This class holds a spinor index that can be dotted or undotted and that also has a variance. More...

#include <idx.h>

Inheritance diagram for GiNaC::spinidx:

Public Member Functions
	spinidx (const ex &v, const ex &dim=2, bool covariant=false, bool dotted=false)
	Construct index with given value, dimension, variance and dot. More...

bool	is_dummy_pair_same_type (const basic &other) const override
	Check whether the index forms a dummy index pair with another index of the same type. 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...

bool	is_dotted () const
	Check whether the index is dotted. More...

bool	is_undotted () const
	Check whether the index is not dotted. More...

ex	toggle_dot () const
	Make a new index with the same value and variance but the opposite dottedness. More...

ex	toggle_variance_dot () const
	Make a new index with the same value but opposite variance and dottedness. More...

Public Member Functions inherited from GiNaC::varidx
	varidx (const ex &v, const ex &dim, bool covariant=false)
	Construct index with given value, dimension and variance. More...

bool	is_dummy_pair_same_type (const basic &other) const override
	Check whether the index forms a dummy index pair with another index of the same type. More...

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...

bool	is_covariant () const
	Check whether the index is covariant. More...

bool	is_contravariant () const
	Check whether the index is contravariant (not covariant). More...

ex	toggle_variance () const
	Make a new index with the same value but the opposite variance. More...

Public Member Functions inherited from GiNaC::idx
	idx (const ex &v, const ex &dim)
	Construct index with given value and dimension. 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	evalf () const override
	By default, basic::evalf would evaluate the index value but we don't want a.1 to become a. More...

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

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...

virtual bool	is_dummy_pair_same_type (const basic &other) const
	Check whether the index forms a dummy index pair with another index of the same type. More...

ex	get_value () const
	Get value of index. More...

bool	is_numeric () const
	Check whether the index is numeric. More...

bool	is_symbolic () const
	Check whether the index is symbolic. More...

ex	get_dim () const
	Get dimension of index space. More...

bool	is_dim_numeric () const
	Check whether the dimension is numeric. More...

bool	is_dim_symbolic () const
	Check whether the dimension is symbolic. More...

ex	replace_dim (const ex &new_dim) const
	Make a new index with the same value but a different dimension. More...

ex	minimal_dim (const idx &other) const
	Return the minimum of the dimensions of this and another index. 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
bool	match_same_type (const basic &other) const override
	Returns true if the attributes of two objects are similar enough for a match. More...

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

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

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

Protected Member Functions inherited from GiNaC::varidx
bool	match_same_type (const basic &other) const override
	Returns true if the attributes of two objects are similar enough for a match. 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::idx
ex	derivative (const symbol &s) const override
	Implementation of ex::diff() for an index always returns 0. More...

bool	match_same_type (const basic &other) const override
	Returns true if the attributes of two objects are similar enough for a match. More...

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	print_index (const print_context &c, unsigned level) const

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

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

void	do_print_latex (const print_latex &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...

Protected Attributes
bool	dotted

Protected Attributes inherited from GiNaC::varidx
bool	covariant
	x.mu, default is contravariant: x~mu More...

Protected Attributes inherited from GiNaC::idx
ex	value
	Expression that constitutes the index (numeric or symbolic name) More...

ex	dim
	Dimension of space (can be symbolic or numeric) More...

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

unsigned	hashvalue
	hash value More...

Detailed Description

This class holds a spinor index that can be dotted or undotted and that also has a variance.

This is used in the Weyl-van-der-Waerden formalism where the dot indicates complex conjugation. There is an associated (asymmetric) metric tensor that can be used to raise/lower spinor indices.

Definition at line 159 of file idx.h.

Constructor & Destructor Documentation

◆ spinidx()

GiNaC::spinidx::spinidx	(	const ex &	v,
		const ex &	dim = `2`,
		bool	covariant = `false`,
		bool	dotted = `false`
	)

Construct index with given value, dimension, variance and dot.

Parameters

v	Value of index (numeric or symbolic)
dim	Dimension of index space (numeric or symbolic)
covariant	Make covariant index (default is contravariant)
dotted	Make covariant dotted (default is undotted)

Definition at line 64 of file idx.cpp.

Member Function Documentation

◆ is_dummy_pair_same_type()

bool GiNaC::spinidx::is_dummy_pair_same_type ( const basic & other ) const

overridevirtual

Check whether the index forms a dummy index pair with another index of the same type.

Reimplemented from GiNaC::varidx.

Definition at line 444 of file idx.cpp.

References dotted.

◆ conjugate()

ex GiNaC::spinidx::conjugate ( ) const

inlineoverridevirtual

Reimplemented from GiNaC::basic.

Definition at line 177 of file idx.h.

References toggle_dot().

◆ archive()

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

overridevirtual

Save (serialize) the object into archive node.

Archive the object.

Losely speaking, this method turns an expression into a byte stream (which can be saved and restored later on, or sent via network, etc.)

Reimplemented from GiNaC::varidx.

Definition at line 126 of file idx.cpp.

References dotted, and n.

◆ read_archive()

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

overridevirtual

Load (deserialize) the object from an archive node.

Construct object from archive_node.

Note: This method is essentially a constructor. However, constructors can't be virtual. So, if unarchiving routines are implemented as constructors one would need to define such a constructor in every class, even if all it does is simply calling constructor of a superclass.

Reimplemented from GiNaC::varidx.

Definition at line 106 of file idx.cpp.

References dotted, and n.

◆ match_same_type()

bool GiNaC::spinidx::match_same_type ( const basic & other ) const

overrideprotectedvirtual

Returns true if the attributes of two objects are similar enough for a match.

This function must not match subexpressions (this is already done by basic::match()). Only attributes not accessible by op() should be compared. This is also the reason why this function doesn't take the wildcard replacement list from match() as an argument: only subexpressions are subject to wildcard matches. Also, this function only needs to be implemented for container classes because is_equal_same_type() is automatically used instead of match_same_type() if nops() == 0.

See also: basic::match

Reimplemented from GiNaC::varidx.

Definition at line 333 of file idx.cpp.

References dotted, and GINAC_ASSERT.

◆ is_dotted()

bool GiNaC::spinidx::is_dotted ( ) const

inline

Check whether the index is dotted.

Definition at line 186 of file idx.h.

References dotted.

◆ is_undotted()

bool GiNaC::spinidx::is_undotted ( ) const

inline

Check whether the index is not dotted.

Definition at line 189 of file idx.h.

References dotted.

◆ toggle_dot()

ex GiNaC::spinidx::toggle_dot ( ) const

Make a new index with the same value and variance but the opposite dottedness.

Definition at line 481 of file idx.cpp.

References GiNaC::basic::clearflag(), dotted, GiNaC::basic::duplicate(), and GiNaC::status_flags::hash_calculated.

Referenced by conjugate().

◆ toggle_variance_dot()

ex GiNaC::spinidx::toggle_variance_dot ( ) const

Make a new index with the same value but opposite variance and dottedness.

Definition at line 489 of file idx.cpp.

References GiNaC::basic::clearflag(), GiNaC::varidx::covariant, dotted, GiNaC::basic::duplicate(), and GiNaC::status_flags::hash_calculated.

◆ do_print()

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

protected

Definition at line 202 of file idx.cpp.

References c, GiNaC::varidx::covariant, dotted, and GiNaC::idx::print_index().

◆ do_print_latex()

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

protected

Definition at line 213 of file idx.cpp.

References c, dotted, and GiNaC::idx::print_index().

◆ do_print_tree()

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

protected

Definition at line 223 of file idx.cpp.

References c, GiNaC::varidx::covariant, GiNaC::idx::dim, dotted, GiNaC::basic::flags, GiNaC::basic::hashvalue, GiNaC::ex::print(), and GiNaC::idx::value.

Member Data Documentation

◆ dotted

bool GiNaC::spinidx::dotted

protected

Definition at line 206 of file idx.h.

Referenced by archive(), do_print(), do_print_latex(), do_print_tree(), is_dotted(), is_dummy_pair_same_type(), is_undotted(), match_same_type(), read_archive(), toggle_dot(), and toggle_variance_dot().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ spinidx()

Member Function Documentation

◆ is_dummy_pair_same_type()

◆ conjugate()

◆ archive()

◆ read_archive()

◆ match_same_type()

◆ is_dotted()

◆ is_undotted()

◆ toggle_dot()

◆ toggle_variance_dot()

◆ do_print()

◆ do_print_latex()

◆ do_print_tree()

Member Data Documentation

◆ dotted