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 (std::auto_ptr< epvector > vp, const ex &oc, bool do_index_renaming=false)
	mul (const ex &lh, const ex &mh, const ex &rh)
unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
bool	info (unsigned inf) const
	Information about the object.
bool	is_polynomial (const ex &var) const
	Check whether this is a polynomial in the given variables.
int	degree (const ex &s) const
	Return degree of highest power in object s.
int	ldegree (const ex &s) const
	Return degree of lowest power in object s.
ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s.
bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern.
ex	eval (int level=0) const
	Perform automatic term rewriting rules in this class.
ex	evalf (int level=0) const
	Evaluate object numerically.
ex	real_part () const
ex	imag_part () const
ex	evalm () const
	Evaluate sums, products and integer powers of matrices.
ex	series (const relational &s, int order, unsigned options=0) const
	Implementation of ex::series() for product.
ex	normal (exmap &repl, exmap &rev_lookup, int level=0) const
	Implementation of ex::normal() for a product.
numeric	integer_content () const
ex	smod (const numeric &xi) const
	Apply symmetric modular homomorphism to an expanded multivariate polynomial.
numeric	max_coefficient () const
	Implementation ex::max_coefficient().
exvector	get_free_indices () const
	Return a vector containing the free indices of an expression.
ex	conjugate () const
ex	algebraic_subs_mul (const exmap &m, unsigned options) const
Protected Member Functions
ex	derivative (const symbol &s) const
	Implementation of ex::diff() for a product.
ex	eval_ncmul (const exvector &v) const
unsigned	return_type () const
return_type_t	return_type_tinfo () const
ex	thisexpairseq (const epvector &v, const ex &oc, bool do_index_renaming=false) const
	Create an object of this type.
ex	thisexpairseq (std::auto_ptr< epvector > vp, const ex &oc, bool do_index_renaming=false) const
expair	split_ex_to_pair (const ex &e) const
	Form an expair from an ex, using the corresponding semantics.
expair	combine_ex_with_coeff_to_pair (const ex &e, const ex &c) const
expair	combine_pair_with_coeff_to_pair (const expair &p, const ex &c) const
ex	recombine_pair_to_ex (const expair &p) const
	Form an ex out of an expair, using the corresponding semantics.
bool	expair_needs_further_processing (epp it)
ex	default_overall_coeff () const
void	combine_overall_coeff (const ex &c)
void	combine_overall_coeff (const ex &c1, const ex &c2)
bool	can_make_flat (const expair &p) const
ex	expand (unsigned options=0) const
	Expand expression, i.e.
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
	Default output to stream.
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
	Python parsable output to stream.
std::auto_ptr< epvector >	expandchildren (unsigned options) const
	Member-wise expand the expairs representing this sequence.
Static Protected Member Functions
static bool	can_be_further_expanded (const ex &e)
Friends
class	add
class	ncmul
class	power

Detailed Description

Product of expressions.

Definition at line 31 of file mul.h.

Constructor & Destructor Documentation

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(), normal(), and smod().

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.

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.

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.

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

Definition at line 92 of file mul.cpp.

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

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

Definition at line 100 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

unsigned GiNaC::mul::precedence ( ) const [inline, virtual]

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::expairseq.

Definition at line 50 of file mul.h.

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

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

Information about the object.

See also:: class info_flags

Reimplemented from GiNaC::expairseq.

Definition at line 274 of file mul.cpp.

References GiNaC::_num1_p, GiNaC::factor(), GiNaC::numeric::info(), GiNaC::ex::info(), and GiNaC::real().

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

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

Check whether this is a polynomial in the given variables.

Reimplemented from GiNaC::basic.

Definition at line 350 of file mul.cpp.

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

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 361 of file mul.cpp.

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

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 378 of file mul.cpp.

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

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 395 of file mul.cpp.

References GiNaC::_ex0, GiNaC::ex::begin(), c, GiNaC::ex::coeff(), and GiNaC::ex::is_zero().

Referenced by print_overall_coeff().

bool GiNaC::mul::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 from GiNaC::basic.

Definition at line 751 of file mul.cpp.

References GiNaC::algebraic_match_mul_with_mul(), GiNaC::has(), and GiNaC::nops().

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

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

Parameters:

level cut-off in recursive evaluation

Reimplemented from GiNaC::expairseq.

Definition at line 442 of file mul.cpp.

References GiNaC::_ex0, GiNaC::_ex1, GiNaC::_num1_p, GiNaC::_num_1_p, c, GiNaC::coeff(), GiNaC::add::combine_pair_with_coeff_to_pair(), GINAC_ASSERT, GiNaC::numeric::is_integer(), GiNaC::numeric::is_pos_integer(), last, likely, GiNaC::numeric::mul(), GiNaC::expairseq::overall_coeff, and GiNaC::expairseq::seq.

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

Evaluate object numerically.

Reimplemented from GiNaC::basic.

Definition at line 558 of file mul.cpp.

References GiNaC::max_recursion_level.

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

Reimplemented from GiNaC::basic.

Definition at line 600 of file mul.cpp.

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

Reimplemented from GiNaC::basic.

Definition at line 607 of file mul.cpp.

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

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 614 of file mul.cpp.

References GiNaC::_ex1, m, GiNaC::matrix::mul_scalar(), and GiNaC::basic::setflag().

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

Implementation of ex::series() for product.

This performs series multiplication when multiplying series.

See also:: ex::series

Reimplemented from GiNaC::basic.

Definition at line 884 of file pseries.cpp.

References GiNaC::_ex1, GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::expand(), GiNaC::factor(), GINAC_ASSERT, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::ldegree(), GiNaC::relational::lhs(), GiNaC::pseries::mul_const(), GiNaC::expairseq::op(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::relational::rhs(), GiNaC::expairseq::seq, GiNaC::ex::series(), and GiNaC::to_int().

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

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

It cancels common factors from fractions.

See also:: ex::normal()

Reimplemented from GiNaC::basic.

Definition at line 2228 of file normal.cpp.

References GiNaC::_ex1, GiNaC::status_flags::dynallocated, GiNaC::frac_cancel(), GiNaC::max_recursion_level, mul(), n, GiNaC::ex::op(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::replace_with_symbol(), GiNaC::expairseq::seq, and GiNaC::basic::setflag().

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

Reimplemented from GiNaC::basic.

Definition at line 340 of file normal.cpp.

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

ex GiNaC::mul::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 from GiNaC::basic.

Definition at line 1232 of file normal.cpp.

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

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

Implementation ex::max_coefficient().

See also:: heur_gcd

Reimplemented from GiNaC::basic.

Definition at line 1183 of file normal.cpp.

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

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

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 488 of file indexed.cpp.

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

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

Reimplemented from GiNaC::expairseq.

Definition at line 826 of file mul.cpp.

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

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

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

It applies the product rule.

See also:: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 862 of file mul.cpp.

References GiNaC::_ex1, GiNaC::ex::begin(), GiNaC::basic::diff(), and GiNaC::expair::swap().

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

Reimplemented from GiNaC::basic.

Definition at line 654 of file mul.cpp.

References GiNaC::ex::begin().

unsigned GiNaC::mul::return_type ( ) const [protected, virtual]

Reimplemented from GiNaC::expairseq.

Definition at line 888 of file mul.cpp.

return_type_t GiNaC::mul::return_type_tinfo ( ) const [protected, virtual]

Reimplemented from GiNaC::basic.

Definition at line 921 of file mul.cpp.

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

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 expaiseq level. In order for this trick to work a derived class must of course override this definition.

Reimplemented from GiNaC::expairseq.

Definition at line 937 of file mul.cpp.

ex GiNaC::mul::thisexpairseq	(	std::auto_ptr< epvector >	vp,
		const ex &	oc,
		bool	do_index_renaming = `false`
	)		const `[protected, virtual]`

Reimplemented from GiNaC::expairseq.

Definition at line 942 of file mul.cpp.

expair GiNaC::mul::split_ex_to_pair ( const ex & e ) const [protected, virtual]

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

See also:: expairseq::recombine_pair_to_ex()

Reimplemented from GiNaC::expairseq.

Definition at line 947 of file mul.cpp.

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

expair GiNaC::mul::combine_ex_with_coeff_to_pair	(	const ex &	e,
		const ex &	c
	)		const `[protected, virtual]`

Reimplemented from GiNaC::expairseq.

Definition at line 957 of file mul.cpp.

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

expair GiNaC::mul::combine_pair_with_coeff_to_pair	(	const expair &	p,
		const ex &	c
	)		const `[protected, virtual]`

Reimplemented from GiNaC::expairseq.

Definition at line 970 of file mul.cpp.

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

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

ex GiNaC::mul::recombine_pair_to_ex ( const expair & p ) const [protected, virtual]

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 983 of file mul.cpp.

References GiNaC::_num1_p, GiNaC::expair::coeff, and GiNaC::expair::rest.

Referenced by do_print(), do_print_latex(), integer_content(), max_coefficient(), normal(), series(), and smod().

bool GiNaC::mul::expair_needs_further_processing ( epp it ) [protected, virtual]

Reimplemented from GiNaC::expairseq.

Definition at line 991 of file mul.cpp.

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

ex GiNaC::mul::default_overall_coeff ( ) const [protected, virtual]

Reimplemented from GiNaC::expairseq.

Definition at line 1014 of file mul.cpp.

References GiNaC::_ex1.

void GiNaC::mul::combine_overall_coeff ( const ex & c ) [protected, virtual]

Reimplemented from GiNaC::expairseq.

Definition at line 1019 of file mul.cpp.

References GINAC_ASSERT.

void GiNaC::mul::combine_overall_coeff	(	const ex &	c1,
		const ex &	c2
	)		`[protected, virtual]`

Reimplemented from GiNaC::expairseq.

Definition at line 1026 of file mul.cpp.

References GINAC_ASSERT.

bool GiNaC::mul::can_make_flat ( const expair & p ) const [protected, virtual]

Reimplemented from GiNaC::expairseq.

Definition at line 1034 of file mul.cpp.

References GiNaC::_num1_p, GiNaC::expair::coeff, and GINAC_ASSERT.

ex GiNaC::mul::expand ( unsigned options = 0 ) const [protected, virtual]

Expand expression, i.e.

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

Reimplemented from GiNaC::expairseq.

Definition at line 1057 of file mul.cpp.

References GiNaC::_ex1, GiNaC::_num0_p, GiNaC::ex::begin(), GiNaC::ex::expand(), factors, GiNaC::get_all_dummy_indices_safely(), GiNaC::ex::is_equal(), GiNaC::ex::is_zero(), n, GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::container< C >::op(), GiNaC::expairseq::overall_coeff, GiNaC::rename_dummy_indices_uniquely(), and GiNaC::expairseq::seq.

void GiNaC::mul::find_real_imag	(	ex &	rp,
		ex &	ip
	)		const `[protected]`

Definition at line 579 of file mul.cpp.

References GiNaC::ex::expand(), GiNaC::factor(), GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), and GiNaC::ex::real_part().

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

Definition at line 767 of file mul.cpp.

References GiNaC::algebraic_match_mul_with_mul(), GiNaC::nops(), GiNaC::op(), GiNaC::ex::subs(), and GiNaC::tryfactsubs().

void GiNaC::mul::print_overall_coeff	(	const print_context &	c,
		const char *	mul_sym
	)		const `[protected]`

Definition at line 120 of file mul.cpp.

References GiNaC::_num1_p, GiNaC::_num_1_p, coeff(), GiNaC::numeric::csgn(), GiNaC::numeric::is_equal(), GiNaC::numeric::is_negative(), GiNaC::numeric::is_rational(), GiNaC::expairseq::overall_coeff, precedence(), GiNaC::basic::print(), and GiNaC::print_context::s.

Referenced by do_print(), and do_print_latex().

void GiNaC::mul::do_print	(	const print_context &	c,
		unsigned	level
	)		const `[protected]`

Default output to stream.

Reimplemented from GiNaC::expairseq.

Definition at line 142 of file mul.cpp.

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

void GiNaC::mul::do_print_latex	(	const print_latex &	c,
		unsigned	level
	)		const `[protected]`

Definition at line 164 of file mul.cpp.

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

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, GiNaC::ex::is_equal(), GiNaC::expairseq::overall_coeff, precedence(), GiNaC::ex::print(), and GiNaC::print_context::s.

void GiNaC::mul::do_print_python_repr	(	const print_python_repr &	c,
		unsigned	level
	)		const `[protected]`

Python parsable output to stream.

Reimplemented from GiNaC::basic.

Definition at line 263 of file mul.cpp.

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

bool GiNaC::mul::can_be_further_expanded ( const ex & e ) [static, protected]

Definition at line 1043 of file mul.cpp.

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

std::auto_ptr< 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 cancallations and thus safe memory.

See also:: mul::expand()

Returns:: pointer to epvector containing expanded representation or zero pointer, if sequence is unchanged.

Reimplemented from GiNaC::expairseq.

Definition at line 1246 of file mul.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::ex::expand(), GiNaC::factor(), and last.

Friends And Related Function Documentation

friend class add [friend]

Definition at line 35 of file mul.h.

friend class ncmul [friend]

Definition at line 36 of file mul.h.

friend class power [friend]

Definition at line 37 of file mul.h.

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

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation