51 of file expairseq.h.

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

Definition at line 32 of file exprseq.h.

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

Definition at line 32 of file fderivative.h.

typedef ex(* GiNaC::eval_funcp)()

Definition at line 148 of file function.h.

typedef ex(* GiNaC::evalf_funcp)()

Definition at line 149 of file function.h.

typedef ex(* GiNaC::conjugate_funcp)()

Definition at line 150 of file function.h.

typedef ex(* GiNaC::real_part_funcp)()

Definition at line 151 of file function.h.

typedef ex(* GiNaC::imag_part_funcp)()

Definition at line 152 of file function.h.

typedef ex(* GiNaC::derivative_funcp)()

Definition at line 153 of file function.h.

typedef ex(* GiNaC::power_funcp)()

Definition at line 154 of file function.h.

typedef ex(* GiNaC::series_funcp)()

Definition at line 155 of file function.h.

typedef void(* GiNaC::print_funcp)()

Definition at line 156 of file function.h.

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

Definition at line 159 of file function.h.

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

Definition at line 160 of file function.h.

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

Definition at line 161 of file function.h.

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

Definition at line 162 of file function.h.

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

Definition at line 163 of file function.h.

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

Definition at line 164 of file function.h.

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

Definition at line 165 of file function.h.

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 166 of file function.h.

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 167 of file function.h.

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 168 of file function.h.

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 169 of file function.h.

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 170 of file function.h.

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 171 of file function.h.

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 172 of file function.h.

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

Definition at line 174 of file function.h.

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

Definition at line 175 of file function.h.

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

Definition at line 176 of file function.h.

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

Definition at line 177 of file function.h.

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

Definition at line 178 of file function.h.

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

Definition at line 179 of file function.h.

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

Definition at line 180 of file function.h.

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 181 of file function.h.

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 182 of file function.h.

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 183 of file function.h.

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 184 of file function.h.

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 185 of file function.h.

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 186 of file function.h.

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 187 of file function.h.

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

Definition at line 189 of file function.h.

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

Definition at line 190 of file function.h.

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

Definition at line 191 of file function.h.

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

Definition at line 192 of file function.h.

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

Definition at line 193 of file function.h.

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

Definition at line 194 of file function.h.

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

Definition at line 195 of file function.h.

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 196 of file function.h.

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 197 of file function.h.

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 198 of file function.h.

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 199 of file function.h.

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 200 of file function.h.

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 201 of file function.h.

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 202 of file function.h.

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

Definition at line 204 of file function.h.

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

Definition at line 205 of file function.h.

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

Definition at line 206 of file function.h.

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

Definition at line 207 of file function.h.

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

Definition at line 208 of file function.h.

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

Definition at line 209 of file function.h.

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

Definition at line 210 of file function.h.

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 211 of file function.h.

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 212 of file function.h.

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 213 of file function.h.

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 214 of file function.h.

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 215 of file function.h.

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 216 of file function.h.

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 217 of file function.h.

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

Definition at line 219 of file function.h.

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

Definition at line 220 of file function.h.

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

Definition at line 221 of file function.h.

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

Definition at line 222 of file function.h.

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

Definition at line 223 of file function.h.

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

Definition at line 224 of file function.h.

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

Definition at line 225 of file function.h.

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 226 of file function.h.

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 227 of file function.h.

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 228 of file function.h.

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 229 of file function.h.

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 230 of file function.h.

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 231 of file function.h.

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 232 of file function.h.

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

Definition at line 234 of file function.h.

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

Definition at line 235 of file function.h.

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

Definition at line 236 of file function.h.

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

Definition at line 237 of file function.h.

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

Definition at line 238 of file function.h.

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

Definition at line 239 of file function.h.

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

Definition at line 240 of file function.h.

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 241 of file function.h.

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 242 of file function.h.

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 243 of file function.h.

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 244 of file function.h.

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 245 of file function.h.

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 246 of file function.h.

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 247 of file function.h.

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

Definition at line 249 of file function.h.

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

Definition at line 250 of file function.h.

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

Definition at line 251 of file function.h.

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

Definition at line 252 of file function.h.

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

Definition at line 253 of file function.h.

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

Definition at line 254 of file function.h.

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 255 of file function.h.

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 256 of file function.h.

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 257 of file function.h.

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 258 of file function.h.

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 259 of file function.h.

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 260 of file function.h.

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 261 of file function.h.

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 262 of file function.h.

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

Definition at line 264 of file function.h.

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

Definition at line 265 of file function.h.

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

Definition at line 266 of file function.h.

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

Definition at line 267 of file function.h.

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

Definition at line 268 of file function.h.

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 269 of file function.h.

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 270 of file function.h.

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 271 of file function.h.

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 272 of file function.h.

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 273 of file function.h.

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 274 of file function.h.

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 275 of file function.h.

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 276 of file function.h.

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 277 of file function.h.

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

Definition at line 279 of file function.h.

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

Definition at line 280 of file function.h.

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

Definition at line 281 of file function.h.

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

Definition at line 282 of file function.h.

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

Definition at line 283 of file function.h.

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

Definition at line 284 of file function.h.

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 285 of file function.h.

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 286 of file function.h.

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 287 of file function.h.

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 288 of file function.h.

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 289 of file function.h.

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 290 of file function.h.

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 291 of file function.h.

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 292 of file function.h.

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

Definition at line 298 of file function.h.

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

Definition at line 299 of file function.h.

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

Definition at line 300 of file function.h.

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

Definition at line 301 of file function.h.

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

Definition at line 302 of file function.h.

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

Definition at line 303 of file function.h.

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

Definition at line 304 of file function.h.

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

Definition at line 305 of file function.h.

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

Definition at line 306 of file function.h.

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

Definition at line 221 of file indexed.h.

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

Definition at line 234 of file integral.cpp.

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

Definition at line 32 of file lst.h.

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

Definition at line 118 of file ncmul.cpp.

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

Definition at line 290 of file ncmul.cpp.

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

Definition at line 291 of file ncmul.cpp.

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

Definition at line 155 of file normal.cpp.

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 46 of file numeric.h.

typedef class_info<print_context_options> GiNaC::print_context_class_info

Definition at line 50 of file print.h.

typedef class_info<registered_class_options> GiNaC::registered_class_info

Definition at line 126 of file registrar.h.

typedef unsigned long GiNaC::p_int

Definition at line 75 of file utils.h.

---

Enumeration Type Documentation

anonymous enum

Enumerator:

callback_registered

Definition at line 298 of file operators.cpp.

---

Function Documentation

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 40 of file add.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

add

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

add

)

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

Write unsigned integer quantity to stream.

Definition at line 175 of file archive.cpp.

Referenced by operator<<().

static unsigned GiNaC::read_unsigned

(

std::istream &

is

)

[static]

Read unsigned integer quantity from stream.

Definition at line 185 of file archive.cpp.

Referenced by operator>>().

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

Write archive_node to binary data stream.

Definition at line 201 of file archive.cpp.

References GiNaC::archive_node::props, and write_unsigned().

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

Write archive to binary data stream.

Definition at line 214 of file archive.cpp.

References GiNaC::archive::atoms, GiNaC::archive::exprs, GiNaC::archive::nodes, and write_unsigned().

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

Read archive_node from binary data stream.

Definition at line 246 of file archive.cpp.

References GiNaC::archive_node::props, and read_unsigned().

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

Read archive from binary data stream.

Definition at line 261 of file archive.cpp.

References GiNaC::archive::atoms, GiNaC::archive::exprs, GiNaC::archive::inverse_atoms, GiNaC::archive::nodes, read_unsigned(), and ToString().

static synthesize_func GiNaC::find_factory_fcn

(

const std::string &

name

)

[static]

Definition at line 519 of file archive.cpp.

References GiNaC::unarchive_table_t::find().

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

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.

template<class T >

bool GiNaC::is_a

(

const basic &

obj

)

[inline]

Check if obj is a T, including base classes.

Definition at line 311 of file basic.h.

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

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 318 of file basic.h.

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

GiNaC::print_func< print_dflt >

(

&diracone::do_print

)

Definition at line 50 of file clifford.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

clifford

)

GiNaC::GINAC_BIND_UNARCHIVER

(

diracone

)

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgamma

)

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgamma5

)

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgammaL

)

GiNaC::GINAC_BIND_UNARCHIVER

(

diracgammaR

)

static bool GiNaC::is_dirac_slash

(

const ex &

seq0

)

[static]

Definition at line 253 of file clifford.cpp.

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

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 311 of file clifford.cpp.

ex GiNaC::dirac_ONE

(

unsigned char

rl = 0

)

Create a Clifford unity object.

Parameters:

rl	Representation label

Returns:

newly constructed object

Definition at line 711 of file clifford.cpp.

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

static unsigned GiNaC::get_dim_uint

(

const ex &

e

)

[static]

Definition at line 717 of file clifford.cpp.

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 728 of file clifford.cpp.

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 771 of file clifford.cpp.

ex GiNaC::dirac_gamma5

(

unsigned char

rl = 0

)

Create a Dirac gamma5 object.

Parameters:

rl	Representation label

Returns:

newly constructed object

Definition at line 783 of file clifford.cpp.

ex GiNaC::dirac_gammaL

(

unsigned char

rl = 0

)

Create a Dirac gammaL object.

Parameters:

rl	Representation label

Returns:

newly constructed object

Definition at line 789 of file clifford.cpp.

ex GiNaC::dirac_gammaR

(

unsigned char

rl = 0

)

Create a Dirac gammaR object.

Parameters:

rl	Representation label

Returns:

newly constructed object

Definition at line 795 of file clifford.cpp.

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 801 of file clifford.cpp.

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 814 of file clifford.cpp.

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 821 of file clifford.cpp.

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 855 of file clifford.cpp.

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 992 of file clifford.cpp.

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 1004 of file clifford.cpp.

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 1014 of file clifford.cpp.

ex GiNaC::clifford_prime

(

const ex &

e

)

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

Definition at line 1080 of file clifford.cpp.

Referenced by clifford_bar().

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 1094 of file clifford.cpp.

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 defines if clifford_ONE should be ignored in the search

Definition at line 1135 of file clifford.cpp.

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

ex GiNaC::clifford_norm

(

const ex &

e

)

Calculation of the norm in the Clifford algebra.

Definition at line 1150 of file clifford.cpp.

ex GiNaC::clifford_inverse

(

const ex &

e

)

Calculation of the inverse in the Clifford algebra.

Definition at line 1155 of file clifford.cpp.

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
e	Clifford unit object

Returns:

Clifford vector with given components

Definition at line 1164 of file clifford.cpp.

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

Definition at line 1172 of file clifford.cpp.

static ex GiNaC::get_clifford_comp	(	const ex &	e,
		const ex &	c
	)		[static]

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

Used in clifford_to_lst().

Definition at line 1216 of file clifford.cpp.

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 1285 of file clifford.cpp.

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 1329 of file clifford.cpp.

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 1356 of file clifford.cpp.

GiNaC::GINAC_DECLARE_UNARCHIVER

(

clifford

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracone

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgamma

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgamma5

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgammaL

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

diracgammaR

)

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 192 of file clifford.h.

References GiNaC::return_type_t::tinfo.

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

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 285 of file clifford.h.

References clifford_prime(), and GiNaC::ex::conjugate().

ex GiNaC::clifford_star

(

const ex &

e

)

[inline]

Reversion of the Clifford algebra, coincides with the conjugate().

Definition at line 288 of file clifford.h.

References GiNaC::ex::conjugate().

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

GiNaC::print_func< print_dflt >

(

&su3t::do_print

)

Definition at line 47 of file color.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

color

)

GiNaC::GINAC_BIND_UNARCHIVER

(

su3one

)

GiNaC::GINAC_BIND_UNARCHIVER

(

su3t

)

GiNaC::GINAC_BIND_UNARCHIVER

(

su3f

)

GiNaC::GINAC_BIND_UNARCHIVER

(

su3d

)

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	Returs sign introduced by index permutation

Returns:

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

Definition at line 200 of file color.cpp.

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 477 of file color.cpp.

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 483 of file color.cpp.

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 495 of file color.cpp.

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 507 of file color.cpp.

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 519 of file color.cpp.

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 526 of file color.cpp.

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 538 of file color.cpp.

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 624 of file color.cpp.

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 636 of file color.cpp.

GiNaC::GINAC_DECLARE_UNARCHIVER

(

color

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3one

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3t

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3f

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

su3d

)

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 36 of file constant.cpp.

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

GiNaC::GINAC_BIND_UNARCHIVER

(

constant

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

constant

)

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

Definition at line 64 of file crc32.h.

References crctab, and len.

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 669 of file ex.h.

References GiNaC::ex::bp.

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

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

Definition at line 353 of file operators.cpp.

References get_print_context().

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

Definition at line 380 of file operators.cpp.

References get_print_context().

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

Definition at line 407 of file operators.cpp.

References get_print_context().

size_t GiNaC::nops

(

const ex &

thisex

)

[inline]

Definition at line 697 of file ex.h.

References GiNaC::ex::nops().

Referenced by GiNaC::mul::algebraic_subs_mul(), GiNaC::mul::do_print_python_repr(), GiNaC::container< C >::do_print_tree(), GiNaC::mul::has(), GiNaC::container< C >::let_op(), and GiNaC::container< C >::op().

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

Definition at line 700 of file ex.h.

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

Referenced by divide(), divide_in_z(), GiNaC::indexed::expand(), gcd(), prem(), quo(), rem(), and sprem().

ex GiNaC::conjugate

(

const ex &

thisex

)

[inline]

Definition at line 703 of file ex.h.

References GiNaC::ex::conjugate().

Referenced by GiNaC::numeric::conjugate(), and conjugate_evalf().

ex GiNaC::real_part

(

const ex &

thisex

)

[inline]

Definition at line 706 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(), 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().

ex GiNaC::imag_part

(

const ex &

thisex

)

[inline]

Definition at line 709 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(), 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().

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

Definition at line 712 of file ex.h.

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

Referenced by GiNaC::mul::has().

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

Definition at line 715 of file ex.h.

References GiNaC::ex::find().

Referenced by GiNaC::exhashmap< T, A >::erase().

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

Definition at line 718 of file ex.h.

References GiNaC::ex::is_polynomial().

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

Definition at line 721 of file ex.h.

References GiNaC::ex::degree().

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

Definition at line 724 of file ex.h.

References GiNaC::ex::ldegree().

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

Definition at line 727 of file ex.h.

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

Referenced by GiNaC::mul::eval(), log_series(), and simplify_indexed().

ex GiNaC::numer

(

const ex &

thisex

)

[inline]

Definition at line 730 of file ex.h.

References GiNaC::ex::numer().

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

ex GiNaC::denom

(

const ex &

thisex

)

[inline]

Definition at line 733 of file ex.h.

References GiNaC::ex::denom().

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

ex GiNaC::numer_denom

(

const ex &

thisex

)

[inline]

Definition at line 736 of file ex.h.

References GiNaC::ex::numer_denom().

Referenced by decomp_rational(), and sqrfree_parfrac().

ex GiNaC::normal	(	const ex &	thisex,
		int	level = 0
	)		[inline]

Definition at line 739 of file ex.h.

References GiNaC::ex::normal().

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

ex GiNaC::to_rational	(	const ex &	thisex,
		lst &	repl_lst
	)		[inline]

Definition at line 742 of file ex.h.

References GiNaC::ex::to_rational().

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

Definition at line 745 of file ex.h.

References GiNaC::ex::to_rational().

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

Definition at line 748 of file ex.h.

References GiNaC::ex::to_polynomial().

ex GiNaC::to_polynomial	(	const ex &	thisex,
		lst &	repl_lst
	)		[inline]

Definition at line 751 of file ex.h.

References GiNaC::ex::to_polynomial().

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

Definition at line 754 of file ex.h.

References GiNaC::ex::collect().

ex GiNaC::eval	(	const ex &	thisex,
		int	level = 0
	)		[inline]

Definition at line 757 of file ex.h.

References GiNaC::ex::eval().

ex GiNaC::evalf	(	const ex &	thisex,
		int	level = 0
	)		[inline]

Definition at line 760 of file ex.h.

References GiNaC::ex::evalf().

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

ex GiNaC::evalm

(

const ex &

thisex

)

[inline]

Definition at line 763 of file ex.h.

References GiNaC::ex::evalm().

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

ex GiNaC::eval_integ

(

const ex &

thisex

)

[inline]

Definition at line 766 of file ex.h.

References GiNaC::ex::eval_integ().

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

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

Definition at line 769 of file ex.h.

References GiNaC::ex::diff().

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

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

Definition at line 772 of file ex.h.

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

Referenced by atan_series(), atanh_series(), lgamma_series(), Li2_series(), log_series(), psi1_series(), and tgamma_series().

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

Definition at line 775 of file ex.h.

References GiNaC::ex::match().

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

Definition at line 778 of file ex.h.

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

Referenced by simplify_indexed(), and simplify_indexed_product().

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

Definition at line 781 of file ex.h.

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

ex GiNaC::symmetrize

(

const ex &

thisex

)

[inline]

Definition at line 784 of file ex.h.

References GiNaC::ex::symmetrize().

Referenced by idx_symmetrization(), symmetrize(), and symmetrize_cyclic().

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

Definition at line 787 of file ex.h.

References GiNaC::ex::symmetrize().

ex GiNaC::antisymmetrize

(

const ex &

thisex

)

[inline]

Definition at line 790 of file ex.h.

References GiNaC::ex::antisymmetrize().

Referenced by antisymmetrize().

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

Definition at line 793 of file ex.h.

References GiNaC::ex::antisymmetrize().

ex GiNaC::symmetrize_cyclic

(

const ex &

thisex

)

[inline]

Definition at line 796 of file ex.h.

References GiNaC::ex::symmetrize_cyclic().

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

Definition at line 799 of file ex.h.

References GiNaC::ex::symmetrize_cyclic().

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

Definition at line 802 of file ex.h.

References GiNaC::ex::op().

Referenced by GiNaC::mul::algebraic_subs_mul(), and GiNaC::mul::do_print_python_repr().

ex GiNaC::lhs

(

const ex &

thisex

)

[inline]

Definition at line 805 of file ex.h.

References GiNaC::ex::lhs().

ex GiNaC::rhs

(

const ex &

thisex

)

[inline]

Definition at line 808 of file ex.h.

References GiNaC::ex::rhs().

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

bool GiNaC::is_zero

(

const ex &

thisex

)

[inline]

Definition at line 811 of file ex.h.

References GiNaC::ex::is_zero().

Referenced by GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::power::eval(), GiNaC::tensepsilon::eval_indexed(), GiNaC::matrix::fraction_free_elimination(), GiNaC::matrix::gauss_elimination(), GiNaC::matrix::mul(), GiNaC::relational::operator safe_bool(), GiNaC::matrix::pivot(), and GiNaC::clifford::same_metric().

void GiNaC::swap	(	ex &	e1,
		ex &	e2
	)		[inline]

Definition at line 814 of file ex.h.

References GiNaC::ex::swap().

Referenced by GiNaC::matrix::pivot().

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

Definition at line 822 of file ex.h.

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

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

Definition at line 825 of file ex.h.

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

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

Definition at line 828 of file ex.h.

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

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 930 of file ex.h.

References GiNaC::ex::bp.

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 937 of file ex.h.

References GiNaC::ex::bp.

template<class T >

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 953 of file ex.h.

References GiNaC::ex::bp, and GINAC_ASSERT.

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 313 of file excompiler.cpp.

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
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 318 of file excompiler.cpp.

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:

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.

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 328 of file excompiler.cpp.

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 333 of file excompiler.cpp.

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 338 of file excompiler.cpp.

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 343 of file excompiler.cpp.

void GiNaC::swap	(	expair &	e1,
		expair &	e2
	)		[inline]

Definition at line 111 of file expair.h.

References GiNaC::expair::swap().

void GiNaC::iter_swap	(	std::vector< expair >::iterator	i1,
		std::vector< expair >::iterator	i2
	)		[inline]

Definition at line 115 of file expair.h.

Referenced by permutation_sign().

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

Definition at line 48 of file expairseq.cpp.

epvector * GiNaC::conjugateepvector

(

const epvector &

)

Complex conjugate every element of an epvector.

Returns zero if this does not change anything.

Definition at line 344 of file expairseq.cpp.

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

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

template<>

GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT_T	(	exprseq	,
		basic	,
		print_func< print_context > &::do_print.print_func< print_tree > &::do_print_tree
	)

Specialization of container::info() for exprseq.

Specialization of container::info() for lst.

Definition at line 27 of file exprseq.cpp.

References GiNaC::info_flags::exprseq.

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

Interface function to the outside world.

Factorizes univariate and multivariate polynomials.

It checks the arguments, tries a square free factorization, and then calls factor_sqrfree to do the hard work.

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]	option	options to influence the factorization

Returns:

factorized expression

Definition at line 2529 of file factor.cpp.

References GiNaC::container< C >::append(), GiNaC::ex::expand(), GiNaC::ex::info(), GiNaC::ex::nops(), GiNaC::ex::op(), poly, pow(), sqrfree(), and syms.

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

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

GiNaC::GINAC_DECLARE_UNARCHIVER

(

fail

)

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

Definition at line 32 of file fderivative.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

fderivative

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

fderivative

)

GiNaC::GINAC_BIND_UNARCHIVER

(

function

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

function

)

template<typename T >

bool GiNaC::is_the_function

(

const ex &

x

)

[inline]

Definition at line 701 of file function.h.

References x.

static unsigned GiNaC::make_hash_seed

(

const std::type_info &

tinfo

)

[inline, static]

Definition at line 27 of file hash_seed.h.

References golden_ratio_hash().

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

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
	)

GiNaC::print_func< print_context >

(

&varidx::do_print

)

Definition at line 45 of file idx.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

idx

)

GiNaC::GINAC_BIND_UNARCHIVER

(

varidx

)

GiNaC::GINAC_BIND_UNARCHIVER

(

spinidx

)

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

Check whether two indices form a dummy pair.

Definition at line 503 of file idx.cpp.

References GiNaC::idx::is_dummy_pair_same_type().

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

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

Check whether two expressions form a dummy index pair.

Definition at line 513 of file idx.cpp.

References is_dummy_pair().

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 522 of file idx.cpp.

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

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

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 562 of file idx.cpp.

References GiNaC::ex::is_equal().

Referenced by simplify_indexed_product().

GiNaC::GINAC_DECLARE_UNARCHIVER

(

idx

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

varidx

)

GiNaC::GINAC_DECLARE_UNARCHIVER

(

spinidx

)

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 239 of file idx.h.

References find_free_and_dummy().

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 248 of file idx.h.

References find_free_and_dummy().

Referenced by GiNaC::indexed::get_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 255 of file idx.h.

References find_free_and_dummy().

size_t GiNaC::count_free_indices

(

const exvector &

v

)

[inline]

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

Definition at line 263 of file idx.h.

References find_free_and_dummy().

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 47 of file indexed.cpp.

GiNaC::GINAC_BIND_UNARCHIVER

(

indexed

)

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 423 of file indexed.cpp.

Referenced by GiNaC::add::get_free_indices(), and simplify_indexed().

template<class T >

size_t GiNaC::number_of_type

(

const exvector &

v

)

Definition at line 532 of file indexed.cpp.

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 549 of file indexed.cpp.

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

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 609 of file indexed.cpp.

Referenced by simplify_indexed(), and simplify_indexed_product().

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 625 of file indexed.cpp.

References is_dummy_pair(), k, m, GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::ex::op(), and GiNaC::ex::subs().

Referenced by simplify_indexed(), and simplify_indexed_product().

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

Definition at line 740 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(), and simplify_indexed_product().

template<class T >

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

Definition at line 771 of file indexed.cpp.

References GiNaC::ex::nops(), and symmetrize().

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.

References _ex2, GiNaC::ex::coeff(), coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::expand(), find_free_and_dummy(), find_variant_indices(), hasindex(), indices_consistent(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), k, GiNaC::ex::nops(), GiNaC::ex::op(), reposition_dummy_indices(), GiNaC::container_storage< C >::seq, simplify_indexed(), and 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 788 of file indexed.cpp.

References _ex0, _ex1, GiNaC::return_types::commutative, GiNaC::scalar_products::evaluate(), find_free_and_dummy(), find_variant_indices(), GINAC_ASSERT, GiNaC::scalar_products::is_defined(), GiNaC::ex::is_zero(), minimal_dim(), product_to_exvector(), r, reposition_dummy_indices(), and simplify_indexed().

Referenced by simplify_indexed().

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

Definition at line 1033 of file indexed.cpp.

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

Referenced by simplify_indexed().

exvector GiNaC::get_all_dummy_indices_safely

(

const ex &

e

)

More reliable version of the form.

The former assumes that e is an expanded epxression.

Definition at line 1397 of file indexed.cpp.

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

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

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 1438 of file indexed.cpp.

References product_to_exvector().

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

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 1463 of file indexed.cpp.

References GiNaC::status_flags::dynallocated, and idx.

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

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 1501 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().

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 1507 of file indexed.cpp.

References get_all_dummy_indices_safely(), GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, rename_dummy_indices_uniquely(), and GiNaC::ex::subs().

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 1523 of file indexed.cpp.

References get_all_dummy_indices_safely(), GiNaC::subs_options::no_index_renaming, GiNaC::subs_options::no_pattern, rename_dummy_indices_uniquely(), and GiNaC::ex::subs().

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 indixes should be neglected

Definition at line 1550 of file indexed.cpp.

References GiNaC::ex::expand(), get_all_dummy_indices(), idx, GiNaC::ex::map(), GiNaC::info_flags::nonnegint, GiNaC::ex::op(), GiNaC::ex::subs(), and to_int().

GiNaC::GINAC_DECLARE_UNARCHIVER

(

indexed

)

static ex GiNaC::conjugate_evalf

(

const ex &

arg

)

[static]

Definition at line 46 of file inifcns.cpp.

References conjugate().

static ex GiNaC::conjugate_eval

(

const ex &

arg

)

[static]

Definition at line 54 of file inifcns.cpp.

References GiNaC::ex::conjugate().

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

Definition at line 59 of file inifcns.cpp.

References GiNaC::ex::print(), and GiNaC::print_context::s.

static ex GiNaC::conjugate_conjugate

(

const ex &

arg

)

[static]

Definition at line 64 of file inifcns.cpp.

static ex GiNaC::conjugate_real_part

(

const ex &

arg

)

[static]

Definition at line 69 of file inifcns.cpp.

References GiNaC::ex::real_part().

static ex GiNaC::conjugate_imag_part

(

const ex &

arg

)

[static]

Definition at line 74 of file inifcns.cpp.

References GiNaC::ex::imag_part().

GiNaC::REGISTER_FUNCTION	(	conjugate_function	,
		eval_func(conjugate_eval).evalf_func(conjugate_evalf).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 GiNaC::real_part_evalf

(

const ex &

arg

)

[static]

Definition at line 91 of file inifcns.cpp.

References real().

static ex GiNaC::real_part_eval

(

const ex &

arg

)

[static]

Definition at line 99 of file inifcns.cpp.

References GiNaC::ex::real_part().

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

Definition at line 104 of file inifcns.cpp.

References GiNaC::ex::print(), and GiNaC::print_context::s.

static ex GiNaC::real_part_conjugate

(

const ex &

arg

)

[static]

Definition at line 109 of file inifcns.cpp.

static ex GiNaC::real_part_real_part

(

const ex &

arg

)

[static]

Definition at line 114 of file inifcns.cpp.

static ex GiNaC::real_part_imag_part

(

const ex &

arg

)

[static]

Definition at line 119 of file inifcns.cpp.

GiNaC::REGISTER_FUNCTION	(	real_part_function	,
		eval_func(real_part_eval).evalf_func(real_part_evalf).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 GiNaC::imag_part_evalf

(

const ex &

arg

)

[static]

Definition at line 136 of file inifcns.cpp.

References imag().

static ex GiNaC::imag_part_eval

(

const ex &

arg

)

[static]

Definition at line 144 of file inifcns.cpp.

References GiNaC::ex::imag_part().

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

Definition at line 149 of file inifcns.cpp.

References GiNaC::ex::print(), and GiNaC::print_context::s.

static ex GiNaC::imag_part_conjugate

(

const ex &

arg

)

[static]

Definition at line 154 of file inifcns.cpp.

static ex GiNaC::imag_part_real_part

(

const ex &

arg

)

[static]

Definition at line 159 of file inifcns.cpp.

static ex GiNaC::imag_part_imag_part

(

const ex &

arg

)

[static]

Definition at line 164 of file inifcns.cpp.

GiNaC::REGISTER_FUNCTION	(	imag_part_function	,
		eval_func(imag_part_eval).evalf_func(imag_part_evalf).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 GiNaC::abs_evalf

(

const ex &

arg

)

[static]

Definition at line 181 of file inifcns.cpp.

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

static ex GiNaC::abs_eval

(

const ex &

arg

)

[static]

Definition at line 189 of file inifcns.cpp.

References abs(), GiNaC::basic::hold(), GiNaC::ex::info(), is_ex_the_function, and GiNaC::info_flags::nonnegative.

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

Definition at line 203 of file inifcns.cpp.

References GiNaC::ex::print(), and GiNaC::print_context::s.

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

Definition at line 208 of file inifcns.cpp.

References GiNaC::ex::print(), and GiNaC::print_context::s.

static ex GiNaC::abs_conjugate

(

const ex &

arg

)

[static]

Definition at line 213 of file inifcns.cpp.

References abs().

static ex GiNaC::abs_real_part

(

const ex &

arg

)

[static]

Definition at line 218 of file inifcns.cpp.

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

static ex GiNaC::abs_imag_part

(

const ex &

arg

)

[static]

Definition at line 223 of file inifcns.cpp.

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

Definition at line 228 of file inifcns.cpp.

References abs(), GiNaC::ex::conjugate(), exp(), GiNaC::basic::hold(), GiNaC::ex::is_equal(), and is_even().

GiNaC::REGISTER_FUNCTION	(	abs	,
		eval_func(abs_eval).evalf_func(abs_evalf).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 GiNaC::step_evalf

(

const ex &

arg

)

[static]

Definition at line 250 of file inifcns.cpp.

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

static ex GiNaC::step_eval

(

const ex &

arg

)

[static]

Definition at line 258 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().

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

Definition at line 287 of file inifcns.cpp.

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

static ex GiNaC::step_conjugate

(

const ex &

arg

)

[static]

Definition at line 303 of file inifcns.cpp.

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

static ex GiNaC::step_real_part

(

const ex &

arg

)

[static]

Definition at line 308 of file inifcns.cpp.

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

static ex GiNaC::step_imag_part

(

const ex &

arg

)

[static]

Definition at line 313 of file inifcns.cpp.

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)
	)

static ex GiNaC::csgn_evalf

(

const ex &

arg

)

[static]

Definition at line 329 of file inifcns.cpp.

References csgn().

static ex GiNaC::csgn_eval

(

const ex &

arg

)

[static]

Definition at line 337 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().

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

Definition at line 366 of file inifcns.cpp.

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

static ex GiNaC::csgn_conjugate

(

const ex &

arg

)

[static]

Definition at line 382 of file inifcns.cpp.

References csgn().