Product of expressions. More...

#include <mul.h>

Inheritance diagram for GiNaC::mul:

Public Member Functions
	mul (const ex &lh, const ex &rh)

	mul (const exvector &v)

	mul (const epvector &v)

	mul (const epvector &v, const ex &oc, bool do_index_renaming=false)

	mul (epvector &&vp)

	mul (epvector &&vp, const ex &oc, bool do_index_renaming=false)

	mul (const ex &lh, const ex &mh, const ex &rh)

unsigned	precedence () const override
	Return relative operator precedence (for parenthezing output). More...

bool	info (unsigned inf) const override
	Information about the object. More...

bool	is_polynomial (const ex &var) const override
	Check whether this is a polynomial in the given variables. More...

int	degree (const ex &s) const override
	Return degree of highest power in object s. More...

int	ldegree (const ex &s) const override
	Return degree of lowest power in object s. More...

ex	coeff (const ex &s, int n=1) const override
	Return coefficient of degree n in object s. More...

bool	has (const ex &other, unsigned options=0) const override
	Test for occurrence of a pattern. More...

ex	eval () const override
	Perform automatic term rewriting rules in this class. More...

ex	evalf () const override
	Evaluate object numerically. More...

ex	real_part () const override

ex	imag_part () const override

ex	evalm () const override
	Evaluate sums, products and integer powers of matrices. More...

ex	series (const relational &s, int order, unsigned options=0) const override
	Implementation of ex::series() for product. More...

ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const override
	Implementation of ex::normal() for a product. More...

numeric	integer_content () const override

ex	smod (const numeric &xi) const override
	Apply symmetric modular homomorphism to an expanded multivariate polynomial. More...

numeric	max_coefficient () const override
	Implementation ex::max_coefficient(). More...

exvector	get_free_indices () const override
	Return a vector containing the free indices of an expression. More...

ex	conjugate () const override

ex	algebraic_subs_mul (const exmap &m, unsigned options) const

Public Member Functions inherited from GiNaC::expairseq
	expairseq (const ex &lh, const ex &rh)

	expairseq (const exvector &v)

	expairseq (const epvector &v, const ex &oc, bool do_index_renaming=false)

	expairseq (epvector &&vp, const ex &oc, bool do_index_renaming=false)

unsigned	precedence () const override
	Return relative operator precedence (for parenthezing output). More...

bool	info (unsigned inf) const override
	Information about the object. More...

size_t	nops () const override
	Number of operands/members. More...

ex	op (size_t i) const override
	Return operand/member at position i. More...

ex	map (map_function &f) const override
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively). More...

ex	eval () const override
	Perform coefficient-wise automatic term rewriting rules in this class. More...

ex	to_rational (exmap &repl) const override
	Implementation of ex::to_rational() for expairseqs. More...

ex	to_polynomial (exmap &repl) const override
	Implementation of ex::to_polynomial() for expairseqs. More...

bool	match (const ex &pattern, exmap &repl_lst) const override
	Check whether the expression matches a given pattern. More...

ex	subs (const exmap &m, unsigned options=0) const override
	Substitute a set of objects by arbitrary expressions. More...

ex	conjugate () const override

void	archive (archive_node &n) const override
	Save (serialize) the object into archive node. More...

void	read_archive (const archive_node &n, lst &syms) override
	Load (deserialize) the object from an archive node. More...

Public Member Functions inherited from GiNaC::basic
virtual	~basic ()
	basic destructor, virtual because class ex will delete objects of derived classes via a basic*. More...

	basic (const basic &other)

const basic &	operator= (const basic &other)
	basic assignment operator: the other object might be of a derived class. More...

virtual basic *	duplicate () const
	Create a clone of this object on the heap. More...

virtual ex	eval () const
	Perform automatic non-interruptive term rewriting rules. More...

virtual ex	evalf () const
	Evaluate object numerically. More...

virtual ex	evalm () const
	Evaluate sums, products and integer powers of matrices. More...

virtual ex	eval_integ () const
	Evaluate integrals, if result is known. More...

virtual ex	eval_indexed (const basic &i) const
	Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression. More...

virtual void	print (const print_context &c, unsigned level=0) const
	Output to stream. More...

virtual void	dbgprint () const
	Little wrapper around print to be called within a debugger. More...

virtual void	dbgprinttree () const
	Little wrapper around printtree to be called within a debugger. More...

virtual unsigned	precedence () const
	Return relative operator precedence (for parenthezing output). More...

virtual bool	info (unsigned inf) const
	Information about the object. More...

virtual size_t	nops () const
	Number of operands/members. More...

virtual ex	op (size_t i) const
	Return operand/member at position i. More...

virtual ex	operator[] (const ex &index) const

virtual ex	operator[] (size_t i) const

virtual ex &	let_op (size_t i)
	Return modifiable operand/member at position i. More...

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. More...

virtual bool	match (const ex &pattern, exmap &repls) const
	Check whether the expression matches a given pattern. More...

virtual ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions. More...

virtual ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively). More...

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. More...

virtual int	degree (const ex &s) const
	Return degree of highest power in object s. More...

virtual int	ldegree (const ex &s) const
	Return degree of lowest power in object s. More...

virtual ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s. More...

virtual ex	expand (unsigned options=0) const
	Expand expression, i.e. More...

virtual ex	collect (const ex &s, bool distributed=false) const
	Sort expanded expression in terms of powers of some object(s). More...

virtual ex	series (const relational &r, int order, unsigned options=0) const
	Default implementation of ex::series(). More...

virtual ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const
	Default implementation of ex::normal(). More...

virtual ex	to_rational (exmap &repl) const
	Default implementation of ex::to_rational(). More...

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. More...

virtual numeric	max_coefficient () const
	Implementation ex::max_coefficient(). More...

virtual exvector	get_free_indices () const
	Return a vector containing the free indices of an expression. More...

virtual ex	add_indexed (const ex &self, const ex &other) const
	Add two indexed expressions. More...

virtual ex	scalar_mul_indexed (const ex &self, const numeric &other) const
	Multiply an indexed expression with a scalar. More...

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. More...

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. More...

void	print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class. More...

virtual void	archive (archive_node &n) const
	Save (serialize) the object into archive node. More...

virtual void	read_archive (const archive_node &n, lst &syms)
	Load (deserialize) the object from an archive node. More...

ex	subs_one_level (const exmap &m, unsigned options) const
	Helper function for subs(). More...

ex	diff (const symbol &s, unsigned nth=1) const
	Default interface of nth derivative ex::diff(s, n). More...

int	compare (const basic &other) const
	Compare objects syntactically to establish canonical ordering. More...

bool	is_equal (const basic &other) const
	Test for syntactic equality. More...

const basic &	hold () const
	Stop further evaluation. More...

unsigned	gethash () const

const basic &	setflag (unsigned f) const
	Set some status_flags. More...

const basic &	clearflag (unsigned f) const
	Clear some status_flags. More...

Public Member Functions inherited from GiNaC::refcounted
	refcounted () noexcept

unsigned int	add_reference () noexcept

unsigned int	remove_reference () noexcept

unsigned int	get_refcount () const noexcept

void	set_refcount (unsigned int r) noexcept

Protected Member Functions
ex	derivative (const symbol &s) const override
	Implementation of ex::diff() for a product. More...

ex	eval_ncmul (const exvector &v) const override

unsigned	return_type () const override

return_type_t	return_type_tinfo () const override

ex	thisexpairseq (const epvector &v, const ex &oc, bool do_index_renaming=false) const override
	Create an object of this type. More...

ex	thisexpairseq (epvector &&vp, const ex &oc, bool do_index_renaming=false) const override

expair	split_ex_to_pair (const ex &e) const override
	Form an expair from an ex, using the corresponding semantics. More...

expair	combine_ex_with_coeff_to_pair (const ex &e, const ex &c) const override

expair	combine_pair_with_coeff_to_pair (const expair &p, const ex &c) const override

ex	recombine_pair_to_ex (const expair &p) const override
	Form an ex out of an expair, using the corresponding semantics. More...

bool	expair_needs_further_processing (epp it) override

ex	default_overall_coeff () const override

void	combine_overall_coeff (const ex &c) override

void	combine_overall_coeff (const ex &c1, const ex &c2) override

bool	can_make_flat (const expair &p) const override

ex	expand (unsigned options=0) const override
	Expand expression, i.e. More...

void	find_real_imag (ex &, ex &) const

void	print_overall_coeff (const print_context &c, const char *mul_sym) const

void	do_print (const print_context &c, unsigned level) const

void	do_print_latex (const print_latex &c, unsigned level) const

void	do_print_csrc (const print_csrc &c, unsigned level) const

void	do_print_python_repr (const print_python_repr &c, unsigned level) const

epvector	expandchildren (unsigned options) const
	Member-wise expand the expairs representing this sequence. More...

Protected Member Functions inherited from GiNaC::expairseq
bool	is_equal_same_type (const basic &other) const override
	Returns true if two objects of same type are equal. More...

unsigned	return_type () const override

unsigned	calchash () const override
	Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so. More...

ex	expand (unsigned options=0) const override
	Expand expression, i.e. More...

virtual ex	thisexpairseq (const epvector &v, const ex &oc, bool do_index_renaming=false) const
	Create an object of this type. More...

virtual ex	thisexpairseq (epvector &&vp, const ex &oc, bool do_index_renaming=false) const

virtual void	printseq (const print_context &c, char delim, unsigned this_precedence, unsigned upper_precedence) const

virtual void	printpair (const print_context &c, const expair &p, unsigned upper_precedence) const

virtual expair	split_ex_to_pair (const ex &e) const
	Form an expair from an ex, using the corresponding semantics. More...

virtual expair	combine_ex_with_coeff_to_pair (const ex &e, const ex &c) const

virtual expair	combine_pair_with_coeff_to_pair (const expair &p, const ex &c) const

virtual ex	recombine_pair_to_ex (const expair &p) const
	Form an ex out of an expair, using the corresponding semantics. More...

virtual bool	expair_needs_further_processing (epp it)

virtual ex	default_overall_coeff () const

virtual void	combine_overall_coeff (const ex &c)

virtual void	combine_overall_coeff (const ex &c1, const ex &c2)

virtual bool	can_make_flat (const expair &p) const

void	do_print (const print_context &c, unsigned level) const

void	do_print_tree (const print_tree &c, unsigned level) const

void	construct_from_2_ex (const ex &lh, const ex &rh)

void	construct_from_2_expairseq (const expairseq &s1, const expairseq &s2)

void	construct_from_expairseq_ex (const expairseq &s, const ex &e)

void	construct_from_exvector (const exvector &v)

void	construct_from_epvector (const epvector &v, bool do_index_renaming=false)

void	construct_from_epvector (epvector &&v, bool do_index_renaming=false)

void	make_flat (const exvector &v)
	Combine this expairseq with argument exvector. More...

void	make_flat (const epvector &v, bool do_index_renaming=false)
	Combine this expairseq with argument epvector. More...

void	canonicalize ()
	Brings this expairseq into a sorted (canonical) form. More...

void	combine_same_terms_sorted_seq ()
	Compact a presorted expairseq by combining all matching expairs to one each. More...

bool	is_canonical () const
	Check if this expairseq is in sorted (canonical) form. More...

epvector	expandchildren (unsigned options) const
	Member-wise expand the expairs in this sequence. More...

epvector	evalchildren () const
	Member-wise evaluate the expairs in this sequence. More...

epvector	subschildren (const exmap &m, unsigned options=0) const
	Member-wise substitute in this sequence. More...

Protected Member Functions inherited from GiNaC::basic
	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. More...

virtual ex	derivative (const symbol &s) const
	Default implementation of ex::diff(). More...

virtual int	compare_same_type (const basic &other) const
	Returns order relation between two objects of same type. More...

virtual bool	is_equal_same_type (const basic &other) const
	Returns true if two objects of same type are equal. More...

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. More...

void	ensure_if_modifiable () const
	Ensure the object may be modified without hurting others, throws if this is not the case. More...

void	do_print (const print_context &c, unsigned level) const
	Default output to stream. More...

void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream. More...

void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream. More...

Static Protected Member Functions
static bool	can_be_further_expanded (const ex &e)

Friends
class	add

class	ncmul

class	power

Additional Inherited Members
Protected Attributes inherited from GiNaC::expairseq
epvector	seq

ex	overall_coeff

Protected Attributes inherited from GiNaC::basic
unsigned	flags
	of type status_flags More...

unsigned	hashvalue
	hash value More...

Detailed Description

Product of expressions.

Definition at line 31 of file mul.h.

Constructor & Destructor Documentation

◆ mul() [1/7]

GiNaC::mul::mul	(	const ex &	lh,
		const ex &	rh
	)

Definition at line 64 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expairseq::construct_from_2_ex(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

Referenced by do_print_latex(), and expand().

◆ mul() [2/7]

GiNaC::mul::mul ( const exvector & v )

Definition at line 71 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expairseq::construct_from_exvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

◆ mul() [3/7]

GiNaC::mul::mul ( const epvector & v )

Definition at line 78 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expairseq::construct_from_epvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

◆ mul() [4/7]

GiNaC::mul::mul	(	const epvector &	v,
		const ex &	oc,
		bool	do_index_renaming = `false`
	)

Definition at line 85 of file mul.cpp.

References GiNaC::expairseq::construct_from_epvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

◆ mul() [5/7]

GiNaC::mul::mul ( epvector && vp )

Definition at line 92 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expairseq::construct_from_epvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

◆ mul() [6/7]

GiNaC::mul::mul	(	epvector &&	vp,
		const ex &	oc,
		bool	do_index_renaming = `false`
	)

Definition at line 99 of file mul.cpp.

References GiNaC::expairseq::construct_from_epvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

◆ mul() [7/7]

GiNaC::mul::mul	(	const ex &	lh,
		const ex &	mh,
		const ex &	rh
	)

Definition at line 106 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expairseq::construct_from_exvector(), factors, GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

Member Function Documentation

◆ precedence()

unsigned GiNaC::mul::precedence ( ) const

inlineoverridevirtual

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::expairseq.

Definition at line 51 of file mul.h.

Referenced by do_print(), do_print_csrc(), do_print_latex(), and print_overall_coeff().

◆ info()

bool GiNaC::mul::info ( unsigned inf ) const

overridevirtual

Information about the object.

See also: class info_flags

Reimplemented from GiNaC::expairseq.

Definition at line 272 of file mul.cpp.

Referenced by expand(), and info().

◆ is_polynomial()

bool GiNaC::mul::is_polynomial ( const ex & var ) const

overridevirtual

Check whether this is a polynomial in the given variables.

Reimplemented from GiNaC::basic.

Definition at line 386 of file mul.cpp.

References GiNaC::info_flags::nonnegint, and GiNaC::expairseq::seq.

◆ degree()

int GiNaC::mul::degree ( const ex & s ) const

overridevirtual

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 397 of file mul.cpp.

References GiNaC::ex::degree(), recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ ldegree()

int GiNaC::mul::ldegree ( const ex & s ) const

overridevirtual

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 412 of file mul.cpp.

References GiNaC::ex::ldegree(), recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ coeff()

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

overridevirtual

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 427 of file mul.cpp.

References GiNaC::_ex0, c, GiNaC::ex::coeff(), coeff(), n, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), and GiNaC::expairseq::seq.

Referenced by coeff(), and print_overall_coeff().

◆ has()

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

overridevirtual

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 from GiNaC::basic.

Definition at line 754 of file mul.cpp.

References GiNaC::has_options::algebraic, GiNaC::algebraic_match_mul_with_mul(), GiNaC::basic::has(), GiNaC::expairseq::nops(), and options.

◆ eval()

ex GiNaC::mul::eval ( ) const

overridevirtual

Perform automatic term rewriting rules in this class.

In the following x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2... stand for such expressions that contain a plain number.

*(...,x;0) -> 0
*(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
*(x;1) -> x
*(;c) -> c

Reimplemented from GiNaC::expairseq.

Definition at line 468 of file mul.cpp.

References GiNaC::_ex0, GiNaC::_ex1, GiNaC::_num1_p, GiNaC::_num_1_p, c, GiNaC::basic::clearflag(), GiNaC::ex::coeff(), GiNaC::add::combine_pair_with_coeff_to_pair(), GiNaC::numeric::div(), GiNaC::expairseq::evalchildren(), GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, GiNaC::basic::flags, GINAC_ASSERT, GiNaC::status_flags::hash_calculated, GiNaC::basic::hold(), GiNaC::ex::is_equal(), GiNaC::numeric::is_integer(), GiNaC::numeric::is_pos_integer(), GiNaC::ex::is_zero(), last, likely, GiNaC::numeric::mul(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, and unlikely.

◆ evalf()

ex GiNaC::mul::evalf ( ) const

overridevirtual

Evaluate object numerically.

Reimplemented from GiNaC::basic.

Definition at line 577 of file mul.cpp.

References GiNaC::ex::evalf(), GiNaC::expairseq::overall_coeff, and GiNaC::expairseq::seq.

◆ real_part()

ex GiNaC::mul::real_part ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 608 of file mul.cpp.

References find_real_imag().

◆ imag_part()

ex GiNaC::mul::imag_part ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 615 of file mul.cpp.

References find_real_imag().

◆ evalm()

ex GiNaC::mul::evalm ( ) const

overridevirtual

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 622 of file mul.cpp.

References GiNaC::_ex1, GiNaC::ex::end(), GiNaC::ex::evalm(), m, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, and split_ex_to_pair().

◆ series()

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

overridevirtual

Implementation of ex::series() for product.

This performs series multiplication when multiplying series.

See also: ex::series

Reimplemented from GiNaC::basic.

Definition at line 863 of file pseries.cpp.

References GiNaC::_ex1, GiNaC::ex::coeff(), GiNaC::ex::expand(), GiNaC::factor(), GINAC_ASSERT, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::ldegree(), GiNaC::pseries::mul_const(), GiNaC::pseries::mul_series(), GiNaC::expairseq::op(), options, order, GiNaC::expairseq::overall_coeff, r, recombine_pair_to_ex(), GiNaC::expairseq::seq, and GiNaC::ex::series().

◆ normal()

ex GiNaC::mul::normal	(	exmap &	repl,
		exmap &	rev_lookup,
		lst &	modifier
	)		const

overridevirtual

Implementation of ex::normal() for a product.

It cancels common factors from fractions.

See also: ex::normal()

Reimplemented from GiNaC::basic.

Definition at line 2401 of file normal.cpp.

References GiNaC::frac_cancel(), n, GiNaC::subs_options::no_pattern, GiNaC::container< C >::nops(), GiNaC::container< C >::op(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ integer_content()

numeric GiNaC::mul::integer_content ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 348 of file normal.cpp.

References GiNaC::abs(), GINAC_ASSERT, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ smod()

ex GiNaC::mul::smod ( const numeric & xi ) const

overridevirtual

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 from GiNaC::basic.

Definition at line 1228 of file normal.cpp.

References GiNaC::basic::clearflag(), GiNaC::status_flags::evaluated, GINAC_ASSERT, GiNaC::status_flags::hash_calculated, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, and GiNaC::smod().

◆ max_coefficient()

numeric GiNaC::mul::max_coefficient ( ) const

overridevirtual

Implementation ex::max_coefficient().

See also: heur_gcd

Reimplemented from GiNaC::basic.

Definition at line 1185 of file normal.cpp.

References GiNaC::abs(), GINAC_ASSERT, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ get_free_indices()

exvector GiNaC::mul::get_free_indices ( ) const

overridevirtual

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 479 of file indexed.cpp.

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

◆ conjugate()

ex GiNaC::mul::conjugate ( ) const

overridevirtual

Reimplemented from GiNaC::expairseq.

Definition at line 829 of file mul.cpp.

References GiNaC::are_ex_trivially_equal(), c, GiNaC::ex::conjugate(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, split_ex_to_pair(), thisexpairseq(), and x.

◆ derivative()

ex GiNaC::mul::derivative ( const symbol & s ) const

overrideprotectedvirtual

Implementation of ex::diff() for a product.

It applies the product rule.

See also: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 863 of file mul.cpp.

References GiNaC::_ex1, GiNaC::ex::coeff(), GiNaC::basic::diff(), GiNaC::expairseq::overall_coeff, GiNaC::pow(), GiNaC::expairseq::seq, split_ex_to_pair(), and GiNaC::expair::swap().

◆ eval_ncmul()

ex GiNaC::mul::eval_ncmul ( const exvector & v ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 660 of file mul.cpp.

References GiNaC::return_types::noncommutative, and GiNaC::expairseq::seq.

◆ return_type()

unsigned GiNaC::mul::return_type ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 889 of file mul.cpp.

References GiNaC::return_types::commutative, GiNaC::return_types::noncommutative, GiNaC::return_types::noncommutative_composite, and GiNaC::expairseq::seq.

◆ return_type_tinfo()

return_type_t GiNaC::mul::return_type_tinfo ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 922 of file mul.cpp.

References GiNaC::return_types::noncommutative, and GiNaC::expairseq::seq.

◆ thisexpairseq() [1/2]

ex GiNaC::mul::thisexpairseq	(	const epvector &	v,
		const ex &	oc,
		bool	do_index_renaming = `false`
	)		const

overrideprotectedvirtual

Create an object of this type.

This method works similar to a constructor. It is useful because expairseq has (at least) two possible different semantics but we want to inherit methods thus avoiding code duplication. Sometimes a method in expairseq has to create a new one of the same semantics, which cannot be done by a ctor because the name (add, mul,...) is unknown on the expairseq level. In order for this trick to work a derived class must of course override this definition.

Reimplemented from GiNaC::expairseq.

Definition at line 936 of file mul.cpp.

Referenced by conjugate().

◆ thisexpairseq() [2/2]

ex GiNaC::mul::thisexpairseq	(	epvector &&	vp,
		const ex &	oc,
		bool	do_index_renaming = `false`
	)		const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 941 of file mul.cpp.

◆ split_ex_to_pair()

expair GiNaC::mul::split_ex_to_pair ( const ex & e ) const

overrideprotectedvirtual

Form an expair from an ex, using the corresponding semantics.

See also: expairseq::recombine_pair_to_ex()

Reimplemented from GiNaC::expairseq.

Definition at line 946 of file mul.cpp.

References GiNaC::_ex1, GiNaC::power::basis, and GiNaC::power::exponent.

Referenced by combine_ex_with_coeff_to_pair(), combine_pair_with_coeff_to_pair(), conjugate(), derivative(), evalm(), expair_needs_further_processing(), expand(), and expandchildren().

◆ combine_ex_with_coeff_to_pair()

expair GiNaC::mul::combine_ex_with_coeff_to_pair	(	const ex &	e,
		const ex &	c
	)		const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 956 of file mul.cpp.

References GiNaC::_ex1, c, GINAC_ASSERT, GiNaC::pow(), and split_ex_to_pair().

◆ combine_pair_with_coeff_to_pair()

expair GiNaC::mul::combine_pair_with_coeff_to_pair	(	const expair &	p,
		const ex &	c
	)		const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 976 of file mul.cpp.

References GiNaC::_ex1, c, GiNaC::expair::coeff, GINAC_ASSERT, GiNaC::ex::is_equal(), GiNaC::pow(), recombine_pair_to_ex(), GiNaC::expair::rest, and split_ex_to_pair().

◆ recombine_pair_to_ex()

ex GiNaC::mul::recombine_pair_to_ex ( const expair & p ) const

overrideprotectedvirtual

Form an ex out of an expair, using the corresponding semantics.

See also: expairseq::split_ex_to_pair()

Reimplemented from GiNaC::expairseq.

Definition at line 999 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expair::coeff, GiNaC::ex::is_equal(), and GiNaC::expair::rest.

Referenced by coeff(), combine_pair_with_coeff_to_pair(), conjugate(), degree(), do_print(), do_print_latex(), eval(), evalm(), expair_needs_further_processing(), expandchildren(), find_real_imag(), info(), integer_content(), ldegree(), max_coefficient(), normal(), series(), and smod().

◆ expair_needs_further_processing()

bool GiNaC::mul::expair_needs_further_processing ( epp it )

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 1007 of file mul.cpp.

References GiNaC::_ex1, GiNaC::expair::is_equal(), recombine_pair_to_ex(), and split_ex_to_pair().

◆ default_overall_coeff()

ex GiNaC::mul::default_overall_coeff ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 1030 of file mul.cpp.

References GiNaC::_ex1.

◆ combine_overall_coeff() [1/2]

void GiNaC::mul::combine_overall_coeff ( const ex & c )

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 1035 of file mul.cpp.

References c, GINAC_ASSERT, and GiNaC::expairseq::overall_coeff.

◆ combine_overall_coeff() [2/2]

void GiNaC::mul::combine_overall_coeff	(	const ex &	c1,
		const ex &	c2
	)

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 1042 of file mul.cpp.

References GINAC_ASSERT, GiNaC::expairseq::overall_coeff, and power.

◆ can_make_flat()

bool GiNaC::mul::can_make_flat ( const expair & p ) const

overrideprotectedvirtual

Reimplemented from GiNaC::expairseq.

Definition at line 1050 of file mul.cpp.

References GiNaC::expair::coeff, GINAC_ASSERT, GiNaC::ex::info(), and GiNaC::info_flags::integer.

◆ expand()

ex GiNaC::mul::expand ( unsigned options = 0 ) const

overrideprotectedvirtual

Expand expression, i.e.

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

Reimplemented from GiNaC::expairseq.

Definition at line 1072 of file mul.cpp.

References GiNaC::_ex1, GiNaC::_num0_p, can_be_further_expanded(), GiNaC::ex::expand(), GiNaC::expand_options::expand_rename_idx, expandchildren(), GiNaC::status_flags::expanded, factors, GiNaC::get_all_dummy_indices_safely(), GiNaC::info_flags::has_indices, info(), GiNaC::info_flags::integer, GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), mul(), GiNaC::numeric::mul(), n, GiNaC::subs_options::no_pattern, GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::container< C >::op(), options, GiNaC::expairseq::overall_coeff, GiNaC::rename_dummy_indices_uniquely(), GiNaC::expairseq::seq, GiNaC::basic::setflag(), and split_ex_to_pair().

◆ algebraic_subs_mul()

ex GiNaC::mul::algebraic_subs_mul	(	const exmap &	m,
		unsigned	options
	)		const

Definition at line 770 of file mul.cpp.

References GiNaC::subs_options::algebraic, GiNaC::algebraic_match_mul_with_mul(), m, GiNaC::subs_options::no_pattern, GiNaC::expairseq::nops(), GiNaC::expairseq::op(), options, GiNaC::pow(), GiNaC::ex::subs(), GiNaC::basic::subs_one_level(), and GiNaC::tryfactsubs().

◆ find_real_imag()

void GiNaC::mul::find_real_imag	(	ex &	rp,
		ex &	ip
	)		const

protected

Definition at line 587 of file mul.cpp.

References GiNaC::ex::expand(), GiNaC::factor(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), GiNaC::expairseq::overall_coeff, GiNaC::ex::real_part(), recombine_pair_to_ex(), and GiNaC::expairseq::seq.

Referenced by imag_part(), and real_part().

◆ print_overall_coeff()

void GiNaC::mul::print_overall_coeff	(	const print_context &	c,
		const char *	mul_sym
	)		const

protected

Definition at line 126 of file mul.cpp.

References GiNaC::_num1_p, GiNaC::_num_1_p, c, coeff(), GiNaC::ex::is_equal(), GiNaC::expairseq::overall_coeff, precedence(), GiNaC::basic::print(), and GiNaC::ex::print().

Referenced by do_print(), and do_print_latex().

◆ do_print()

void GiNaC::mul::do_print	(	const print_context &	c,
		unsigned	level
	)		const

protected

Definition at line 148 of file mul.cpp.

References c, precedence(), GiNaC::ex::print(), print_overall_coeff(), recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ do_print_latex()

void GiNaC::mul::do_print_latex	(	const print_latex &	c,
		unsigned	level
	)		const

protected

Definition at line 168 of file mul.cpp.

References c, GINAC_ASSERT, mul(), precedence(), print_overall_coeff(), recombine_pair_to_ex(), and GiNaC::expairseq::seq.

◆ do_print_csrc()

void GiNaC::mul::do_print_csrc	(	const print_csrc &	c,
		unsigned	level
	)		const

protected

Definition at line 208 of file mul.cpp.

References GiNaC::_ex1, GiNaC::_ex_1, c, GiNaC::basic::ex, GiNaC::ex::is_equal(), GiNaC::info_flags::negint, GiNaC::expairseq::overall_coeff, power, precedence(), GiNaC::ex::print(), and GiNaC::expairseq::seq.

◆ do_print_python_repr()

void GiNaC::mul::do_print_python_repr	(	const print_python_repr &	c,
		unsigned	level
	)		const

protected

Definition at line 261 of file mul.cpp.

References c, GiNaC::expairseq::nops(), GiNaC::expairseq::op(), and GiNaC::ex::print().

◆ can_be_further_expanded()

bool GiNaC::mul::can_be_further_expanded ( const ex & e )

staticprotected

Definition at line 1058 of file mul.cpp.

References GiNaC::ex::info(), GiNaC::ex::op(), GiNaC::info_flags::posint, and GiNaC::expairseq::seq.

Referenced by expand().

◆ expandchildren()

epvector GiNaC::mul::expandchildren ( unsigned options ) const

protected

Member-wise expand the expairs representing this sequence.

This must be overridden from expairseq::expandchildren() and done iteratively in order to allow for early cancellations and thus safe memory.

See also: mul::expand()

Returns: epvector containing expanded pairs, empty if no members had to be changed.

Definition at line 1258 of file mul.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::ex::expand(), GiNaC::factor(), last, options, recombine_pair_to_ex(), GiNaC::expairseq::seq, and split_ex_to_pair().

Referenced by expand().

Friends And Related Function Documentation

◆ add

friend class add

friend

Definition at line 35 of file mul.h.

◆ ncmul

friend class ncmul

friend

Definition at line 36 of file mul.h.

◆ power

friend class power

friend

Definition at line 37 of file mul.h.

Referenced by combine_overall_coeff(), and do_print_csrc().

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ mul() [1/7]

◆ mul() [2/7]

◆ mul() [3/7]

◆ mul() [4/7]

◆ mul() [5/7]

◆ mul() [6/7]

◆ mul() [7/7]

Member Function Documentation

◆ precedence()

◆ info()

◆ is_polynomial()

◆ degree()

◆ ldegree()

◆ coeff()

◆ has()

◆ eval()

◆ evalf()

◆ real_part()

◆ imag_part()

◆ evalm()

◆ series()

◆ normal()

◆ integer_content()

◆ smod()

◆ max_coefficient()

◆ get_free_indices()

◆ conjugate()

◆ derivative()

◆ eval_ncmul()

◆ return_type()

◆ return_type_tinfo()

◆ thisexpairseq() [1/2]

◆ thisexpairseq() [2/2]

◆ split_ex_to_pair()

◆ combine_ex_with_coeff_to_pair()

◆ combine_pair_with_coeff_to_pair()

◆ recombine_pair_to_ex()

◆ expair_needs_further_processing()

◆ default_overall_coeff()

◆ combine_overall_coeff() [1/2]

◆ combine_overall_coeff() [2/2]

◆ can_make_flat()

◆ expand()

◆ algebraic_subs_mul()

◆ find_real_imag()

◆ print_overall_coeff()

◆ do_print()

◆ do_print_latex()

◆ do_print_csrc()

◆ do_print_python_repr()

◆ can_be_further_expanded()

◆ expandchildren()

Friends And Related Function Documentation

◆ add

◆ ncmul

◆ power