This class describes the symmetry of a group of indices. More...

#include <symmetry.h>

Inheritance diagram for GiNaC::symmetry:

Public Types
enum	symmetry_type { none , symmetric , antisymmetric , cyclic }
	Type of symmetry. More...

Public Member Functions
	symmetry (unsigned i)
	Create leaf node that represents one index. More...

	symmetry (symmetry_type t, const symmetry &c1, const symmetry &c2)
	Create node with two children. More...

void	archive (archive_node &n) const override
	Save (a.k.a. More...

void	read_archive (const archive_node &n, lst &syms) override
	Read (a.k.a. More...

symmetry_type	get_type () const
	Get symmetry type. More...

void	set_type (symmetry_type t)
	Set symmetry type. More...

symmetry &	add (const symmetry &c)
	Add child node, check index sets for consistency. More...

void	validate (unsigned n)
	Verify that all indices of this node are in the range [0..n-1]. More...

bool	has_symmetry () const
	Check whether this node actually represents any kind of symmetry. More...

bool	has_nonsymmetric () const
	Check whether this node involves anything non symmetric. More...

bool	has_cyclic () const
	Check whether this node involves a cyclic symmetry. 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
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...

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

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

Private Attributes
symmetry_type	type
	Type of symmetry described by this node. More...

std::set< unsigned >	indices
	Sorted union set of all indices handled by this node. More...

exvector	children
	Vector of child nodes. More...

Friends
class	sy_is_less

class	sy_swap

int	canonicalize (exvector::iterator v, const symmetry &symm)
	Canonicalize the order of elements of an expression vector, according to the symmetry properties defined in a symmetry tree. More...

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

unsigned	hashvalue
	hash value More...

Detailed Description

This class describes the symmetry of a group of indices.

These objects can be grouped into a tree to form complex mixed symmetries.

Definition at line 38 of file symmetry.h.

Member Enumeration Documentation

◆ symmetry_type

enum GiNaC::symmetry::symmetry_type

Type of symmetry.

Enumerator
none	no symmetry properties
symmetric	totally symmetric
antisymmetric	totally antisymmetric
cyclic	cyclic symmetry

Definition at line 49 of file symmetry.h.

Constructor & Destructor Documentation

◆ symmetry() [1/2]

GiNaC::symmetry::symmetry ( unsigned i )

Create leaf node that represents one index.

Definition at line 70 of file symmetry.cpp.

References GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, indices, and GiNaC::basic::setflag().

◆ symmetry() [2/2]

GiNaC::symmetry::symmetry	(	symmetry_type	t,
		const symmetry &	c1,
		const symmetry &	c2
	)

Create node with two children.

Definition at line 76 of file symmetry.cpp.

References add(), GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, and GiNaC::basic::setflag().

Member Function Documentation

◆ archive()

void GiNaC::symmetry::archive ( archive_node & n ) const

overridevirtual

Save (a.k.a.

Archive the object.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 119 of file symmetry.cpp.

References children, indices, n, and type.

◆ read_archive()

void GiNaC::symmetry::read_archive	(	const archive_node &	n,
		lst &	syms
	)

overridevirtual

Read (a.k.a.

Construct object from archive_node.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 87 of file symmetry.cpp.

References add(), indices, n, and type.

◆ calchash()

unsigned GiNaC::symmetry::calchash ( ) const

overrideprotectedvirtual

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

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

Reimplemented from GiNaC::basic.

Definition at line 183 of file symmetry.cpp.

References children, GiNaC::status_flags::evaluated, GiNaC::basic::flags, GiNaC::status_flags::hash_calculated, GiNaC::basic::hashvalue, indices, GiNaC::make_hash_seed(), none, GiNaC::rotate_left(), GiNaC::basic::setflag(), and type.

◆ get_type()

symmetry_type GiNaC::symmetry::get_type ( ) const

inline

Get symmetry type.

Definition at line 76 of file symmetry.h.

References type.

◆ set_type()

void GiNaC::symmetry::set_type ( symmetry_type t )

inline

Set symmetry type.

Definition at line 79 of file symmetry.h.

References type.

Referenced by GiNaC::sy_anti(), GiNaC::sy_cycl(), and GiNaC::sy_symm().

◆ add()

symmetry & GiNaC::symmetry::add ( const symmetry & c )

Add child node, check index sets for consistency.

Definition at line 289 of file symmetry.cpp.

References c, children, GINAC_ASSERT, indices, none, and type.

Referenced by read_archive(), GiNaC::sy_anti(), GiNaC::sy_cycl(), GiNaC::sy_none(), GiNaC::sy_symm(), symmetry(), and validate().

◆ validate()

void GiNaC::symmetry::validate ( unsigned n )

Verify that all indices of this node are in the range [0..n-1].

This function throws an exception if the verification fails. If the top node has a type != none and no children, add all indices in the range [0..n-1] as children.

Definition at line 312 of file symmetry.cpp.

References add(), indices, n, none, and type.

◆ has_symmetry()

bool GiNaC::symmetry::has_symmetry ( ) const

inline

Check whether this node actually represents any kind of symmetry.

Definition at line 91 of file symmetry.h.

References children, none, and type.

◆ has_nonsymmetric()

bool GiNaC::symmetry::has_nonsymmetric ( ) const

Check whether this node involves anything non symmetric.

Definition at line 265 of file symmetry.cpp.

References antisymmetric, children, cyclic, has_nonsymmetric(), and type.

Referenced by has_nonsymmetric().

◆ has_cyclic()

bool GiNaC::symmetry::has_cyclic ( ) const

Check whether this node involves a cyclic symmetry.

Definition at line 277 of file symmetry.cpp.

References children, cyclic, has_cyclic(), and type.

Referenced by has_cyclic().

◆ do_print()

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

protected

Definition at line 206 of file symmetry.cpp.

References antisymmetric, c, children, cyclic, indices, none, symmetric, and type.

◆ do_print_tree()

void GiNaC::symmetry::do_print_tree	(	const print_tree &	c,
		unsigned	level
	)		const

protected

Definition at line 232 of file symmetry.cpp.

References antisymmetric, c, children, cyclic, GiNaC::basic::flags, GiNaC::basic::hashvalue, indices, none, symmetric, and type.

Friends And Related Function Documentation

◆ sy_is_less

friend class sy_is_less

friend

Definition at line 40 of file symmetry.h.

◆ sy_swap

friend class sy_swap

friend

Definition at line 41 of file symmetry.h.

◆ canonicalize

int canonicalize	(	exvector::iterator	v,
		const symmetry &	symm
	)

friend

Canonicalize the order of elements of an expression vector, according to the symmetry properties defined in a symmetry tree.

Parameters

v	Start of expression vector
symm	Root node of symmetry tree

Returns: the overall sign introduced by the reordering (+1, -1 or 0) or numeric_limits<int>::max() if nothing changed

Definition at line 438 of file symmetry.cpp.

Member Data Documentation

◆ type

symmetry_type GiNaC::symmetry::type

private

Type of symmetry described by this node.

Definition at line 103 of file symmetry.h.

Referenced by add(), archive(), calchash(), do_print(), do_print_tree(), get_type(), has_cyclic(), has_nonsymmetric(), has_symmetry(), read_archive(), set_type(), and validate().

◆ indices

std::set<unsigned> GiNaC::symmetry::indices

private

Sorted union set of all indices handled by this node.

Definition at line 106 of file symmetry.h.

Referenced by add(), archive(), calchash(), do_print(), do_print_tree(), read_archive(), symmetry(), and validate().

◆ children

exvector GiNaC::symmetry::children

private

Vector of child nodes.

Definition at line 109 of file symmetry.h.

Referenced by add(), archive(), calchash(), do_print(), do_print_tree(), has_cyclic(), has_nonsymmetric(), and has_symmetry().

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

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Friends

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ symmetry_type

Constructor & Destructor Documentation

◆ symmetry() [1/2]

◆ symmetry() [2/2]

Member Function Documentation

◆ archive()

◆ read_archive()

◆ calchash()

◆ get_type()

◆ set_type()

◆ add()

◆ validate()

◆ has_symmetry()

◆ has_nonsymmetric()

◆ has_cyclic()

◆ do_print()

◆ do_print_tree()

Friends And Related Function Documentation

◆ sy_is_less

◆ sy_swap

◆ canonicalize

Member Data Documentation

◆ type

◆ indices

◆ children