Sum of expressions. More...

#include <add.h>

Inheritance diagram for GiNaC::add:

Public Member Functions
	add (const ex &lh, const ex &rh)
	add (const exvector &v)
	add (const epvector &v)
	add (const epvector &v, const ex &oc)
	add (std::auto_ptr< epvector > vp, const ex &oc)
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.
ex	eval (int level=0) const
	Perform automatic term rewriting rules in this class.
ex	evalm () const
	Evaluate sums, products and integer powers of matrices.
ex	series (const relational &r, int order, unsigned options=0) const
	Implementation of ex::series() for sums.
ex	normal (exmap &repl, exmap &rev_lookup, int level=0) const
	Implementation of ex::normal() for a sum.
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().
ex	conjugate () const
ex	real_part () const
ex	imag_part () const
exvector	get_free_indices () const
	Return a vector containing the free indices of an expression.
ex	eval_ncmul (const exvector &v) const
Protected Member Functions
ex	derivative (const symbol &s) const
	Implementation of ex::diff() for a sum.
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.
ex	expand (unsigned options=0) const
	Expand expression, i.e.
void	print_add (const print_context &c, const char openbrace, const char closebrace, const char *mul_sym, unsigned level) 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.
Friends
class	mul
class	power

Detailed Description

Sum of expressions.

Definition at line 31 of file add.h.

Constructor & Destructor Documentation

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

Definition at line 61 of file add.cpp.

References GiNaC::_ex0, GiNaC::expairseq::construct_from_2_ex(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

Referenced by coeff(), conjugate(), derivative(), eval(), evalm(), expand(), imag_part(), real_part(), smod(), and thisexpairseq().

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

Definition at line 68 of file add.cpp.

References GiNaC::_ex0, GiNaC::expairseq::construct_from_exvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

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

Definition at line 75 of file add.cpp.

References GiNaC::_ex0, GiNaC::expairseq::construct_from_epvector(), GINAC_ASSERT, GiNaC::expairseq::is_canonical(), and GiNaC::expairseq::overall_coeff.

GiNaC::add::add	(	const epvector &	v,
		const ex &	oc
	)

Definition at line 82 of file add.cpp.

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

GiNaC::add::add	(	std::auto_ptr< epvector >	vp,
		const ex &	oc
	)

Definition at line 89 of file add.cpp.

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

Member Function Documentation

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

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::expairseq.

Definition at line 48 of file add.h.

Referenced by do_print_csrc(), and print_add().

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

Information about the object.

See also:: class info_flags

Reimplemented from GiNaC::expairseq.

Definition at line 221 of file add.cpp.

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

Check whether this is a polynomial in the given variables.

Reimplemented from GiNaC::basic.

Definition at line 263 of file add.cpp.

References GiNaC::expairseq::seq.

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

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 273 of file add.cpp.

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

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

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 290 of file add.cpp.

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

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

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 307 of file add.cpp.

References GiNaC::_ex0, add(), GiNaC::clifford_max_label(), GiNaC::ncmul::coeff(), GiNaC::ex::coeff(), combine_ex_with_coeff_to_pair(), GiNaC::dirac_ONE(), GiNaC::status_flags::dynallocated, GiNaC::ex::is_zero(), GiNaC::expairseq::overall_coeff, and GiNaC::expairseq::seq.

Referenced by print_add(), and smod().

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

Perform automatic term rewriting rules in this class.

In the following x stands for a symbolic variables of type ex and c stands for such an expression that contain a plain number.

+(;c) -> c
+(x;0) -> x

Parameters:

level cut-off in recursive evaluation

Reimplemented from GiNaC::expairseq.

Definition at line 344 of file add.cpp.

References GiNaC::_num1_p, add(), GiNaC::return_types::commutative, GiNaC::status_flags::dynallocated, GiNaC::expairseq::evalchildren(), GiNaC::status_flags::evaluated, GiNaC::basic::flags, GINAC_ASSERT, GiNaC::basic::hold(), GiNaC::ex::is_zero(), last, GiNaC::numeric::mul(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, GiNaC::basic::setflag(), and unlikely.

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

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 407 of file add.cpp.

References add(), GiNaC::matrix::add(), GiNaC::status_flags::dynallocated, GiNaC::ex::evalm(), m, GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::expairseq::seq, and split_ex_to_pair().

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

Implementation of ex::series() for sums.

This performs series addition when adding pseries objects.

See also:: ex::series

Reimplemented from GiNaC::basic.

Definition at line 776 of file pseries.cpp.

References GiNaC::_ex1, GiNaC::expairseq::op(), GiNaC::expairseq::overall_coeff, GiNaC::expairseq::seq, and GiNaC::ex::series().

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

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

It expands terms and performs fractional addition.

See also:: ex::normal

Reimplemented from GiNaC::basic.

Definition at line 2169 of file normal.cpp.

References GiNaC::_ex1, GiNaC::status_flags::dynallocated, expand(), GiNaC::frac_cancel(), GiNaC::gcd(), GINAC_ASSERT, GiNaC::max_recursion_level, n, GiNaC::ex::op(), GiNaC::expairseq::overall_coeff, recombine_pair_to_ex(), GiNaC::replace_with_symbol(), and GiNaC::expairseq::seq.

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

Reimplemented from GiNaC::basic.

Definition at line 322 of file normal.cpp.

References GiNaC::_num0_p, GiNaC::_num1_p, c, GiNaC::denom(), GiNaC::gcd(), GINAC_ASSERT, GiNaC::lcm(), GiNaC::numer(), GiNaC::expairseq::overall_coeff, and GiNaC::expairseq::seq.

ex GiNaC::add::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 1214 of file normal.cpp.

References add(), coeff(), GiNaC::status_flags::dynallocated, GINAC_ASSERT, GiNaC::numeric::is_zero(), GiNaC::expairseq::overall_coeff, and GiNaC::expairseq::seq.

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

Implementation ex::max_coefficient().

See also:: heur_gcd

Reimplemented from GiNaC::basic.

Definition at line 1166 of file normal.cpp.

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

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

Reimplemented from GiNaC::expairseq.

Definition at line 439 of file add.cpp.

References add(), GiNaC::are_ex_trivially_equal(), GiNaC::ex::conjugate(), GiNaC::expairseq::nops(), and GiNaC::expairseq::op().

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

Reimplemented from GiNaC::basic.

Definition at line 465 of file add.cpp.

References add(), GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::is_zero(), GiNaC::expairseq::overall_coeff, GiNaC::info_flags::real, GiNaC::ex::real_part(), recombine_pair_to_ex(), GiNaC::expairseq::seq, GiNaC::basic::setflag(), and split_ex_to_pair().

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

Reimplemented from GiNaC::basic.

Definition at line 483 of file add.cpp.

References add(), GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::imag_part(), GiNaC::ex::is_zero(), GiNaC::expairseq::overall_coeff, GiNaC::info_flags::real, recombine_pair_to_ex(), GiNaC::expairseq::seq, GiNaC::basic::setflag(), and split_ex_to_pair().

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

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 473 of file indexed.cpp.

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

ex GiNaC::add::eval_ncmul ( const exvector & v ) const [virtual]

Reimplemented from GiNaC::basic.

Definition at line 501 of file add.cpp.

References GiNaC::expairseq::seq.

ex GiNaC::add::derivative ( const symbol & y ) const [protected, virtual]

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

It differentiates each term.

See also:: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 513 of file add.cpp.

References GiNaC::_ex0, add(), combine_ex_with_coeff_to_pair(), GiNaC::status_flags::dynallocated, GiNaC::expairseq::seq, and GiNaC::basic::setflag().

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

Reimplemented from GiNaC::expairseq.

Definition at line 534 of file add.cpp.

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

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

Reimplemented from GiNaC::basic.

Definition at line 542 of file add.cpp.

References GiNaC::expairseq::seq.

ex GiNaC::add::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 551 of file add.cpp.

References add(), and GiNaC::status_flags::dynallocated.

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

Reimplemented from GiNaC::expairseq.

Definition at line 557 of file add.cpp.

References add(), and GiNaC::status_flags::dynallocated.

expair GiNaC::add::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 562 of file add.cpp.

References GiNaC::_ex1, GiNaC::basic::clearflag(), GiNaC::status_flags::dynallocated, GiNaC::status_flags::evaluated, GiNaC::status_flags::hash_calculated, mul, GiNaC::expairseq::overall_coeff, and GiNaC::basic::setflag().

Referenced by evalm(), imag_part(), and real_part().

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

Reimplemented from GiNaC::expairseq.

Definition at line 577 of file add.cpp.

References GiNaC::_ex1, GiNaC::basic::clearflag(), GiNaC::status_flags::dynallocated, GiNaC::status_flags::evaluated, GINAC_ASSERT, GiNaC::status_flags::hash_calculated, GiNaC::ex::is_equal(), mul, GiNaC::expairseq::overall_coeff, and GiNaC::basic::setflag().

Referenced by coeff(), derivative(), and GiNaC::power::expand_add_2().

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

Reimplemented from GiNaC::expairseq.

Definition at line 603 of file add.cpp.

References GiNaC::_ex1, GiNaC::_num1_p, GiNaC::expair::coeff, GINAC_ASSERT, and GiNaC::expair::rest.

Referenced by GiNaC::mul::eval(), and GiNaC::power::expand_add_2().

ex GiNaC::add::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 617 of file add.cpp.

References GiNaC::_num1_p, GiNaC::expair::coeff, GiNaC::status_flags::dynallocated, mul, GiNaC::expair::rest, and GiNaC::basic::setflag().

Referenced by eval(), evalm(), GiNaC::power::expand(), imag_part(), info(), normal(), and real_part().

ex GiNaC::add::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 625 of file add.cpp.

References add(), GiNaC::status_flags::dynallocated, GiNaC::expairseq::expandchildren(), GiNaC::status_flags::expanded, GiNaC::expairseq::overall_coeff, and GiNaC::basic::setflag().

Referenced by normal().

void GiNaC::add::print_add	(	const print_context &	c,
		const char *	openbrace,
		const char *	closebrace,
		const char *	mul_sym,
		unsigned	level
	)		const `[protected]`