This class is the ABC (abstract base class) of GiNaC's class hierarchy. More...

#include <basic.h>

Inheritance diagram for GiNaC::basic:

Public Member Functions
virtual	~basic ()
	basic destructor, virtual because class ex will delete objects of derived classes via a basic*.
	basic (const basic &other)
const basic &	operator= (const basic &other)
	basic assignment operator: the other object might be of a derived class.
virtual basic *	duplicate () const
	Create a clone of this object on the heap.
virtual ex	eval (int level=0) const
	Perform automatic non-interruptive term rewriting rules.
virtual ex	evalf (int level=0) const
	Evaluate object numerically.
virtual ex	evalm () const
	Evaluate sums, products and integer powers of matrices.
virtual ex	eval_integ () const
	Evaluate integrals, if result is known.
virtual ex	eval_indexed (const basic &i) const
	Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression.
virtual void	print (const print_context &c, unsigned level=0) const
	Output to stream.
virtual void	dbgprint () const
	Little wrapper around print to be called within a debugger.
virtual void	dbgprinttree () const
	Little wrapper around printtree to be called within a debugger.
virtual unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
virtual bool	info (unsigned inf) const
	Information about the object.
virtual size_t	nops () const
	Number of operands/members.
virtual ex	op (size_t i) const
	Return operand/member at position i.
virtual ex	operator[] (const ex &index) const
virtual ex	operator[] (size_t i) const
virtual ex &	let_op (size_t i)
	Return modifyable operand/member at position i.
virtual ex &	operator[] (const ex &index)
virtual ex &	operator[] (size_t i)
virtual bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern.
virtual bool	match (const ex &pattern, exmap &repls) const
	Check whether the expression matches a given pattern.
virtual ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions.
virtual ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively).
virtual void	accept (GiNaC::visitor &v) const
virtual bool	is_polynomial (const ex &var) const
	Check whether this is a polynomial in the given variables.
virtual int	degree (const ex &s) const
	Return degree of highest power in object s.
virtual int	ldegree (const ex &s) const
	Return degree of lowest power in object s.
virtual ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s.
virtual ex	expand (unsigned options=0) const
	Expand expression, i.e.
virtual ex	collect (const ex &s, bool distributed=false) const
	Sort expanded expression in terms of powers of some object(s).
virtual ex	series (const relational &r, int order, unsigned options=0) const
	Default implementation of ex::series().
virtual ex	normal (exmap &repl, exmap &rev_lookup, int level=0) const
	Default implementation of ex::normal().
virtual ex	to_rational (exmap &repl) const
	Default implementation of ex::to_rational().
virtual ex	to_polynomial (exmap &repl) const
virtual numeric	integer_content () const
virtual ex	smod (const numeric &xi) const
	Apply symmetric modular homomorphism to an expanded multivariate polynomial.
virtual numeric	max_coefficient () const
	Implementation ex::max_coefficient().
virtual exvector	get_free_indices () const
	Return a vector containing the free indices of an expression.
virtual ex	add_indexed (const ex &self, const ex &other) const
	Add two indexed expressions.
virtual ex	scalar_mul_indexed (const ex &self, const numeric &other) const
	Multiply an indexed expression with a scalar.
virtual bool	contract_with (exvector::iterator self, exvector::iterator other, exvector &v) const
	Try to contract two indexed expressions that appear in the same product.
virtual unsigned	return_type () const
virtual return_type_t	return_type_tinfo () const
virtual ex	conjugate () const
virtual ex	real_part () const
virtual ex	imag_part () const
template<class T >
void	print_dispatch (const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class.
void	print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class.
virtual void	archive (archive_node &n) const
	Save (serialize) the object into archive node.
virtual void	read_archive (const archive_node &n, lst &syms)
	Load (deserialize) the object from an archive node.
ex	subs_one_level (const exmap &m, unsigned options) const
	Helper function for subs().
ex	diff (const symbol &s, unsigned nth=1) const
	Default interface of nth derivative ex::diff(s, n).
int	compare (const basic &other) const
	Compare objects syntactically to establish canonical ordering.
bool	is_equal (const basic &other) const
	Test for syntactic equality.
const basic &	hold () const
	Stop further evaluation.
unsigned	gethash () const
const basic &	setflag (unsigned f) const
	Set some status_flags.
const basic &	clearflag (unsigned f) const
	Clear some status_flags.
Protected Member Functions
	basic ()
virtual ex	eval_ncmul (const exvector &v) const
virtual bool	match_same_type (const basic &other) const
	Returns true if the attributes of two objects are similar enough for a match.
virtual ex	derivative (const symbol &s) const
	Default implementation of ex::diff().
virtual int	compare_same_type (const basic &other) const
	Returns order relation between two objects of same type.
virtual bool	is_equal_same_type (const basic &other) const
	Returns true if two objects of same type are equal.
virtual unsigned	calchash () const
	Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so.
void	ensure_if_modifiable () const
	Ensure the object may be modified without hurting others, throws if this is not the case.
void	do_print (const print_context &c, unsigned level) const
	Default output to stream.
void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream.
void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream.
Protected Attributes
unsigned	flags
	of type status_flags
unsigned	hashvalue
	hash value
Friends
class	ex

Detailed Description

This class is the ABC (abstract base class) of GiNaC's class hierarchy.

Definition at line 104 of file basic.h.

Constructor & Destructor Documentation

GiNaC::basic::basic ( ) [inline, protected]

Definition at line 112 of file basic.h.

Referenced by duplicate().

virtual GiNaC::basic::~basic ( ) [inline, virtual]

basic destructor, virtual because class ex will delete objects of derived classes via a basic*.

Definition at line 117 of file basic.h.

References GiNaC::status_flags::dynallocated, flags, GiNaC::refcounted::get_refcount(), and GINAC_ASSERT.

GiNaC::basic::basic ( const basic & other )

Member Function Documentation

const basic & GiNaC::basic::operator= ( const basic & other )

basic assignment operator: the other object might be of a derived class.

Definition at line 64 of file basic.cpp.

References GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, flags, GiNaC::status_flags::hash_calculated, hashvalue, and GiNaC::refcounted::set_refcount().

virtual basic* GiNaC::basic::duplicate ( ) const [inline, virtual]

Create a clone of this object on the heap.

One can think of this as simulating a virtual copy constructor which is needed for instance by the refcounted construction of an ex from a basic.

Reimplemented in GiNaC::possymbol, and GiNaC::realsymbol.

Definition at line 131 of file basic.h.

References basic().

Referenced by GiNaC::ex::construct_from_basic(), GiNaC::idx::map(), map(), GiNaC::idx::replace_dim(), GiNaC::idx::subs(), subs(), GiNaC::spinidx::toggle_dot(), GiNaC::varidx::toggle_variance(), and GiNaC::spinidx::toggle_variance_dot().

ex GiNaC::basic::eval ( int level = 0 ) const [virtual]

Perform automatic non-interruptive term rewriting rules.

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::indexed, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::numeric, GiNaC::expairseq, GiNaC::fderivative, GiNaC::ncmul, GiNaC::power, GiNaC::relational, GiNaC::mul, GiNaC::add, GiNaC::pseries, GiNaC::symbol, and GiNaC::integral.

Definition at line 414 of file basic.cpp.

References hold().

Referenced by GiNaC::ncmul::conjugate(), and GiNaC::ex::construct_from_basic().

ex GiNaC::basic::evalf ( int level = 0 ) const [virtual]

Evaluate object numerically.

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::fderivative, GiNaC::power, GiNaC::mul, GiNaC::idx, GiNaC::pseries, GiNaC::constant, GiNaC::symbol, and GiNaC::integral.

Definition at line 428 of file basic.cpp.

References map(), GiNaC::max_recursion_level, and nops().

Referenced by GiNaC::evalf().

ex GiNaC::basic::evalm ( ) const [virtual]

Evaluate sums, products and integer powers of matrices.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::ncmul, GiNaC::power, GiNaC::pseries, GiNaC::mul, and GiNaC::add.

Definition at line 450 of file basic.cpp.

References map(), GiNaC::map_evalm, and nops().

ex GiNaC::basic::eval_integ ( ) const [virtual]

Evaluate integrals, if result is known.

Reimplemented in GiNaC::pseries, and GiNaC::integral.

Definition at line 464 of file basic.cpp.

References map(), GiNaC::map_eval_integ, and nops().

ex GiNaC::basic::eval_ncmul ( const exvector & v ) const [protected, virtual]

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::power, GiNaC::mul, GiNaC::relational, GiNaC::add, GiNaC::clifford, GiNaC::color, and GiNaC::integral.

Definition at line 698 of file basic.cpp.

References GiNaC::hold_ncmul().

ex GiNaC::basic::eval_indexed ( const basic & i ) const [virtual]

Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression.

Reimplemented in GiNaC::tensepsilon, GiNaC::spinmetric, GiNaC::structure< T, ComparisonPolicy >, GiNaC::su3d, GiNaC::matrix, GiNaC::su3f, GiNaC::minkmetric, GiNaC::tensmetric, and GiNaC::tensdelta.

Definition at line 474 of file basic.cpp.

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

void GiNaC::basic::print	(	const print_context &	c,
		unsigned	level = `0`
	)		const `[virtual]`

Output to stream.

This performs double dispatch on the dynamic type of *this and the dynamic type of the supplied print context.

Parameters:

c	print context object that describes the output formatting
level	value that is used to identify the precedence or indentation level for placing parentheses and formatting

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, and GiNaC::fderivative.

Definition at line 116 of file basic.cpp.

References print_dispatch().

Referenced by dbgprint(), dbgprinttree(), GiNaC::expairseq::is_equal_same_type(), GiNaC::add::print_add(), GiNaC::mul::print_overall_coeff(), GiNaC::pseries::print_series(), and GiNaC::print_sym_pow().

void GiNaC::basic::dbgprint ( ) const [virtual]

Little wrapper around print to be called within a debugger.

This is needed because you cannot call foo.print(cout) from within the debugger because it might not know what cout is. This method can be invoked with no argument and it will simply print to stdout.

See also:: basic::print; basic::dbgprinttree

Definition at line 199 of file basic.cpp.

References print().

void GiNaC::basic::dbgprinttree ( ) const [virtual]

Little wrapper around printtree to be called within a debugger.

See also:: basic::dbgprint

Definition at line 208 of file basic.cpp.

References print().

unsigned GiNaC::basic::precedence ( ) const [virtual]

Return relative operator precedence (for parenthezing output).

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::indexed, GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::expairseq, GiNaC::ncmul, GiNaC::relational, GiNaC::clifford, GiNaC::power, GiNaC::mul, GiNaC::add, GiNaC::pseries, and GiNaC::integral.

Definition at line 214 of file basic.cpp.

bool GiNaC::basic::info ( unsigned inf ) const [virtual]

Information about the object.

See also:: class info_flags

Reimplemented in GiNaC::container< C >, GiNaC::tensepsilon, GiNaC::indexed, GiNaC::structure< T, ComparisonPolicy >, GiNaC::spinmetric, GiNaC::minkmetric, GiNaC::numeric, GiNaC::tensmetric, GiNaC::expairseq, GiNaC::tensdelta, GiNaC::ncmul, GiNaC::relational, GiNaC::power, GiNaC::mul, GiNaC::constant, GiNaC::idx, GiNaC::add, and GiNaC::symbol.

Definition at line 222 of file basic.cpp.

Referenced by GiNaC::matrix::gauss_elimination(), and GiNaC::matrix::solve().

size_t GiNaC::basic::nops ( ) const [virtual]

Number of operands/members.

Reimplemented in GiNaC::container< C >, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::expairseq, GiNaC::clifford, GiNaC::relational, GiNaC::power, GiNaC::idx, GiNaC::integral, and GiNaC::pseries.

Definition at line 229 of file basic.cpp.

Referenced by calchash(), derivative(), do_print_tree(), GiNaC::tensmetric::eval_indexed(), GiNaC::minkmetric::eval_indexed(), GiNaC::matrix::eval_indexed(), GiNaC::spinmetric::eval_indexed(), GiNaC::tensepsilon::eval_indexed(), eval_integ(), evalf(), evalm(), expand(), has(), map(), match(), normal(), and subs().

ex GiNaC::basic::op ( size_t i ) const [virtual]

Return operand/member at position i.

Reimplemented in GiNaC::container< C >, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::expairseq, GiNaC::clifford, GiNaC::relational, GiNaC::power, GiNaC::idx, GiNaC::integral, and GiNaC::pseries.

Definition at line 238 of file basic.cpp.

Referenced by calchash(), do_print_tree(), GiNaC::tensmetric::eval_indexed(), GiNaC::minkmetric::eval_indexed(), GiNaC::matrix::eval_indexed(), GiNaC::spinmetric::eval_indexed(), GiNaC::tensepsilon::eval_indexed(), has(), map(), match(), operator[](), and subs().

ex GiNaC::basic::operator[] ( const ex & index ) const [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >.

Definition at line 250 of file basic.cpp.

References op(), and GiNaC::to_int().

ex GiNaC::basic::operator[] ( size_t i ) const [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >.

Definition at line 258 of file basic.cpp.

References op().

ex & GiNaC::basic::let_op ( size_t i ) [virtual]

Return modifyable operand/member at position i.

Reimplemented in GiNaC::container< C >, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::clifford, and GiNaC::integral.

Definition at line 244 of file basic.cpp.

References ensure_if_modifiable().

Referenced by map(), operator[](), and subs().

ex & GiNaC::basic::operator[] ( const ex & index ) [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >.

Definition at line 263 of file basic.cpp.

References let_op(), and GiNaC::to_int().

ex & GiNaC::basic::operator[] ( size_t i ) [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >.

Definition at line 271 of file basic.cpp.

References let_op().

bool GiNaC::basic::has	(	const ex &	pattern,
		unsigned	options = `0`
	)		const `[virtual]`

Test for occurrence of a pattern.

An object 'has' a pattern if it matches the pattern itself or one of the children 'has' it. As a consequence (according to the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y) is false.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::power, and GiNaC::mul.

Definition at line 280 of file basic.cpp.

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

Referenced by GiNaC::power::has(), is_polynomial(), and series().

bool GiNaC::basic::match	(	const ex &	pattern,
		exmap &	repl_lst
	)		const `[virtual]`

Check whether the expression matches a given pattern.

For every wildcard object in the pattern, a pair with the wildcard as a key and matching expression as a value is added to repl_lst.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::expairseq, and GiNaC::wildcard.

Definition at line 528 of file basic.cpp.

References is_equal(), is_equal_same_type(), GiNaC::ex::match(), match_same_type(), GiNaC::ex::nops(), nops(), GiNaC::ex::op(), and op().

Referenced by has(), and subs_one_level().

bool GiNaC::basic::match_same_type ( const basic & other ) const [protected, virtual]

Returns true if the attributes of two objects are similar enough for a match.

This function must not match subexpressions (this is already done by basic::match()). Only attributes not accessible by op() should be compared. This is also the reason why this function doesn't take the wildcard replacement list from match() as an argument: only subexpressions are subject to wildcard matches. Also, this function only needs to be implemented for container classes because is_equal_same_type() is automatically used instead of match_same_type() if nops() == 0.

See also:: basic::match

Reimplemented in GiNaC::function, GiNaC::spinidx, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::varidx, GiNaC::fderivative, GiNaC::relational, GiNaC::idx, GiNaC::clifford, and GiNaC::color.

Definition at line 756 of file basic.cpp.

Referenced by match().

ex GiNaC::basic::subs	(	const exmap &	m,
		unsigned	options = `0`
	)		const `[virtual]`

Substitute a set of objects by arbitrary expressions.

The ex returned will already be evaluated.

Reimplemented in GiNaC::container< C >, GiNaC::structure< T, ComparisonPolicy >, GiNaC::matrix, GiNaC::numeric, GiNaC::expairseq, GiNaC::clifford, GiNaC::power, GiNaC::relational, GiNaC::idx, GiNaC::pseries, and GiNaC::symbol.

Definition at line 618 of file basic.cpp.

References GiNaC::are_ex_trivially_equal(), clearflag(), duplicate(), GiNaC::status_flags::dynallocated, GiNaC::status_flags::expanded, GiNaC::status_flags::hash_calculated, let_op(), nops(), op(), setflag(), GiNaC::ex::subs(), and subs_one_level().

Referenced by GiNaC::tensmetric::eval_indexed().

ex GiNaC::basic::map ( map_function & f ) const [virtual]

Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively).

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::expairseq, GiNaC::relational, GiNaC::power, and GiNaC::idx.

Definition at line 294 of file basic.cpp.

References GiNaC::are_ex_trivially_equal(), clearflag(), duplicate(), GiNaC::status_flags::dynallocated, GiNaC::status_flags::expanded, GiNaC::status_flags::hash_calculated, let_op(), n, nops(), op(), and setflag().

Referenced by derivative(), eval_integ(), evalf(), evalm(), expand(), and normal().

virtual void GiNaC::basic::accept ( GiNaC::visitor & v ) const [inline, virtual]

Definition at line 175 of file basic.h.

bool GiNaC::basic::is_polynomial ( const ex & var ) const [virtual]

Check whether this is a polynomial in the given variables.

Reimplemented in GiNaC::numeric, GiNaC::symbol, GiNaC::power, GiNaC::constant, GiNaC::mul, and GiNaC::add.

Definition at line 320 of file basic.cpp.

References has(), and is_equal().

int GiNaC::basic::degree ( const ex & s ) const [virtual]

Return degree of highest power in object s.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::ncmul, GiNaC::power, GiNaC::mul, GiNaC::add, GiNaC::pseries, and GiNaC::integral.

Definition at line 326 of file basic.cpp.

References is_equal().

Referenced by collect().

int GiNaC::basic::ldegree ( const ex & s ) const [virtual]

Return degree of lowest power in object s.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::ncmul, GiNaC::power, GiNaC::mul, GiNaC::add, GiNaC::pseries, and GiNaC::integral.

Definition at line 332 of file basic.cpp.

References is_equal().

Referenced by collect().

ex GiNaC::basic::coeff	(	const ex &	s,
		int	n = `1`
	)		const `[virtual]`

Return coefficient of degree n in object s.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::ncmul, GiNaC::power, GiNaC::mul, GiNaC::add, and GiNaC::pseries.

Definition at line 338 of file basic.cpp.

References GiNaC::_ex0, GiNaC::_ex1, and is_equal().

Referenced by collect(), GiNaC::expairseq::read_archive(), series(), and GiNaC::sqrfree_parfrac().

ex GiNaC::basic::expand ( unsigned options = 0 ) const [virtual]

Expand expression, i.e.

multiply it out and return the result as a new expression.

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::indexed, GiNaC::expairseq, GiNaC::mul, GiNaC::power, GiNaC::add, GiNaC::ncmul, GiNaC::pseries, and GiNaC::integral.

Definition at line 808 of file basic.cpp.

References GiNaC::status_flags::expanded, map(), nops(), and setflag().

Referenced by collect(), GiNaC::expand(), GiNaC::matrix::fraction_free_elimination(), and GiNaC::matrix::pivot().

ex GiNaC::basic::collect	(	const ex &	s,
		bool	distributed = `false`
	)		const `[virtual]`

Sort expanded expression in terms of powers of some object(s).

Parameters:

s	object(s) to sort in
distributed	recursive or distributed form (only used when s is a list)

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, and GiNaC::pseries.

Definition at line 349 of file basic.cpp.

References GiNaC::_ex0, GiNaC::_ex1, GiNaC::ex::begin(), GiNaC::container< C >::begin(), GiNaC::ex::coeff(), coeff(), GiNaC::ex::collect(), GiNaC::ex::degree(), degree(), GiNaC::status_flags::dynallocated, GiNaC::ex::end(), GiNaC::container< C >::end(), expand(), ldegree(), n, GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::pow(), and x.

ex GiNaC::basic::derivative ( const symbol & s ) const [protected, virtual]

Default implementation of ex::diff().

It maps the operation on the operands (or returns 0 when the object has no operands).

See also:: ex::diff

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::indexed, GiNaC::numeric, GiNaC::power, GiNaC::ncmul, GiNaC::fderivative, GiNaC::mul, GiNaC::pseries, GiNaC::add, GiNaC::symbol, GiNaC::integral, GiNaC::constant, and GiNaC::idx.

Definition at line 716 of file basic.cpp.

References GiNaC::_ex0, map(), and nops().

Referenced by diff().

ex GiNaC::basic::series	(	const relational &	r,
		int	order,
		unsigned	options = `0`
	)		const `[virtual]`

Default implementation of ex::series().

This performs Taylor expansion.

See also:: ex::series

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::fderivative, GiNaC::power, GiNaC::integral, GiNaC::mul, GiNaC::add, GiNaC::pseries, and GiNaC::symbol.

Definition at line 635 of file pseries.cpp.

References GiNaC::_ex0, GiNaC::_ex1, coeff(), GiNaC::ex::diff(), GiNaC::ex::expand(), has(), GiNaC::numeric::inverse(), GiNaC::ex::is_zero(), GiNaC::relational::lhs(), GiNaC::numeric::mul(), n, GiNaC::subs_options::no_pattern, and GiNaC::ex::subs().

Referenced by GiNaC::power::series().

ex GiNaC::basic::normal	(	exmap &	repl,
		exmap &	rev_lookup,
		int	level = `0`
	)		const `[virtual]`

Default implementation of ex::normal().

It normalizes the children and replaces the object with a temporary symbol.

See also:: ex::normal

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::power, GiNaC::mul, GiNaC::add, GiNaC::pseries, and GiNaC::symbol.

Definition at line 2056 of file normal.cpp.

References GiNaC::_ex1, GiNaC::status_flags::dynallocated, map(), GiNaC::max_recursion_level, nops(), and GiNaC::replace_with_symbol().

Referenced by GiNaC::matrix::determinant(), and GiNaC::matrix::solve().

ex GiNaC::basic::to_rational ( exmap & repl ) const [virtual]

Default implementation of ex::to_rational().

This replaces the object with a temporary symbol.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::expairseq, GiNaC::power, and GiNaC::symbol.

Definition at line 2479 of file normal.cpp.

References GiNaC::replace_with_symbol().

ex GiNaC::basic::to_polynomial ( exmap & repl ) const [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::expairseq, GiNaC::power, and GiNaC::symbol.

Definition at line 2484 of file normal.cpp.

References GiNaC::replace_with_symbol().

numeric GiNaC::basic::integer_content ( ) const [virtual]

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::mul, and GiNaC::add.

Definition at line 312 of file normal.cpp.

References GiNaC::_num1_p.

ex GiNaC::basic::smod ( const numeric & xi ) const [virtual]

Apply symmetric modular homomorphism to an expanded multivariate polynomial.

This function is usually used internally by heur_gcd().

Parameters:

xi modulus

Returns:: mapped polynomial

See also:: heur_gcd

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::mul, and GiNaC::add.

Definition at line 1204 of file normal.cpp.

numeric GiNaC::basic::max_coefficient ( ) const [virtual]

Implementation ex::max_coefficient().

See also:: heur_gcd

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::mul, and GiNaC::add.

Definition at line 1156 of file normal.cpp.

References GiNaC::_num1_p.

exvector GiNaC::basic::get_free_indices ( ) const [virtual]

Return a vector containing the free indices of an expression.

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::indexed, GiNaC::mul, GiNaC::ncmul, GiNaC::add, and GiNaC::integral.

Definition at line 678 of file basic.cpp.

ex GiNaC::basic::add_indexed	(	const ex &	self,
		const ex &	other
	)		const `[virtual]`

Add two indexed expressions.

They are guaranteed to be of class indexed (or a subclass) and their indices are compatible. This function is used internally by simplify_indexed().

Parameters:

self	First indexed expression; its base object is *this
other	Second indexed expression

Returns:: sum of self and other

See also:: ex::simplify_indexed()

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, and GiNaC::matrix.

Definition at line 490 of file basic.cpp.

ex GiNaC::basic::scalar_mul_indexed	(	const ex &	self,
		const numeric &	other
	)		const `[virtual]`

Multiply an indexed expression with a scalar.

This function is used internally by simplify_indexed().

Parameters:

self	Indexed expression; its base object is *this
other	Numeric value

Returns:: product of self and other

See also:: ex::simplify_indexed()

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, and GiNaC::matrix.

Definition at line 502 of file basic.cpp.

bool GiNaC::basic::contract_with	(	exvector::iterator	self,
		exvector::iterator	other,
		exvector &	v
	)		const `[virtual]`

Try to contract two indexed expressions that appear in the same product.

If a contraction exists, the function overwrites one or both of the expressions and returns true. Otherwise it returns false. It is guaranteed that both expressions are of class indexed (or a subclass) and that at least one dummy index has been found. This functions is used internally by simplify_indexed().

Parameters:

self	Pointer to first indexed expression; its base object is *this
other	Pointer to second indexed expression
v	The complete vector of factors

Returns:: true if the contraction was successful, false otherwise

See also:: ex::simplify_indexed()

Reimplemented in GiNaC::structure< T, ComparisonPolicy >, GiNaC::tensepsilon, GiNaC::spinmetric, GiNaC::su3d, GiNaC::diracgamma, GiNaC::matrix, GiNaC::su3f, GiNaC::cliffordunit, GiNaC::su3t, GiNaC::tensmetric, and GiNaC::tensdelta.

Definition at line 519 of file basic.cpp.

unsigned GiNaC::basic::return_type ( ) const [virtual]

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::tensepsilon, GiNaC::indexed, GiNaC::matrix, GiNaC::su3d, GiNaC::minkmetric, GiNaC::su3f, GiNaC::expairseq, GiNaC::tensmetric, GiNaC::power, GiNaC::ncmul, GiNaC::mul, GiNaC::relational, GiNaC::add, GiNaC::tensdelta, GiNaC::clifford, GiNaC::color, GiNaC::integral, GiNaC::tensor, and GiNaC::fail.

Definition at line 763 of file basic.cpp.

References GiNaC::return_types::commutative.

return_type_t GiNaC::basic::return_type_tinfo ( ) const [virtual]

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::indexed, GiNaC::power, GiNaC::ncmul, GiNaC::mul, GiNaC::relational, GiNaC::add, GiNaC::clifford, GiNaC::color, and GiNaC::integral.

Definition at line 768 of file basic.cpp.

References GiNaC::return_type_t::rl, and GiNaC::return_type_t::tinfo.

ex GiNaC::basic::conjugate ( ) const [virtual]

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::spinidx, GiNaC::diracgammaR, GiNaC::diracgammaL, GiNaC::diracgamma5, GiNaC::matrix, GiNaC::numeric, GiNaC::realsymbol, GiNaC::expairseq, GiNaC::power, GiNaC::mul, GiNaC::ncmul, GiNaC::add, GiNaC::pseries, GiNaC::integral, GiNaC::symbol, and GiNaC::constant.

Definition at line 683 of file basic.cpp.

ex GiNaC::basic::real_part ( ) const [virtual]

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::indexed, GiNaC::matrix, GiNaC::numeric, GiNaC::realsymbol, GiNaC::power, GiNaC::ncmul, GiNaC::add, GiNaC::mul, GiNaC::pseries, GiNaC::symbol, and GiNaC::constant.

Definition at line 688 of file basic.cpp.

ex GiNaC::basic::imag_part ( ) const [virtual]

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::indexed, GiNaC::matrix, GiNaC::numeric, GiNaC::realsymbol, GiNaC::power, GiNaC::ncmul, GiNaC::add, GiNaC::mul, GiNaC::pseries, GiNaC::symbol, and GiNaC::constant.

Definition at line 693 of file basic.cpp.

int GiNaC::basic::compare_same_type ( const basic & other ) const [protected, virtual]

Returns order relation between two objects of same type.

This needs to be implemented by each class. It may never return anything else than 0, signalling equality, or +1 and -1 signalling inequality and determining the canonical ordering. (Perl hackers will wonder why C++ doesn't feature the spaceship operator <=> for denoting just this.)

Definition at line 731 of file basic.cpp.

References GiNaC::compare_pointers().

Referenced by compare(), GiNaC::symbol::derivative(), and is_equal_same_type().

bool GiNaC::basic::is_equal_same_type ( const basic & other ) const [protected, virtual]

Returns true if two objects of same type are equal.

Normally needs not be reimplemented as long as it wasn't overwritten by some parent class, since it just calls compare_same_type(). The reason why this function exists is that sometimes it is easier to determine equality than an order relation and then it can be overridden.

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::expairseq, GiNaC::fderivative, GiNaC::symbol, and GiNaC::constant.

Definition at line 741 of file basic.cpp.

References compare_same_type().

Referenced by is_equal(), and match().

unsigned GiNaC::basic::calchash ( ) const [protected, virtual]

Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so.

The method inherited from class basic computes a hash value based on the type and hash values of possible members. For this reason it is well suited for container classes but atomic classes should override this implementation because otherwise they would all end up with the same hashvalue.

Reimplemented in GiNaC::function, GiNaC::structure< T, ComparisonPolicy >, GiNaC::numeric, GiNaC::expairseq, GiNaC::symmetry, GiNaC::relational, GiNaC::symbol, GiNaC::constant, GiNaC::idx, and GiNaC::wildcard.

Definition at line 782 of file basic.cpp.

References GiNaC::status_flags::evaluated, flags, GiNaC::ex::gethash(), GiNaC::status_flags::hash_calculated, hashvalue, GiNaC::make_hash_seed(), nops(), op(), GiNaC::rotate_left(), and setflag().

Referenced by gethash().

template<class T >

void GiNaC::basic::print_dispatch	(	const print_context &	c,
		unsigned	level
	)		const `[inline]`

Like print(), but dispatch to the specified class.

Can be used by implementations of print methods to dispatch to the method of the superclass.

See also:: basic::print

Definition at line 237 of file basic.h.

Referenced by print().

void GiNaC::basic::print_dispatch	(	const registered_class_info &	ri,
		const print_context &	c,
		unsigned	level
	)		const

Like print(), but dispatch to the specified class.

Can be used by implementations of print methods to dispatch to the method of the superclass.

See also:: basic::print

Definition at line 126 of file basic.cpp.

References c, GiNaC::class_info< OPT >::get_parent(), and GiNaC::class_info< OPT >::options.

void GiNaC::basic::archive ( archive_node & n ) const [virtual]

Save (serialize) the object into archive node.

Archive the object.

Losely speaking, this method turns an expression into a byte stream (which can be saved and restored later on, or sent via network, etc.)

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::spinidx, GiNaC::tensepsilon, GiNaC::indexed, GiNaC::varidx, GiNaC::matrix, GiNaC::numeric, GiNaC::minkmetric, GiNaC::expairseq, GiNaC::symmetry, GiNaC::power, GiNaC::fderivative, GiNaC::pseries, GiNaC::relational, GiNaC::symbol, GiNaC::integral, GiNaC::constant, GiNaC::idx, GiNaC::clifford, GiNaC::color, and GiNaC::wildcard.

Definition at line 100 of file basic.cpp.

References GiNaC::archive_node::add_string().

void GiNaC::basic::read_archive	(	const archive_node &	n,
		lst &	syms
	)		`[virtual]`

Load (deserialize) the object from an archive node.

Construct object from archive_node.

Note:: This method is essentially a constructor. However, constructors can't be virtual. So, if unarchiving routines are implemented as constructors one would need to define such a constructor in every class, even if all it does is simply calling constructor of a superclass.

Reimplemented in GiNaC::function, GiNaC::container< C >, GiNaC::spinidx, GiNaC::tensepsilon, GiNaC::indexed, GiNaC::matrix, GiNaC::varidx, GiNaC::numeric, GiNaC::minkmetric, GiNaC::expairseq, GiNaC::symmetry, GiNaC::power, GiNaC::fderivative, GiNaC::pseries, GiNaC::relational, GiNaC::symbol, GiNaC::integral, GiNaC::constant, GiNaC::idx, GiNaC::clifford, GiNaC::color, and GiNaC::wildcard.

Definition at line 96 of file basic.cpp.

ex GiNaC::basic::subs_one_level	(	const exmap &	m,
		unsigned	options
	)		const

Helper function for subs().

Does not recurse into subexpressions.

Definition at line 594 of file basic.cpp.

References GiNaC::ex::find(), match(), GiNaC::subs_options::no_pattern, and GiNaC::ex::subs().

Referenced by GiNaC::symbol::subs(), GiNaC::relational::subs(), GiNaC::power::subs(), GiNaC::expairseq::subs(), GiNaC::numeric::subs(), and subs().

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

Default interface of nth derivative ex::diff(s, n).

It should be called instead of ::derivative(s) for first derivatives and for nth derivatives it just recurses down.

Parameters:

s	symbol to differentiate in
nth	order of differentiation

See also:: ex::diff

Definition at line 658 of file basic.cpp.

References derivative(), GiNaC::ex::diff(), GiNaC::status_flags::evaluated, ex, flags, and GiNaC::ex::is_zero().

Referenced by GiNaC::mul::derivative(), and GiNaC::function::derivative().

int GiNaC::basic::compare ( const basic & other ) const

Compare objects syntactically to establish canonical ordering.

All compare functions return: -1 for *this less than other, 0 equal, 1 greater.

Definition at line 828 of file basic.cpp.

References compare_same_type(), and gethash().

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

bool GiNaC::basic::is_equal ( const basic & other ) const

Test for syntactic equality.

This is only a quick test, meaning objects should be in the same domain. You might have to .expand(), .normal() objects first, depending on the domain of your computation, to get a more reliable answer.