This class holds a relation consisting of two expressions and a logical relation between them. More...

#include <relational.h>

Inheritance diagram for GiNaC::relational:

Classes
struct	safe_bool_helper

Public Types
enum	operators { equal , not_equal , less , less_or_equal , greater , greater_or_equal }

Public Member Functions
	relational (const ex &lhs, const ex &rhs, operators oper=equal)

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

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

ex	canonical () const
	Returns an equivalent relational with zero right-hand side. More...

ex	lhs () const

ex	rhs () const

	operator safe_bool () const
	Cast the relational into a Boolean, mainly for evaluation within an if-statement. More...

safe_bool	operator! () 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*. 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
ex	eval_ncmul (const exvector &v) const override

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	return_type () const override

return_type_t	return_type_tinfo () const override

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_python_repr (const print_python_repr &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
ex	lh

ex	rh

operators	o

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

unsigned	hashvalue
	hash value More...

Private Types
typedef void(safe_bool_helper::*	safe_bool) ()

Private Member Functions
safe_bool	make_safe_bool (bool) const

Detailed Description

This class holds a relation consisting of two expressions and a logical relation between them.

Definition at line 34 of file relational.h.

Member Typedef Documentation

◆ safe_bool

typedef void(safe_bool_helper::* GiNaC::relational::safe_bool) ()

private

Definition at line 94 of file relational.h.

Member Enumeration Documentation

◆ operators

enum GiNaC::relational::operators

Enumerator
equal
not_equal
less
less_or_equal
greater
greater_or_equal

Definition at line 40 of file relational.h.

Constructor & Destructor Documentation

◆ relational()

GiNaC::relational::relational	(	const ex &	lhs,
		const ex &	rhs,
		operators	oper = `equal`
	)

Definition at line 52 of file relational.cpp.

Referenced by canonical(), and subs().

Member Function Documentation

◆ precedence()

unsigned GiNaC::relational::precedence ( ) const

inlineoverridevirtual

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::basic.

Definition at line 55 of file relational.h.

Referenced by do_print().

◆ info()

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

overridevirtual

Information about the object.

See also: class info_flags

Reimplemented from GiNaC::basic.

Definition at line 134 of file relational.cpp.

References equal, greater, greater_or_equal, less, less_or_equal, not_equal, o, GiNaC::info_flags::relation, GiNaC::info_flags::relation_equal, GiNaC::info_flags::relation_greater, GiNaC::info_flags::relation_greater_or_equal, GiNaC::info_flags::relation_less, GiNaC::info_flags::relation_less_or_equal, and GiNaC::info_flags::relation_not_equal.

Referenced by operator safe_bool().

◆ nops()

size_t GiNaC::relational::nops ( ) const

overridevirtual

Number of operands/members.

Reimplemented from GiNaC::basic.

Definition at line 155 of file relational.cpp.

◆ op()

ex GiNaC::relational::op ( size_t i ) const

overridevirtual

Return operand/member at position i.

Reimplemented from GiNaC::basic.

Definition at line 160 of file relational.cpp.

References GINAC_ASSERT, lh, and rh.

◆ map()

ex GiNaC::relational::map ( map_function & f ) const

overridevirtual

Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively).

Reimplemented from GiNaC::basic.

Definition at line 167 of file relational.cpp.

References GiNaC::are_ex_trivially_equal(), lh, o, and rh.

◆ subs()

ex GiNaC::relational::subs	(	const exmap &	m,
		unsigned	options = `0`
	)		const

overridevirtual

Substitute a set of objects by arbitrary expressions.

The ex returned will already be evaluated.

Reimplemented from GiNaC::basic.

Definition at line 179 of file relational.cpp.

References GiNaC::are_ex_trivially_equal(), lh, m, o, options, relational(), rh, GiNaC::ex::subs(), and GiNaC::basic::subs_one_level().

◆ archive()

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

overridevirtual

Save (a.k.a.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 71 of file relational.cpp.

References lh, n, o, and rh.

◆ read_archive()

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

overridevirtual

Read (a.k.a.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 59 of file relational.cpp.

References lh, n, o, and rh.

◆ canonical()

ex GiNaC::relational::canonical ( ) const

Returns an equivalent relational with zero right-hand side.

Definition at line 353 of file relational.cpp.

References GiNaC::_ex0, lh, o, relational(), and rh.

◆ eval_ncmul()

ex GiNaC::relational::eval_ncmul ( const exvector & v ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 190 of file relational.cpp.

References GiNaC::ex::eval_ncmul(), and lh.

◆ match_same_type()

bool GiNaC::relational::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::basic.

Definition at line 230 of file relational.cpp.

References GINAC_ASSERT, and o.

◆ return_type()

unsigned GiNaC::relational::return_type ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 238 of file relational.cpp.

References GINAC_ASSERT, lh, GiNaC::ex::return_type(), and rh.

◆ return_type_tinfo()

return_type_t GiNaC::relational::return_type_tinfo ( ) const

overrideprotectedvirtual

Reimplemented from GiNaC::basic.

Definition at line 244 of file relational.cpp.

References GINAC_ASSERT, lh, GiNaC::ex::return_type_tinfo(), and rh.

◆ calchash()

unsigned GiNaC::relational::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 250 of file relational.cpp.

References equal, GiNaC::status_flags::evaluated, GiNaC::basic::flags, GiNaC::ex::gethash(), greater, greater_or_equal, GiNaC::status_flags::hash_calculated, GiNaC::basic::hashvalue, less, less_or_equal, lh, GiNaC::make_hash_seed(), not_equal, o, rh, GiNaC::rotate_left(), and GiNaC::basic::setflag().

◆ do_print()

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

protected

Definition at line 112 of file relational.cpp.

References c, lh, o, precedence(), GiNaC::ex::print(), GiNaC::print_operator(), and rh.

◆ do_print_python_repr()

void GiNaC::relational::do_print_python_repr	(	const print_python_repr &	c,
		unsigned	level
	)		const

protected

Definition at line 123 of file relational.cpp.

References c, lh, o, GiNaC::ex::print(), GiNaC::print_operator(), and rh.

◆ lhs()

ex GiNaC::relational::lhs ( ) const

inline

Definition at line 81 of file relational.h.

References lh.

Referenced by GiNaC::atan_series(), GiNaC::atanh_series(), GiNaC::beta_series(), GiNaC::Li2_series(), GiNaC::log_series(), GiNaC::tan_series(), and GiNaC::tanh_series().

◆ rhs()

ex GiNaC::relational::rhs ( ) const

inline

Definition at line 82 of file relational.h.

References rh.

Referenced by GiNaC::atan_series(), GiNaC::atanh_series(), GiNaC::Li2_series(), and GiNaC::log_series().

◆ make_safe_bool()

relational::safe_bool GiNaC::relational::make_safe_bool ( bool cond ) const

private

Definition at line 299 of file relational.cpp.

References GiNaC::relational::safe_bool_helper::nonnull().

Referenced by operator safe_bool(), and operator!().

◆ operator safe_bool()

GiNaC::relational::operator relational::safe_bool ( ) const

Cast the relational into a Boolean, mainly for evaluation within an if-statement.

Note that (a<b) == false does not imply (a>=b) == true in the general symbolic case. A false result means the comparison is either false or undecidable (except of course for !=, where true means either unequal or undecidable).

Definition at line 309 of file relational.cpp.

References GiNaC::_num0_p, equal, greater, greater_or_equal, GiNaC::ex::info(), info(), GiNaC::ex::is_zero(), GiNaC::is_zero(), less, less_or_equal, lh, make_safe_bool(), GiNaC::info_flags::negative, GiNaC::info_flags::nonnegative, not_equal, o, GiNaC::info_flags::positive, and rh.

◆ operator!()

relational::safe_bool GiNaC::relational::operator! ( ) const

inline

Definition at line 114 of file relational.h.

References make_safe_bool().

Member Data Documentation

◆ lh

ex GiNaC::relational::lh

protected

Definition at line 105 of file relational.h.

Referenced by archive(), calchash(), canonical(), do_print(), do_print_python_repr(), eval_ncmul(), lhs(), map(), op(), operator safe_bool(), read_archive(), return_type(), return_type_tinfo(), and subs().

◆ rh

ex GiNaC::relational::rh

protected

Definition at line 106 of file relational.h.

Referenced by archive(), calchash(), canonical(), do_print(), do_print_python_repr(), map(), op(), operator safe_bool(), read_archive(), return_type(), return_type_tinfo(), rhs(), and subs().

◆ o

operators GiNaC::relational::o

protected

Definition at line 107 of file relational.h.

Referenced by archive(), calchash(), canonical(), do_print(), do_print_python_repr(), info(), map(), match_same_type(), operator safe_bool(), read_archive(), and subs().

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

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Types

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ safe_bool

Member Enumeration Documentation

◆ operators

Constructor & Destructor Documentation

◆ relational()

Member Function Documentation

◆ precedence()

◆ info()

◆ nops()

◆ op()

◆ map()

◆ subs()

◆ archive()

◆ read_archive()

◆ canonical()

◆ eval_ncmul()

◆ match_same_type()

◆ return_type()

◆ return_type_tinfo()

◆ calchash()

◆ do_print()

◆ do_print_python_repr()

◆ lhs()

◆ rhs()

◆ make_safe_bool()

◆ operator safe_bool()

◆ operator!()

Member Data Documentation

◆ lh

◆ rh

◆ o