Non-commutative product of expressions. More...

#include <ncmul.h>

Inheritance diagram for GiNaC::ncmul:

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

	ncmul (const ex &f1, const ex &f2, const ex &f3)

	ncmul (const ex &f1, const ex &f2, const ex &f3, const ex &f4)

	ncmul (const ex &f1, const ex &f2, const ex &f3, const ex &f4, const ex &f5)

	ncmul (const ex &f1, const ex &f2, const ex &f3, const ex &f4, const ex &f5, const ex &f6)

	ncmul (const exvector &v)

	ncmul (exvector &&v)

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

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

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

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

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

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

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

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

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

ex	thiscontainer (const exvector &v) const override

ex	thiscontainer (exvector &&v) const override

ex	conjugate () const override

ex	real_part () const override

ex	imag_part () const override

const exvector &	get_factors () const

Public Member Functions inherited from GiNaC::container< C >
	container (STLT const &s)

	container (STLT &&v)

	container (exvector::const_iterator b, exvector::const_iterator e)

	container (std::initializer_list< ex > il)

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

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

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

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

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

void	archive (archive_node &n) const override
	Archive the object.

container &	prepend (const ex &b)
	Add element at front.

container &	append (const ex &b)
	Add element at back.

container &	remove_first ()
	Remove first element.

container &	remove_last ()
	Remove last element.

container &	remove_all ()
	Remove all elements.

container &	sort ()
	Sort elements.

container &	unique ()
	Remove adjacent duplicate elements.

const_iterator	begin () const

const_iterator	end () const

const_reverse_iterator	rbegin () const

const_reverse_iterator	rend () const

Public Member Functions inherited from GiNaC::basic
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	evalf () const
	Evaluate object numerically.

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 ex	operator[] (const ex &index) const

virtual ex	operator[] (size_t i) const

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	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 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, lst &modifier) 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 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.

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.

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.

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 non-commutative product.

unsigned	return_type () const override

return_type_t	return_type_tinfo () const override

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

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

size_t	count_factors (const ex &e) const

void	append_factors (exvector &v, const ex &e) const

exvector	expandchildren (unsigned options) const

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

virtual ex	thiscontainer (const STLT &v) const
	Similar to duplicate(), but with a preset sequence.

virtual ex	thiscontainer (STLT &&v) const
	Similar to duplicate(), but with a preset sequence (which gets pilfered).

virtual void	printseq (const print_context &c, char openbracket, char delim, char closebracket, unsigned this_precedence, unsigned upper_precedence=0) const
	Print sequence of contained elements.

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

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

void	do_print_python (const print_python &c, unsigned level) const

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

STLT	subschildren (const exmap &m, unsigned options=0) const

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.

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

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 Member Functions inherited from GiNaC::container_storage< C >
	container_storage ()

	container_storage (size_t n, const ex &e)

	container_storage (std::initializer_list< ex > il)

template<class In >
	container_storage (In b, In e)

void	reserve (size_t)

	~container_storage ()

void	reserve (size_t n)

void	reserve (std::vector< ex > &v, size_t n)

Friends
class	power

ex	reeval_ncmul (const exvector &v)

ex	hold_ncmul (const exvector &v)

Additional Inherited Members
Public Types inherited from GiNaC::container< C >
typedef STLT::const_iterator	const_iterator

typedef STLT::const_reverse_iterator	const_reverse_iterator

Protected Types inherited from GiNaC::container< C >
typedef container_storage< C >::STLT	STLT

Protected Types inherited from GiNaC::container_storage< C >
typedef C< ex >	STLT

Static Protected Member Functions inherited from GiNaC::container< C >
static unsigned	get_default_flags ()
	Specialization of container::get_default_flags() for lst.

static char	get_open_delim ()
	Specialization of container::get_open_delim() for lst.

static char	get_close_delim ()
	Specialization of container::get_close_delim() for lst.

Static Protected Member Functions inherited from GiNaC::container_storage< C >
static void	reserve (STLT &, size_t)

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

unsigned	hashvalue
	hash value

Protected Attributes inherited from GiNaC::container_storage< C >
STLT	seq

Detailed Description

Non-commutative product of expressions.

Definition at line 32 of file ncmul.h.

Constructor & Destructor Documentation

◆ ncmul() [1/7]

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

Definition at line 59 of file ncmul.cpp.

◆ ncmul() [2/7]

GiNaC::ncmul::ncmul	(	const ex &	f1,
		const ex &	f2,
		const ex &	f3
	)

Definition at line 63 of file ncmul.cpp.

◆ ncmul() [3/7]

GiNaC::ncmul::ncmul	(	const ex &	f1,
		const ex &	f2,
		const ex &	f3,
		const ex &	f4
	)

Definition at line 67 of file ncmul.cpp.

◆ ncmul() [4/7]

GiNaC::ncmul::ncmul	(	const ex &	f1,
		const ex &	f2,
		const ex &	f3,
		const ex &	f4,
		const ex &	f5
	)

Definition at line 72 of file ncmul.cpp.

◆ ncmul() [5/7]

GiNaC::ncmul::ncmul	(	const ex &	f1,
		const ex &	f2,
		const ex &	f3,
		const ex &	f4,
		const ex &	f5,
		const ex &	f6
	)

Definition at line 77 of file ncmul.cpp.

◆ ncmul() [6/7]

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

Definition at line 82 of file ncmul.cpp.

◆ ncmul() [7/7]

GiNaC::ncmul::ncmul ( exvector && v )

Definition at line 86 of file ncmul.cpp.

Member Function Documentation

◆ precedence()

unsigned GiNaC::ncmul::precedence ( ) const

inlineoverridevirtual

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::container< C >.

Definition at line 57 of file ncmul.h.

Referenced by do_print(), and do_print_csrc().

◆ info()

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

overridevirtual

Information about the object.

See also: class info_flags

Reimplemented from GiNaC::container< C >.

Definition at line 112 of file ncmul.cpp.

◆ degree()

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

overridevirtual

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 195 of file ncmul.cpp.

References GiNaC::basic::is_equal(), and GiNaC::container_storage< C >::seq.

◆ ldegree()

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

overridevirtual

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 207 of file ncmul.cpp.

References GiNaC::basic::is_equal(), and GiNaC::container_storage< C >::seq.

◆ expand()

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

overridevirtual

Expand expression, i.e.

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

Reimplemented from GiNaC::basic.

Definition at line 119 of file ncmul.cpp.

References GiNaC::_ex1, expandchildren(), GiNaC::status_flags::expanded, k, GiNaC::container< C >::op(), options, GiNaC::rename_dummy_indices_uniquely(), GiNaC::container_storage< C >::seq, and GiNaC::basic::setflag().

◆ coeff()

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

overridevirtual

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 219 of file ncmul.cpp.

References GiNaC::_ex0, GiNaC::_ex1, c, GiNaC::ex::coeff(), GiNaC::basic::is_equal(), n, and GiNaC::container_storage< C >::seq.

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

◆ eval()

ex GiNaC::ncmul::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.

ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...) (associativity)
ncmul(x) -> x
ncmul() -> 1
ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...)) (pull out commutative elements)
ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2)) (collect elements of same type)
ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)

Reimplemented from GiNaC::basic.

Definition at line 288 of file ncmul.cpp.

References GiNaC::_ex1, append_factors(), GiNaC::return_types::commutative, count_factors(), GiNaC::status_flags::evaluated, GiNaC::factor(), factors, GiNaC::basic::flags, GINAC_ASSERT, GiNaC::make_flat_inserter::handle_factor(), GiNaC::return_types::noncommutative, GiNaC::return_types::noncommutative_composite, GiNaC::container_storage< C >::reserve(), and GiNaC::container_storage< C >::seq.

◆ evalm()

ex GiNaC::ncmul::evalm ( ) const

overridevirtual

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 423 of file ncmul.cpp.

References GiNaC::ex::begin(), GiNaC::matrix::mul(), and GiNaC::container_storage< C >::seq.

◆ get_free_indices()

exvector GiNaC::ncmul::get_free_indices ( ) const

overridevirtual

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 495 of file indexed.cpp.

References GiNaC::find_free_and_dummy(), GiNaC::ex::get_free_indices(), GiNaC::container< C >::nops(), and GiNaC::container< C >::op().

◆ thiscontainer() [1/2]

ex GiNaC::ncmul::thiscontainer ( const exvector & v ) const

override

Definition at line 449 of file ncmul.cpp.

◆ thiscontainer() [2/2]

ex GiNaC::ncmul::thiscontainer ( exvector && v ) const

override

Definition at line 454 of file ncmul.cpp.

◆ conjugate()

ex GiNaC::ncmul::conjugate ( ) const

overridevirtual

Reimplemented from GiNaC::container< C >.

Definition at line 459 of file ncmul.cpp.

References GiNaC::container< C >::begin(), GiNaC::container< C >::conjugate(), GiNaC::container< C >::end(), GiNaC::is_clifford_tinfo(), GiNaC::return_types::noncommutative, GiNaC::container< C >::nops(), return_type(), and return_type_tinfo().

◆ real_part()

ex GiNaC::ncmul::real_part ( ) const

overridevirtual

Reimplemented from GiNaC::container< C >.

Definition at line 478 of file ncmul.cpp.

References GiNaC::basic::real_part().

◆ imag_part()

ex GiNaC::ncmul::imag_part ( ) const

overridevirtual

Reimplemented from GiNaC::container< C >.

Definition at line 483 of file ncmul.cpp.

References GiNaC::basic::imag_part().

◆ derivative()

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

overrideprotectedvirtual

Implementation of ex::diff() for a non-commutative product.

It applies the product rule.

See also: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 493 of file ncmul.cpp.

References GiNaC::ex::diff(), GiNaC::container_storage< C >::seq, and GiNaC::ex::swap().

◆ return_type()

unsigned GiNaC::ncmul::return_type ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 515 of file ncmul.cpp.

References GiNaC::return_types::commutative, GiNaC::container< C >::end(), GINAC_ASSERT, GiNaC::return_types::noncommutative, GiNaC::return_types::noncommutative_composite, and GiNaC::container_storage< C >::seq.

Referenced by conjugate().

◆ return_type_tinfo()

return_type_t GiNaC::ncmul::return_type_tinfo ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 545 of file ncmul.cpp.

References GiNaC::return_types::noncommutative, and GiNaC::container_storage< C >::seq.

Referenced by conjugate().

◆ do_print()

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

protected

Definition at line 101 of file ncmul.cpp.

References c, precedence(), and GiNaC::container< C >::printseq().

◆ do_print_csrc()

void GiNaC::ncmul::do_print_csrc	(	const print_context &	c,
		unsigned	level
	)		const

protected

Definition at line 106 of file ncmul.cpp.

References c, precedence(), and GiNaC::container< C >::printseq().

◆ count_factors()

size_t GiNaC::ncmul::count_factors ( const ex & e ) const

protected

Definition at line 252 of file ncmul.cpp.

References GiNaC::return_types::commutative, count_factors(), factors, GiNaC::ex::nops(), GiNaC::ex::op(), and GiNaC::ex::return_type().

Referenced by count_factors(), and eval().

◆ append_factors()

void GiNaC::ncmul::append_factors	(	exvector &	v,
		const ex &	e
	)		const

protected

Definition at line 265 of file ncmul.cpp.

References append_factors(), GiNaC::return_types::commutative, GiNaC::ex::nops(), GiNaC::ex::op(), and GiNaC::ex::return_type().

Referenced by append_factors(), and eval().

◆ expandchildren()

exvector GiNaC::ncmul::expandchildren ( unsigned options ) const

protected

Definition at line 569 of file ncmul.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::container< C >::end(), GiNaC::ex::expand(), options, and GiNaC::container_storage< C >::seq.

Referenced by expand().

◆ get_factors()

const exvector & GiNaC::ncmul::get_factors ( ) const

Definition at line 599 of file ncmul.cpp.

References GiNaC::container_storage< C >::seq.

Friends And Related Symbol Documentation

◆ power

friend class power

friend

Definition at line 36 of file ncmul.h.

◆ reeval_ncmul

ex reeval_ncmul ( const exvector & v )

friend

Definition at line 608 of file ncmul.cpp.

◆ hold_ncmul

ex hold_ncmul ( const exvector & v )

friend

Definition at line 613 of file ncmul.cpp.

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

Public Member Functions

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ncmul() [1/7]

◆ ncmul() [2/7]

◆ ncmul() [3/7]

◆ ncmul() [4/7]

◆ ncmul() [5/7]

◆ ncmul() [6/7]

◆ ncmul() [7/7]

Member Function Documentation

◆ precedence()

◆ info()

◆ degree()

◆ ldegree()

◆ expand()

◆ coeff()

◆ eval()

◆ evalm()

◆ get_free_indices()

◆ thiscontainer() [1/2]

◆ thiscontainer() [2/2]

◆ conjugate()

◆ real_part()

◆ imag_part()

◆ derivative()

◆ return_type()

◆ return_type_tinfo()

◆ do_print()

◆ do_print_csrc()

◆ count_factors()

◆ append_factors()

◆ expandchildren()

◆ get_factors()

Friends And Related Symbol Documentation

◆ power

◆ reeval_ncmul

◆ hold_ncmul