Lightweight wrapper for GiNaC's symbolic objects. More...

#include <ex.h>

Public Member Functions
	ex () noexcept

	ex (const basic &other)

	ex (int i)

	ex (unsigned int i)

	ex (long i)

	ex (unsigned long i)

	ex (long long i)

	ex (unsigned long long i)

	ex (double const d)

	ex (const std::string &s, const ex &l)
	Construct ex from string and a list of symbols.

void	swap (ex &other) noexcept
	Efficiently swap the contents of two expressions.

const_iterator	begin () const noexcept

const_iterator	end () const noexcept

const_preorder_iterator	preorder_begin () const

const_preorder_iterator	preorder_end () const noexcept

const_postorder_iterator	postorder_begin () const

const_postorder_iterator	postorder_end () const noexcept

ex	eval () const

ex	evalf () const

ex	evalm () const

ex	eval_ncmul (const exvector &v) const

ex	eval_integ () const

void	print (const print_context &c, unsigned level=0) const
	Print expression to stream.

void	dbgprint () const
	Little wrapper arount print to be called within a debugger.

void	dbgprinttree () const
	Little wrapper arount printtree to be called within a debugger.

bool	info (unsigned inf) const

size_t	nops () const

ex	op (size_t i) const

ex	operator[] (const ex &index) const

ex	operator[] (size_t i) const

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

ex &	operator[] (const ex &index)

ex &	operator[] (size_t i)

ex	lhs () const
	Left hand side of relational expression.

ex	rhs () const
	Right hand side of relational expression.

ex	conjugate () const

ex	real_part () const

ex	imag_part () const

bool	has (const ex &pattern, unsigned options=0) const

bool	find (const ex &pattern, exset &found) const
	Find all occurrences of a pattern.

bool	match (const ex &pattern) const
	Check whether expression matches a specified pattern.

bool	match (const ex &pattern, exmap &repls) const

ex	subs (const exmap &m, unsigned options=0) const

ex	subs (const lst &ls, const lst &lr, unsigned options=0) const
	Substitute objects in an expression (syntactic substitution) and return the result as a new expression.

ex	subs (const ex &e, unsigned options=0) const
	Substitute objects in an expression (syntactic substitution) and return the result as a new expression.

ex	map (map_function &f) const

ex	map (ex(*f)(const ex &e)) const

void	accept (visitor &v) const

void	traverse_preorder (visitor &v) const
	Traverse expression tree with given visitor, preorder traversal.

void	traverse_postorder (visitor &v) const
	Traverse expression tree with given visitor, postorder traversal.

void	traverse (visitor &v) const

bool	is_polynomial (const ex &vars) const
	Check whether expression is a polynomial.

int	degree (const ex &s) const

int	ldegree (const ex &s) const

ex	coeff (const ex &s, int n=1) const

ex	lcoeff (const ex &s) const

ex	tcoeff (const ex &s) const

ex	expand (unsigned options=0) const
	Expand an expression.

ex	collect (const ex &s, bool distributed=false) const

ex	diff (const symbol &s, unsigned nth=1) const
	Compute partial derivative of an expression.

ex	series (const ex &r, int order, unsigned options=0) const
	Compute the truncated series expansion of an expression.

ex	normal () const
	Normalization of rational functions.

ex	to_rational (exmap &repl) const
	Rationalization of non-rational functions.

ex	to_polynomial (exmap &repl) const

ex	numer () const
	Get numerator of an expression.

ex	denom () const
	Get denominator of an expression.

ex	numer_denom () const
	Get numerator and denominator of an expression.

ex	unit (const ex &x) const
	Compute unit part (= sign of leading coefficient) of a multivariate polynomial in Q[x].

ex	content (const ex &x) const
	Compute content part (= unit normal GCD of all coefficients) of a multivariate polynomial in Q[x].

numeric	integer_content () const
	Compute the integer content (= GCD of all numeric coefficients) of an expanded polynomial.

ex	primpart (const ex &x) const
	Compute primitive part of a multivariate polynomial in Q[x].

ex	primpart (const ex &x, const ex &cont) const
	Compute primitive part of a multivariate polynomial in Q[x] when the content part is already known.

void	unitcontprim (const ex &x, ex &u, ex &c, ex &p) const
	Compute unit part, content part, and primitive part of a multivariate polynomial in Q[x].

ex	smod (const numeric &xi) const

numeric	max_coefficient () const
	Return maximum (absolute value) coefficient of a polynomial.

exvector	get_free_indices () const

ex	simplify_indexed (unsigned options=0) const
	Simplify/canonicalize expression containing indexed objects.

ex	simplify_indexed (const scalar_products &sp, unsigned options=0) const
	Simplify/canonicalize expression containing indexed objects.

int	compare (const ex &other) const

bool	is_equal (const ex &other) const

bool	is_zero () const

bool	is_zero_matrix () const
	Check whether expression is zero or zero matrix.

ex	symmetrize () const
	Symmetrize expression over its free indices.

ex	symmetrize (const lst &l) const
	Symmetrize expression over a list of objects (symbols, indices).

ex	antisymmetrize () const
	Antisymmetrize expression over its free indices.

ex	antisymmetrize (const lst &l) const
	Antisymmetrize expression over a list of objects (symbols, indices).

ex	symmetrize_cyclic () const
	Symmetrize expression by cyclic permutation over its free indices.

ex	symmetrize_cyclic (const lst &l) const
	Symmetrize expression by cyclic permutation over a list of objects (symbols, indices).

unsigned	return_type () const

return_type_t	return_type_tinfo () const

unsigned	gethash () const

Private Member Functions
void	makewriteable ()
	Make this ex writable (if more than one ex handle the same basic) by unlinking the object and creating an unshared copy of it.

void	share (const ex &other) const
	Share equal objects between expressions.

Static Private Member Functions
static ptr< basic >	construct_from_basic (const basic &other)
	Helper function for the ex-from-basic constructor.

static basic &	construct_from_int (int i)

static basic &	construct_from_uint (unsigned int i)

static basic &	construct_from_long (long i)

static basic &	construct_from_ulong (unsigned long i)

static basic &	construct_from_longlong (long long i)

static basic &	construct_from_ulonglong (unsigned long long i)

static basic &	construct_from_double (double d)

static ptr< basic >	construct_from_string_and_lst (const std::string &s, const ex &l)

Private Attributes
ptr< basic >	bp
	pointer to basic object managed by this

Friends
class	archive_node

bool	are_ex_trivially_equal (const ex &, const ex &)
	Compare two objects of class quickly without doing a deep tree traversal.

template<class T >
const T &	ex_to (const ex &)
	Return a reference to the basic-derived class T object embedded in an expression.

template<class T >
bool	is_a (const ex &)
	Check if ex is a handle to a T, including base classes.

template<class T >
bool	is_exactly_a (const ex &)
	Check if ex is a handle to a T, not including base classes.

Detailed Description

Lightweight wrapper for GiNaC's symbolic objects.

It holds a pointer to the other object in order to do garbage collection by the method of reference counting. I.e., it is a smart pointer. Also, the constructor ex::ex(const basic & other) calls the methods that do automatic evaluation. E.g., x-x turns automatically into 0.

Definition at line 73 of file ex.h.

Constructor & Destructor Documentation

◆ ex() [1/10]

GiNaC::ex::ex ( )

inlinenoexcept

Definition at line 263 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [2/10]

GiNaC::ex::ex ( const basic & other )

inline

Definition at line 269 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [3/10]

GiNaC::ex::ex ( int i )

inline

Definition at line 275 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [4/10]

GiNaC::ex::ex ( unsigned int i )

inline

Definition at line 281 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [5/10]

GiNaC::ex::ex ( long i )

inline

Definition at line 287 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [6/10]

GiNaC::ex::ex ( unsigned long i )

inline

Definition at line 293 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [7/10]

GiNaC::ex::ex ( long long i )

inline

Definition at line 299 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [8/10]

GiNaC::ex::ex ( unsigned long long i )

inline

Definition at line 305 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [9/10]

GiNaC::ex::ex ( double const d )

inline

Definition at line 311 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

◆ ex() [10/10]

GiNaC::ex::ex	(	const std::string &	s,
		const ex &	l
	)

inline

Construct ex from string and a list of symbols.

The input grammar is similar to the GiNaC output format. All symbols and indices to be used in the expression must be specified in a lst in the second argument. Undefined symbols and other parser errors will throw an exception.

Definition at line 317 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

Member Function Documentation

◆ swap()

void GiNaC::ex::swap ( ex & other )

inlinenoexcept

Efficiently swap the contents of two expressions.

Definition at line 105 of file ex.h.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

Referenced by GiNaC::ncmul::derivative(), GiNaC::ex_swap::operator()(), GiNaC::swap(), GiNaC::expair::swap(), and std::swap().

◆ begin()

const_iterator GiNaC::ex::begin ( ) const

inlinenoexcept

◆ end()

const_iterator GiNaC::ex::end ( ) const

inlinenoexcept

Definition at line 668 of file ex.h.

References nops().

Referenced by GiNaC::abs_expand(), GiNaC::mul::evalm(), GiNaC::exp_expand(), GiNaC::G3_eval(), GiNaC::G3_evalf(), GiNaC::Li_print_latex(), GiNaC::log_expand(), and GiNaC::rename_dummy_indices_uniquely().

◆ preorder_begin()

const_preorder_iterator GiNaC::ex::preorder_begin ( ) const

inline

Definition at line 673 of file ex.h.

References nops().

◆ preorder_end()

const_preorder_iterator GiNaC::ex::preorder_end ( ) const

inlinenoexcept

Definition at line 678 of file ex.h.

◆ postorder_begin()

const_postorder_iterator GiNaC::ex::postorder_begin ( ) const

inline

Definition at line 683 of file ex.h.

References nops().

◆ postorder_end()

const_postorder_iterator GiNaC::ex::postorder_end ( ) const

inlinenoexcept

Definition at line 688 of file ex.h.

◆ eval()

ex GiNaC::ex::eval ( ) const

inline

Definition at line 121 of file ex.h.

References bp, and eval().

Referenced by eval(), and GiNaC::eval().

◆ evalf()

ex GiNaC::ex::evalf ( ) const

inline

Definition at line 122 of file ex.h.

References bp, and evalf().

◆ evalm()

ex GiNaC::ex::evalm ( ) const

inline

Definition at line 123 of file ex.h.

References bp, and evalm().

Referenced by evalm(), GiNaC::add::evalm(), GiNaC::mul::evalm(), GiNaC::power::evalm(), GiNaC::pseries::evalm(), GiNaC::evalm(), and is_zero_matrix().

◆ eval_ncmul()

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

inline

Definition at line 124 of file ex.h.

References bp, and eval_ncmul().

Referenced by eval_ncmul(), GiNaC::integral::eval_ncmul(), and GiNaC::relational::eval_ncmul().

◆ eval_integ()

ex GiNaC::ex::eval_integ ( ) const

inline

Definition at line 125 of file ex.h.

References bp, and eval_integ().

Referenced by eval_integ(), GiNaC::integral::eval_integ(), GiNaC::pseries::eval_integ(), and GiNaC::eval_integ().

◆ print()

void GiNaC::ex::print	(	const print_context &	c,
		unsigned	level = `0`
	)		const

Print expression to stream.

The formatting of the output is determined by the kind of print_context object that is passed. Possible formattings include ginsh-parsable output (the default), tree-like output for debugging, and C++ source.

See also: print_context

Definition at line 55 of file ex.cpp.

References bp, and c.

◆ dbgprint()

void GiNaC::ex::dbgprint ( ) const

Little wrapper arount print to be called within a debugger.

Definition at line 61 of file ex.cpp.

References bp.

◆ dbgprinttree()

void GiNaC::ex::dbgprinttree ( ) const

Little wrapper arount printtree to be called within a debugger.

Definition at line 67 of file ex.cpp.

References bp.

◆ info()

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

inline

Definition at line 133 of file ex.h.

References bp.

◆ nops()

size_t GiNaC::ex::nops ( ) const

inline

Definition at line 136 of file ex.h.

References bp.

Referenced by GiNaC::abs_expand(), GiNaC::matrix::add_indexed(), GiNaC::algebraic_match_mul_with_mul(), GiNaC::ncmul::append_factors(), GiNaC::basic::collect(), GiNaC::collect_symbols(), GiNaC::color_trace(), GiNaC::ncmul::count_factors(), GiNaC::csgn_eval(), GiNaC::const_postorder_iterator::descend(), GiNaC::divide(), end(), GiNaC::indexed::eval(), GiNaC::exp_expand(), GiNaC::indexed::expand(), GiNaC::integral::expand(), GiNaC::mul::expand(), find(), GiNaC::find_common_factor(), GiNaC::G2_eval(), GiNaC::G2_evalf(), GiNaC::G3_eval(), GiNaC::G3_evalf(), GiNaC::gcd_pf_mul(), GiNaC::get_all_dummy_indices_safely(), GiNaC::get_first_symbol(), GiNaC::get_symbol_stats(), GiNaC::H_evalf(), GiNaC::hasindex(), GiNaC::haswild(), GiNaC::const_preorder_iterator::increment(), GiNaC::lcmcoeff(), GiNaC::Li2_series(), GiNaC::Li_deriv(), GiNaC::Li_eval(), GiNaC::Li_evalf(), GiNaC::log_expand(), GiNaC::lsolve(), GiNaC::expairseq::match(), GiNaC::basic::match(), GiNaC::multiply_lcm(), GiNaC::nops(), postorder_begin(), preorder_begin(), GiNaC::product_to_exvector(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::matrix::scalar_mul_indexed(), GiNaC::integral::series(), GiNaC::step_eval(), GiNaC::symminfo::symminfo(), traverse_postorder(), traverse_preorder(), GiNaC::zeta1_evalf(), and GiNaC::zeta2_evalf().

◆ op()

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

inline

Definition at line 137 of file ex.h.

References bp, and op().

Referenced by GiNaC::abs_eval(), GiNaC::matrix::add_indexed(), GiNaC::algebraic_match_mul_with_mul(), GiNaC::ncmul::append_factors(), GiNaC::atan_series(), GiNaC::atanh_series(), GiNaC::mul::can_be_further_expanded(), GiNaC::basic::collect(), GiNaC::collect_symbols(), GiNaC::color_trace(), GiNaC::su3f::contract_with(), GiNaC::su3d::contract_with(), GiNaC::matrix::contract_with(), GiNaC::cos_eval(), GiNaC::cosh_eval(), GiNaC::ncmul::count_factors(), GiNaC::csgn_eval(), GiNaC::decomp_rational(), denom(), GiNaC::const_postorder_iterator::descend(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::epsilon_tensor(), GiNaC::epsilon_tensor(), GiNaC::indexed::eval(), GiNaC::power::eval(), GiNaC::integral::eval_integ(), GiNaC::exp_eval(), GiNaC::indexed::expand(), GiNaC::integral::expand(), GiNaC::mul::expand(), find(), GiNaC::find_common_factor(), GiNaC::matrix::fraction_free_elimination(), GiNaC::G2_eval(), GiNaC::G2_evalf(), GiNaC::G3_eval(), GiNaC::G3_evalf(), GiNaC::gcd_pf_mul(), GiNaC::gcd_pf_pow(), GiNaC::gcd_pf_pow_pow(), GiNaC::get_all_dummy_indices_safely(), GiNaC::get_first_symbol(), GiNaC::clifford::get_metric(), GiNaC::H_evalf(), GiNaC::power::has(), GiNaC::hasindex(), GiNaC::haswild(), GiNaC::const_preorder_iterator::increment(), GiNaC::lcmcoeff(), GiNaC::Li2_series(), GiNaC::Li_deriv(), GiNaC::Li_evalf(), GiNaC::log_eval(), GiNaC::lorentz_eps(), GiNaC::lsolve(), GiNaC::expairseq::match(), GiNaC::basic::match(), GiNaC::multiply_lcm(), normal(), GiNaC::basic::normal(), GiNaC::power::normal(), numer(), GiNaC::op(), op(), GiNaC::op0_is_equal::operator()(), GiNaC::ex_base_is_less::operator()(), GiNaC::const_iterator::operator*(), GiNaC::const_iterator::operator[](), GiNaC::Order_eval(), GiNaC::product_to_exvector(), GiNaC::replace_with_symbol(), GiNaC::clifford::same_metric(), GiNaC::matrix::scalar_mul_indexed(), GiNaC::sin_eval(), GiNaC::sinh_eval(), GiNaC::spmapkey::spmapkey(), GiNaC::sqrfree_parfrac(), GiNaC::step_eval(), subs(), GiNaC::symminfo::symminfo(), GiNaC::tan_eval(), GiNaC::tanh_eval(), traverse_postorder(), traverse_preorder(), GiNaC::tryfactsubs(), and GiNaC::zeta2_deriv().

◆ operator[]() [1/4]

ex GiNaC::ex::operator[] ( const ex & index ) const

inline

Definition at line 138 of file ex.h.

References bp.

◆ operator[]() [2/4]

ex GiNaC::ex::operator[] ( size_t i ) const

inline

Definition at line 139 of file ex.h.

References bp.

◆ let_op()

ex & GiNaC::ex::let_op ( size_t i )

Return modifiable operand/member at position i.

Definition at line 207 of file ex.cpp.

References bp, and makewriteable().

Referenced by GiNaC::H_evalf().

◆ operator[]() [3/4]

ex & GiNaC::ex::operator[] ( const ex & index )

Definition at line 213 of file ex.cpp.

References bp, and makewriteable().

◆ operator[]() [4/4]

ex & GiNaC::ex::operator[] ( size_t i )

Definition at line 219 of file ex.cpp.

References bp, and makewriteable().

◆ lhs()

ex GiNaC::ex::lhs ( ) const

Left hand side of relational expression.

Definition at line 226 of file ex.cpp.

References bp.

Referenced by GiNaC::fsolve(), GiNaC::lhs(), GiNaC::pseries::pseries(), GiNaC::pseries::pseries(), GiNaC::Eisenstein_kernel::series(), GiNaC::Eisenstein_h_kernel::series(), GiNaC::modular_form_kernel::series(), GiNaC::mul::series(), and GiNaC::power::series().

◆ rhs()

ex GiNaC::ex::rhs ( ) const

Right hand side of relational expression.

Definition at line 234 of file ex.cpp.

References bp.

Referenced by GiNaC::fsolve(), GiNaC::pseries::pseries(), GiNaC::pseries::pseries(), GiNaC::rhs(), GiNaC::Eisenstein_h_kernel::series(), GiNaC::pseries::series(), GiNaC::mul::series(), GiNaC::power::series(), and GiNaC::symbol::series().

◆ conjugate()

ex GiNaC::ex::conjugate ( ) const

inline

Definition at line 147 of file ex.h.

References bp, and conjugate().

◆ real_part()

ex GiNaC::ex::real_part ( ) const

inline

Definition at line 148 of file ex.h.

References bp, and real_part().

Referenced by GiNaC::abs_eval(), GiNaC::asinh_conjugate(), GiNaC::atan_conjugate(), GiNaC::conjugate_real_part(), GiNaC::mul::find_real_imag(), GiNaC::power::imag_part(), GiNaC::pseries::imag_part(), real_part(), GiNaC::add::real_part(), GiNaC::power::real_part(), GiNaC::pseries::real_part(), GiNaC::real_part(), and GiNaC::real_part_eval().

◆ imag_part()

ex GiNaC::ex::imag_part ( ) const

inline

◆ has()

bool GiNaC::ex::has	(	const ex &	pattern,
		unsigned	options = `0`
	)		const

inline

Definition at line 152 of file ex.h.

References bp, and options.

Referenced by GiNaC::power::degree(), GiNaC::integral::eval(), GiNaC::integral::eval_integ(), GiNaC::integral::expand(), GiNaC::basic::has(), GiNaC::has(), GiNaC::power::is_polynomial(), and GiNaC::power::ldegree().

◆ find()

bool GiNaC::ex::find	(	const ex &	pattern,
		exset &	found
	)		const

Find all occurrences of a pattern.

The found matches are appended to the "found" list. If the expression itself matches the pattern, the children are not further examined. This function returns true when any matches were found.

Definition at line 106 of file ex.cpp.

References find(), match(), nops(), and op().

Referenced by GiNaC::divide_in_z(), GiNaC::scalar_products::evaluate(), find(), GiNaC::find(), GiNaC::pseries::mul_series(), GiNaC::replace_with_symbol(), GiNaC::idx::subs(), and GiNaC::basic::subs_one_level().

◆ match() [1/2]

bool GiNaC::ex::match ( const ex & pattern ) const

Check whether expression matches a specified pattern.

Definition at line 96 of file ex.cpp.

References bp, and match().

Referenced by find(), GiNaC::power::has(), match(), GiNaC::basic::match(), GiNaC::match(), and GiNaC::tryfactsubs().

◆ match() [2/2]

bool GiNaC::ex::match	(	const ex &	pattern,
		exmap &	repls
	)		const

inline

Definition at line 155 of file ex.h.

References bp.

◆ subs() [1/3]

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

inline

Definition at line 842 of file ex.h.

References bp, m, options, and subs().

Referenced by GiNaC::adaptivesimpson(), GiNaC::mul::algebraic_subs_mul(), GiNaC::atan_series(), GiNaC::atanh_series(), GiNaC::beta_series(), GiNaC::collect_common_factors(), GiNaC::integral::conjugate(), GiNaC::csgn_series(), denom(), GiNaC::integral::derivative(), GiNaC::divide_in_z(), GiNaC::EllipticE_series(), GiNaC::EllipticK_series(), GiNaC::eta_series(), GiNaC::tensdelta::eval_indexed(), GiNaC::integral::eval_integ(), GiNaC::integral::evalf(), GiNaC::expand_dummy_sum(), GiNaC::fsolve(), GiNaC::gcd(), GiNaC::clifford::get_metric(), GiNaC::H_evalf(), GiNaC::heur_gcd_z(), GiNaC::modular_form_kernel::is_numeric(), GiNaC::user_defined_kernel::is_numeric(), GiNaC::user_defined_kernel::Laurent_series(), GiNaC::lgamma_series(), GiNaC::Li2_series(), GiNaC::Li_series(), GiNaC::log_series(), normal(), GiNaC::basic::normal(), GiNaC::power::normal(), numer(), numer_denom(), GiNaC::psi1_series(), GiNaC::psi2_series(), GiNaC::rename_dummy_indices(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::rename_dummy_indices_uniquely(), GiNaC::tensor::replace_contr_index(), GiNaC::replace_with_symbol(), GiNaC::replace_with_symbol(), GiNaC::S_series(), GiNaC::basic::series(), GiNaC::integral::series(), GiNaC::power::series(), GiNaC::step_series(), subs(), GiNaC::subs(), GiNaC::subs(), GiNaC::subs(), GiNaC::basic::subs(), subs(), GiNaC::clifford::subs(), GiNaC::idx::subs(), GiNaC::power::subs(), GiNaC::pseries::subs(), GiNaC::relational::subs(), GiNaC::basic::subs_one_level(), GiNaC::container< C >::subschildren(), GiNaC::expairseq::subschildren(), GiNaC::subsvalue(), GiNaC::symm(), GiNaC::symmetrize_cyclic(), GiNaC::tan_series(), GiNaC::tanh_series(), and GiNaC::tgamma_series().

◆ subs() [2/3]

ex GiNaC::ex::subs	(	const lst &	ls,
		const lst &	lr,
		unsigned	options = `0`
	)		const

Substitute objects in an expression (syntactic substitution) and return the result as a new expression.

Definition at line 121 of file ex.cpp.

References GiNaC::container< C >::begin(), bp, GiNaC::container< C >::end(), GINAC_ASSERT, lr, m, GiNaC::container< C >::nops(), options, GiNaC::subs_options::pattern_is_not_product, and GiNaC::subs_options::pattern_is_product.

◆ subs() [3/3]

ex GiNaC::ex::subs	(	const ex &	e,
		unsigned	options = `0`
	)		const

Substitute objects in an expression (syntactic substitution) and return the result as a new expression.

There are two valid types of replacement arguments: 1) a relational like object==ex and 2) a list of relationals lst{object1==ex1,object2==ex2,...}.

Definition at line 145 of file ex.cpp.

References bp, GINAC_ASSERT, info(), GiNaC::info_flags::list, m, op(), options, GiNaC::subs_options::pattern_is_not_product, GiNaC::subs_options::pattern_is_product, r, GiNaC::info_flags::relation_equal, and subs().

◆ map() [1/2]

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

inline

Definition at line 163 of file ex.h.

References bp, and map().

Referenced by GiNaC::color_trace(), GiNaC::expand_dummy_sum(), and map().

◆ map() [2/2]

ex GiNaC::ex::map ( ex(*)(const ex &e) f ) const

◆ accept()

void GiNaC::ex::accept ( visitor & v ) const

inline

Definition at line 167 of file ex.h.

References bp.

Referenced by traverse_postorder(), and traverse_preorder().

◆ traverse_preorder()

void GiNaC::ex::traverse_preorder ( visitor & v ) const

Traverse expression tree with given visitor, preorder traversal.

Definition at line 187 of file ex.cpp.

References accept(), n, nops(), op(), and traverse_preorder().

Referenced by traverse(), and traverse_preorder().

◆ traverse_postorder()

void GiNaC::ex::traverse_postorder ( visitor & v ) const

Traverse expression tree with given visitor, postorder traversal.

Definition at line 197 of file ex.cpp.

References accept(), n, nops(), op(), and traverse_postorder().

Referenced by traverse_postorder().

◆ traverse()

void GiNaC::ex::traverse ( visitor & v ) const

inline

Definition at line 170 of file ex.h.

References traverse_preorder().

◆ is_polynomial()

bool GiNaC::ex::is_polynomial ( const ex & vars ) const

Check whether expression is a polynomial.

Definition at line 242 of file ex.cpp.

References bp.

Referenced by GiNaC::is_polynomial(), and GiNaC::power::is_polynomial().

◆ degree()

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

inline

Definition at line 174 of file ex.h.

References bp.

Referenced by GiNaC::basic::collect(), content(), GiNaC::integral::degree(), GiNaC::mul::degree(), GiNaC::power::degree(), GiNaC::degree(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::get_symbol_stats(), GiNaC::heur_gcd_z(), lcoeff(), GiNaC::prem(), GiNaC::quo(), GiNaC::rem(), GiNaC::resultant(), GiNaC::sprem(), and GiNaC::sr_gcd().

◆ ldegree()

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

inline

Definition at line 175 of file ex.h.

References bp.

Referenced by content(), GiNaC::gcd_pf_pow(), GiNaC::get_symbol_stats(), GiNaC::mul::ldegree(), GiNaC::power::ldegree(), GiNaC::ldegree(), GiNaC::Order_series(), GiNaC::resultant(), GiNaC::mul::series(), GiNaC::power::series(), and tcoeff().

◆ coeff()

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

inline

Definition at line 176 of file ex.h.

References bp, coeff(), and n.

Referenced by GiNaC::Bernoulli_polynomial(), coeff(), GiNaC::add::coeff(), GiNaC::mul::coeff(), GiNaC::ncmul::coeff(), GiNaC::pseries::coeff(), GiNaC::coeff(), GiNaC::basic::collect(), content(), GiNaC::pseries::convert_to_poly(), GiNaC::mul::derivative(), GiNaC::pseries::derivative(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::pseries::eval_integ(), GiNaC::pseries::evalm(), GiNaC::pseries::expand(), GiNaC::power::expand_add_2(), GiNaC::expairseq::expandchildren(), GiNaC::pseries::exponop(), GiNaC::generalised_Bernoulli_number(), GiNaC::add::imag_part(), lcoeff(), GiNaC::lsolve(), GiNaC::expairseq::make_flat(), GiNaC::pseries::normal(), GiNaC::prem(), GiNaC::pseries::print_series(), GiNaC::quo(), GiNaC::add::real_part(), GiNaC::rem(), GiNaC::resultant(), GiNaC::mul::series(), GiNaC::integration_kernel::series_coeff(), GiNaC::sprem(), GiNaC::sqrfree_parfrac(), GiNaC::expairseq::subschildren(), and tcoeff().

◆ lcoeff()

ex GiNaC::ex::lcoeff ( const ex & s ) const

inline

Definition at line 177 of file ex.h.

References coeff(), and degree().

Referenced by content(), GiNaC::get_symbol_stats(), GiNaC::sr_gcd(), and unit().

◆ tcoeff()

ex GiNaC::ex::tcoeff ( const ex & s ) const

inline

Definition at line 178 of file ex.h.

References coeff(), and ldegree().

◆ expand()

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

Expand an expression.

Parameters

options see GiNaC::expand_options

Definition at line 74 of file ex.cpp.

References bp, expand(), GiNaC::status_flags::expanded, and options.

Referenced by GiNaC::abs_expand(), GiNaC::binomial_sym(), GiNaC::color_trace(), content(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::exp_expand(), GiNaC::expand(), GiNaC::expand(), expand(), GiNaC::indexed::expand(), GiNaC::integral::expand(), GiNaC::mul::expand(), GiNaC::power::expand(), GiNaC::pseries::expand(), GiNaC::expand_dummy_sum(), GiNaC::expairseq::expandchildren(), GiNaC::mul::expandchildren(), GiNaC::ncmul::expandchildren(), GiNaC::mul::find_real_imag(), GiNaC::frac_cancel(), GiNaC::matrix::fraction_free_elimination(), GiNaC::gcd(), GiNaC::heur_gcd_z(), GiNaC::log_expand(), GiNaC::lsolve(), GiNaC::expand_map_function::operator()(), GiNaC::prem(), GiNaC::quo(), GiNaC::rem(), GiNaC::resultant(), GiNaC::basic::series(), GiNaC::mul::series(), GiNaC::power::series(), GiNaC::sprem(), GiNaC::sqrfree_parfrac(), GiNaC::sr_gcd(), GiNaC::matrix::trace(), unit(), and unitcontprim().

◆ collect()

ex GiNaC::ex::collect	(	const ex &	s,
		bool	distributed = `false`
	)		const

inline

Definition at line 182 of file ex.h.

References bp, and collect().

Referenced by GiNaC::matrix::charpoly(), collect(), and GiNaC::collect().

◆ diff()

ex GiNaC::ex::diff	(	const symbol &	s,
		unsigned	nth = `1`
	)		const

Compute partial derivative of an expression.

Parameters

s	symbol by which the expression is derived
nth	order of derivative (default 1)

Returns: partial derivative as a new expression

Definition at line 87 of file ex.cpp.

References bp, and diff().

Referenced by GiNaC::abs_expl_derivative(), GiNaC::conjugate_expl_derivative(), GiNaC::fderivative::derivative(), GiNaC::function::derivative(), GiNaC::integral::derivative(), GiNaC::ncmul::derivative(), GiNaC::power::derivative(), GiNaC::pseries::derivative(), GiNaC::diff(), GiNaC::basic::diff(), diff(), GiNaC::fsolve(), GiNaC::imag_part_expl_derivative(), GiNaC::log_series(), GiNaC::Order_expl_derivative(), GiNaC::real_part_expl_derivative(), GiNaC::basic::series(), and GiNaC::sqrfree_yun().

◆ series()

ex GiNaC::ex::series	(	const ex &	r,
		int	order,
		unsigned	options = `0`
	)		const

Compute the truncated series expansion of an expression.

This function returns an expression containing an object of class pseries to represent the series. If the series does not terminate within the given truncation order, the last term of the series will be an order term.

Parameters

r	expansion relation, lhs holds variable and rhs holds point
order	truncation order of series calculations
options	of class series_options

Returns: an expression holding a pseries object

Definition at line 1272 of file pseries.cpp.

References GiNaC::_ex0, bp, options, order, r, and series().

Referenced by GiNaC::Bernoulli_polynomial(), GiNaC::EllipticE_series(), GiNaC::EllipticK_series(), GiNaC::generalised_Bernoulli_number(), GiNaC::modular_form_kernel::Laurent_series(), GiNaC::integration_kernel::Laurent_series(), GiNaC::Eisenstein_kernel::Laurent_series(), GiNaC::Eisenstein_h_kernel::Laurent_series(), GiNaC::user_defined_kernel::Laurent_series(), GiNaC::Li2_series(), GiNaC::Li_series(), GiNaC::log_series(), GiNaC::Eisenstein_h_kernel::q_expansion_modular_form(), GiNaC::S_series(), series(), GiNaC::series(), GiNaC::add::series(), GiNaC::integral::series(), GiNaC::Eisenstein_kernel::series(), GiNaC::Eisenstein_h_kernel::series(), GiNaC::modular_form_kernel::series(), GiNaC::pseries::series(), GiNaC::mul::series(), GiNaC::power::series(), and GiNaC::tgamma_series().

◆ normal()

ex GiNaC::ex::normal ( ) const

Normalization of rational functions.

This function converts an expression to its normal form "numerator/denominator", where numerator and denominator are (relatively prime) polynomials. Any subexpressions which are not rational functions (like non-rational numbers, non-integer powers or functions like sin(), cos() etc.) are replaced by temporary symbols which are re-substituted by the (normalized) subexpressions before normal() returns (this way, any expression can be treated as a rational function). normal() is applied recursively to arguments of functions etc.

Returns: normalized expression

Definition at line 2519 of file normal.cpp.

References bp, GINAC_ASSERT, GiNaC::subs_options::no_pattern, GiNaC::container< C >::nops(), normal(), op(), GiNaC::container< C >::op(), and subs().

Referenced by denom(), GiNaC::matrix::determinant(), GiNaC::matrix::fraction_free_elimination(), GiNaC::matrix::gauss_elimination(), normal(), GiNaC::normal(), GiNaC::add::normal(), GiNaC::power::normal(), GiNaC::pseries::normal(), numer(), numer_denom(), and GiNaC::matrix::trace().

◆ to_rational()

ex GiNaC::ex::to_rational ( exmap & repl ) const

Rationalization of non-rational functions.

This function converts a general expression to a rational function by replacing all non-rational subexpressions (like non-rational numbers, non-integer powers or functions like sin(), cos() etc.) to temporary symbols. This makes it possible to use functions like gcd() and divide() on non-rational functions by applying to_rational() on the arguments, calling the desired function and re-substituting the temporary symbols in the result. To make the last step possible, all temporary symbols and their associated expressions are collected in the map specified by the repl parameter, ready to be passed as an argument to ex::subs().

Parameters

repl	collects all temporary symbols and their replacements

Returns: rationalized expression

Definition at line 2627 of file normal.cpp.

References bp, and to_rational().

Referenced by GiNaC::matrix::determinant(), GiNaC::matrix::fraction_free_elimination(), GiNaC::to_rational(), to_rational(), GiNaC::expairseq::to_rational(), and GiNaC::power::to_rational().

◆ to_polynomial()

ex GiNaC::ex::to_polynomial ( exmap & repl ) const

Definition at line 2632 of file normal.cpp.

References bp, and to_polynomial().

Referenced by GiNaC::find_common_factor(), GiNaC::to_polynomial(), to_polynomial(), GiNaC::expairseq::to_polynomial(), and GiNaC::power::to_polynomial().

◆ numer()

ex GiNaC::ex::numer ( ) const

Get numerator of an expression.

If the expression is not of the normal form "numerator/denominator", it is first converted to this form and then the numerator is returned.

See also: ex::normal

Returns: numerator

Definition at line 2544 of file normal.cpp.

References bp, GINAC_ASSERT, GiNaC::subs_options::no_pattern, GiNaC::container< C >::nops(), normal(), op(), GiNaC::container< C >::op(), and subs().

Referenced by GiNaC::numer(), and GiNaC::numer().

◆ denom()

ex GiNaC::ex::denom ( ) const

Get denominator of an expression.

If the expression is not of the normal form "numerator/denominator", it is first converted to this form and then the denominator is returned.

See also: ex::normal

Returns: denominator

Definition at line 2569 of file normal.cpp.

References bp, GINAC_ASSERT, GiNaC::subs_options::no_pattern, GiNaC::container< C >::nops(), normal(), op(), GiNaC::container< C >::op(), and subs().

Referenced by GiNaC::denom(), and GiNaC::denom().

◆ numer_denom()

ex GiNaC::ex::numer_denom ( ) const

Get numerator and denominator of an expression.

If the expression is not of the normal form "numerator/denominator", it is first converted to this form and then a list [numerator, denominator] is returned.

See also: ex::normal

Returns: a list [numerator, denominator]

Definition at line 2594 of file normal.cpp.

References bp, GINAC_ASSERT, GiNaC::subs_options::no_pattern, GiNaC::container< C >::nops(), normal(), GiNaC::container< C >::op(), and subs().

Referenced by GiNaC::matrix::fraction_free_elimination(), and GiNaC::numer_denom().

◆ unit()

ex GiNaC::ex::unit ( const ex & x ) const

Compute unit part (= sign of leading coefficient) of a multivariate polynomial in Q[x].

The product of unit part, content part, and primitive part is the polynomial itself.

Parameters

x	main variable

Returns: unit part

See also: ex::content, ex::primpart, ex::unitcontprim

Definition at line 923 of file normal.cpp.

References GiNaC::_ex1, GiNaC::_ex_1, c, expand(), GiNaC::get_first_symbol(), info(), lcoeff(), GiNaC::info_flags::negative, unit(), and x.

Referenced by content(), GiNaC::frac_cancel(), and unit().

◆ content()

ex GiNaC::ex::content ( const ex & x ) const

Compute content part (= unit normal GCD of all coefficients) of a multivariate polynomial in Q[x].

The product of unit part, content part, and primitive part is the polynomial itself.

Parameters

x	main variable

Returns: content part

See also: ex::unit, ex::primpart, ex::unitcontprim

Definition at line 945 of file normal.cpp.

References GiNaC::_ex0, c, coeff(), cont, degree(), expand(), GiNaC::gcd(), info(), GiNaC::info_flags::integer, integer_content(), is_zero(), lcoeff(), ldegree(), GiNaC::info_flags::negative, r, unit(), and x.

Referenced by GiNaC::sr_gcd(), and unitcontprim().

◆ integer_content()

numeric GiNaC::ex::integer_content ( ) const

Compute the integer content (= GCD of all numeric coefficients) of an expanded polynomial.

For a polynomial with rational coefficients, this returns g/l where g is the GCD of the coefficients' numerators and l is the LCM of the coefficients' denominators.

Returns: integer content

Definition at line 318 of file normal.cpp.

References bp, and GiNaC::numeric::integer_content().

Referenced by content(), GiNaC::power::eval(), GiNaC::gcd(), and GiNaC::heur_gcd_z().

◆ primpart() [1/2]

ex GiNaC::ex::primpart ( const ex & x ) const

Compute primitive part of a multivariate polynomial in Q[x].

The result will be a unit-normal polynomial with a content part of 1. The product of unit part, content part, and primitive part is the polynomial itself.

Parameters

x	main variable

Returns: primitive part

See also: ex::unit, ex::content, ex::unitcontprim

Definition at line 981 of file normal.cpp.

References c, unitcontprim(), and x.

Referenced by GiNaC::sr_gcd().

◆ primpart() [2/2]

ex GiNaC::ex::primpart	(	const ex &	x,
		const ex &	c
	)		const

Compute primitive part of a multivariate polynomial in Q[x] when the content part is already known.

This function is faster in computing the primitive part than the previous function.

Parameters

x	main variable
c	previously computed content part

Returns: primitive part

Definition at line 997 of file normal.cpp.

References GiNaC::_ex0, GiNaC::_ex1, c, is_zero(), GiNaC::quo(), unit, and x.

◆ unitcontprim()

void GiNaC::ex::unitcontprim	(	const ex &	x,
		ex &	u,
		ex &	c,
		ex &	p
	)		const

Compute unit part, content part, and primitive part of a multivariate polynomial in Q[x].

The product of the three parts is the polynomial itself.

Parameters

x	main variable
u	unit part (returned)
c	content part (returned)
p	primitive part (returned)

See also: ex::unit, ex::content, ex::primpart

Definition at line 1022 of file normal.cpp.

References GiNaC::_ex0, GiNaC::_ex1, GiNaC::_ex_1, GiNaC::abs(), c, content(), expand(), info(), is_zero(), GiNaC::info_flags::negative, GiNaC::quo(), unit, and x.

Referenced by GiNaC::gcd(), and primpart().

◆ smod()

ex GiNaC::ex::smod ( const numeric & xi ) const

inline

Definition at line 203 of file ex.h.

References bp, and smod().

Referenced by GiNaC::interpolate(), and smod().

◆ max_coefficient()

numeric GiNaC::ex::max_coefficient ( ) const

Return maximum (absolute value) coefficient of a polynomial.

This function is used internally by heur_gcd().

Returns: maximum coefficient

See also: heur_gcd

Definition at line 1154 of file normal.cpp.

References bp, and GiNaC::numeric::max_coefficient().

Referenced by GiNaC::heur_gcd_z().

◆ get_free_indices()

exvector GiNaC::ex::get_free_indices ( ) const

inline

Definition at line 207 of file ex.h.

References bp.

Referenced by antisymmetrize(), GiNaC::get_all_dummy_indices_safely(), GiNaC::add::get_free_indices(), GiNaC::integral::get_free_indices(), GiNaC::mul::get_free_indices(), GiNaC::ncmul::get_free_indices(), GiNaC::clifford::get_metric(), GiNaC::clifford::same_metric(), symmetrize(), and symmetrize_cyclic().

◆ simplify_indexed() [1/2]

ex GiNaC::ex::simplify_indexed ( unsigned options = 0 ) const

Simplify/canonicalize expression containing indexed objects.

This performs contraction of dummy indices where possible and checks whether the free indices in sums are consistent.

Parameters

options Simplification options (currently unused)

Returns: simplified expression

Definition at line 1257 of file indexed.cpp.

References GiNaC::simplify_indexed().

Referenced by GiNaC::tensepsilon::contract_with(), GiNaC::simplify_indexed(), and GiNaC::simplify_indexed().

◆ simplify_indexed() [2/2]

ex GiNaC::ex::simplify_indexed	(	const scalar_products &	sp,
		unsigned	options = `0`
	)		const

Simplify/canonicalize expression containing indexed objects.

This performs contraction of dummy indices where possible, checks whether the free indices in sums are consistent, and automatically replaces scalar products by known values if desired.

Parameters

sp	Scalar products to be replaced automatically
options	Simplification options (currently unused)

Returns: simplified expression

Definition at line 1272 of file indexed.cpp.

References GiNaC::simplify_indexed().

◆ compare()

int GiNaC::ex::compare ( const ex & other ) const

inline

Definition at line 323 of file ex.h.

References bp, and share().

Referenced by GiNaC::expair::compare(), GiNaC::expairseq::construct_from_2_ex(), GiNaC::expair::is_less(), GiNaC::error_and_integral_is_less::operator()(), GiNaC::ex_is_less::operator()(), GiNaC::expair_rest_is_less::operator()(), GiNaC::symminfo_is_less_by_symmterm::operator()(), GiNaC::symminfo_is_less_by_orig::operator()(), GiNaC::terminfo_is_less::operator()(), GiNaC::spmapkey::operator<(), and GiNaC::spmapkey::spmapkey().

◆ is_equal()

bool GiNaC::ex::is_equal ( const ex & other ) const

inline

Definition at line 346 of file ex.h.

References bp, and share().

Referenced by GiNaC::abs_power(), GiNaC::acos_eval(), GiNaC::acosh_eval(), GiNaC::matrix::add_indexed(), GiNaC::asin_eval(), GiNaC::atan2_eval(), GiNaC::atan_eval(), GiNaC::atan_series(), GiNaC::atanh_eval(), GiNaC::atanh_series(), GiNaC::beta_eval(), GiNaC::power::coeff(), GiNaC::pseries::coeff(), GiNaC::add::combine_ex_with_coeff_to_pair(), GiNaC::mul::combine_pair_with_coeff_to_pair(), GiNaC::conjugateepvector(), GiNaC::power::degree(), GiNaC::pseries::degree(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::mul::do_print_csrc(), GiNaC::power::do_print_csrc(), GiNaC::power::do_print_csrc_cl_N(), GiNaC::power::do_print_dflt(), GiNaC::power::do_print_latex(), GiNaC::expairseq::do_print_tree(), GiNaC::epsilon_tensor(), GiNaC::epsilon_tensor(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::matrix::eval_indexed(), GiNaC::tensdelta::eval_indexed(), GiNaC::tensmetric::eval_indexed(), GiNaC::mul::expand(), GiNaC::find_common_factor(), GiNaC::frac_cancel(), GiNaC::gcd(), GiNaC::gcd_pf_pow(), GiNaC::gcd_pf_pow_pow(), GiNaC::make_flat_inserter::handle_factor(), GiNaC::power::imag_part(), GiNaC::mul::info(), GiNaC::expair::is_canonical_numeric(), GiNaC::pseries::is_compatible_to(), GiNaC::idx::is_dummy_pair_same_type(), GiNaC::expair::is_equal(), GiNaC::expairseq::is_equal_same_type(), is_zero(), GiNaC::power::ldegree(), GiNaC::pseries::ldegree(), GiNaC::Li2_eval(), GiNaC::Li2_series(), GiNaC::Li_eval(), GiNaC::log_eval(), GiNaC::lorentz_eps(), GiNaC::expairseq::map(), GiNaC::expairseq::match(), GiNaC::idx::match_same_type(), GiNaC::minimal_dim(), GiNaC::pseries::mul_series(), GiNaC::multiply_lcm(), GiNaC::expairseq::nops(), GiNaC::power::normal(), GiNaC::expairseq::op(), GiNaC::ex_is_equal::operator()(), GiNaC::op0_is_equal::operator()(), GiNaC::idx_is_equal_ignore_dim::operator()(), GiNaC::spmapkey::operator==(), GiNaC::add::print_add(), GiNaC::mul::print_overall_coeff(), GiNaC::expairseq::printseq(), GiNaC::product_to_exvector(), GiNaC::quo(), GiNaC::power::real_part(), GiNaC::mul::recombine_pair_to_ex(), GiNaC::rem(), GiNaC::replace_with_symbol(), GiNaC::clifford::same_metric(), GiNaC::pseries::series(), GiNaC::power::series(), GiNaC::add::split_ex_to_pair(), and GiNaC::sqrfree_yun().

◆ is_zero()

bool GiNaC::ex::is_zero ( ) const

inline

Definition at line 214 of file ex.h.

References GiNaC::_ex0, and is_equal().

Referenced by GiNaC::acos_conjugate(), GiNaC::acos_eval(), GiNaC::acosh_conjugate(), GiNaC::acosh_eval(), GiNaC::pseries::add_series(), GiNaC::asin_conjugate(), GiNaC::asin_eval(), GiNaC::asinh_eval(), GiNaC::atan(), GiNaC::atan(), GiNaC::atan2_eval(), GiNaC::atan_eval(), GiNaC::atanh_conjugate(), GiNaC::atanh_eval(), GiNaC::add::coeff(), content(), GiNaC::cosh_eval(), GiNaC::add::degree(), GiNaC::fderivative::derivative(), GiNaC::function::derivative(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::basic::diff(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::add::do_print_csrc(), GiNaC::matrix::echelon_form(), GiNaC::add::eval(), GiNaC::function::eval(), GiNaC::indexed::eval(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::pseries::evalm(), GiNaC::exp_eval(), GiNaC::mul::expand(), GiNaC::pseries::expand(), GiNaC::power::expand_add(), GiNaC::power::expand_add_2(), GiNaC::find_common_factor(), GiNaC::mul::find_real_imag(), GiNaC::frac_cancel(), GiNaC::matrix::fraction_free_elimination(), GiNaC::gcd(), GiNaC::heur_gcd_z(), GiNaC::add::imag_part(), GiNaC::add::info(), GiNaC::interpolate(), GiNaC::is_zero(), GiNaC::is_zero(), is_zero_matrix(), GiNaC::add::ldegree(), GiNaC::lgamma_conjugate(), GiNaC::Li2_conjugate(), GiNaC::Li2_eval(), GiNaC::Li2_series(), GiNaC::Li3_eval(), GiNaC::Li_series(), GiNaC::log(), GiNaC::log_conjugate(), GiNaC::log_eval(), GiNaC::log_series(), GiNaC::matrix::markowitz_elimination(), GiNaC::pseries::mul_series(), GiNaC::pseries::normal(), GiNaC::relational::operator safe_bool(), GiNaC::Order_eval(), GiNaC::prem(), primpart(), GiNaC::add::print_add(), GiNaC::pseries::print_series(), GiNaC::quo(), GiNaC::add::real_part(), GiNaC::rem(), GiNaC::S_series(), GiNaC::clifford::same_metric(), GiNaC::basic::series(), GiNaC::power::series(), GiNaC::symbol::series(), GiNaC::sinh_eval(), GiNaC::add::smod(), GiNaC::sprem(), GiNaC::sqrfree_yun(), GiNaC::tanh_eval(), unitcontprim(), and GiNaC::indexed::validate().

◆ is_zero_matrix()

bool GiNaC::ex::is_zero_matrix ( ) const

Check whether expression is zero or zero matrix.

Definition at line 256 of file ex.cpp.

References evalm(), and is_zero().

◆ symmetrize() [1/2]

ex GiNaC::ex::symmetrize ( ) const

Symmetrize expression over its free indices.

Definition at line 1279 of file indexed.cpp.

References get_free_indices(), and GiNaC::symmetrize().

Referenced by GiNaC::symmetrize(), and GiNaC::symmetrize().

◆ symmetrize() [2/2]

ex GiNaC::ex::symmetrize ( const lst & l ) const

Symmetrize expression over a list of objects (symbols, indices).

Definition at line 556 of file symmetry.cpp.

References GiNaC::container< C >::begin(), GiNaC::container< C >::end(), and GiNaC::symm().

◆ antisymmetrize() [1/2]

ex GiNaC::ex::antisymmetrize ( ) const

Antisymmetrize expression over its free indices.

Definition at line 1285 of file indexed.cpp.

References GiNaC::antisymmetrize(), and get_free_indices().

Referenced by GiNaC::antisymmetrize(), and GiNaC::antisymmetrize().

◆ antisymmetrize() [2/2]

ex GiNaC::ex::antisymmetrize ( const lst & l ) const

Antisymmetrize expression over a list of objects (symbols, indices).

Definition at line 563 of file symmetry.cpp.

References GiNaC::container< C >::begin(), GiNaC::container< C >::end(), and GiNaC::symm().

◆ symmetrize_cyclic() [1/2]

ex GiNaC::ex::symmetrize_cyclic ( ) const

Symmetrize expression by cyclic permutation over its free indices.

Definition at line 1291 of file indexed.cpp.

References get_free_indices(), and GiNaC::symmetrize_cyclic().

Referenced by GiNaC::symmetrize_cyclic(), and GiNaC::symmetrize_cyclic().

◆ symmetrize_cyclic() [2/2]

ex GiNaC::ex::symmetrize_cyclic ( const lst & l ) const

Symmetrize expression by cyclic permutation over a list of objects (symbols, indices).

Definition at line 571 of file symmetry.cpp.

References GiNaC::container< C >::begin(), GiNaC::container< C >::end(), and GiNaC::symmetrize_cyclic().

◆ return_type()

unsigned GiNaC::ex::return_type ( ) const

inline

Definition at line 231 of file ex.h.

References bp.

Referenced by GiNaC::ncmul::append_factors(), GiNaC::ncmul::count_factors(), GiNaC::power::eval(), GiNaC::exmul(), GiNaC::matrix::mul_scalar(), GiNaC::indexed::return_type(), GiNaC::integral::return_type(), GiNaC::power::return_type(), and GiNaC::relational::return_type().

◆ return_type_tinfo()

return_type_t GiNaC::ex::return_type_tinfo ( ) const

inline

Definition at line 232 of file ex.h.

References bp.

Referenced by GiNaC::color_trace(), GiNaC::indexed::return_type_tinfo(), GiNaC::integral::return_type_tinfo(), GiNaC::power::return_type_tinfo(), and GiNaC::relational::return_type_tinfo().

◆ gethash()

unsigned GiNaC::ex::gethash ( ) const

inline

Definition at line 234 of file ex.h.

References bp.

Referenced by GiNaC::basic::calchash(), GiNaC::expairseq::calchash(), GiNaC::function::calchash(), GiNaC::idx::calchash(), and GiNaC::relational::calchash().

◆ construct_from_basic()

ptr< basic > GiNaC::ex::construct_from_basic ( const basic & other )

staticprivate

Helper function for the ex-from-basic constructor.

This is where GiNaC's automatic evaluator and memory management are implemented.

See also: ex::ex(const basic &)

Definition at line 293 of file ex.cpp.

References bp, GiNaC::basic::duplicate(), GiNaC::status_flags::dynallocated, GiNaC::basic::eval(), GiNaC::status_flags::evaluated, GiNaC::basic::flags, GiNaC::refcounted::get_refcount(), GINAC_ASSERT, and GiNaC::basic::setflag().

◆ construct_from_int()

basic & GiNaC::ex::construct_from_int ( int i )

staticprivate

Definition at line 351 of file ex.cpp.

References GiNaC::_num0_p, GiNaC::_num10_p, GiNaC::_num11_p, GiNaC::_num12_p, GiNaC::_num1_p, GiNaC::_num2_p, GiNaC::_num3_p, GiNaC::_num4_p, GiNaC::_num5_p, GiNaC::_num6_p, GiNaC::_num7_p, GiNaC::_num8_p, GiNaC::_num9_p, GiNaC::_num_10_p, GiNaC::_num_11_p, GiNaC::_num_12_p, GiNaC::_num_1_p, GiNaC::_num_2_p, GiNaC::_num_3_p, GiNaC::_num_4_p, GiNaC::_num_5_p, GiNaC::_num_6_p, GiNaC::_num_7_p, GiNaC::_num_8_p, and GiNaC::_num_9_p.

Referenced by construct_from_longlong().

◆ construct_from_uint()

basic & GiNaC::ex::construct_from_uint ( unsigned int i )

staticprivate

Definition at line 409 of file ex.cpp.

References GiNaC::_num0_p, GiNaC::_num10_p, GiNaC::_num11_p, GiNaC::_num12_p, GiNaC::_num1_p, GiNaC::_num2_p, GiNaC::_num3_p, GiNaC::_num4_p, GiNaC::_num5_p, GiNaC::_num6_p, GiNaC::_num7_p, GiNaC::_num8_p, and GiNaC::_num9_p.

Referenced by construct_from_ulonglong().

◆ construct_from_long()

basic & GiNaC::ex::construct_from_long ( long i )

staticprivate

Definition at line 443 of file ex.cpp.

References GiNaC::_num0_p, GiNaC::_num10_p, GiNaC::_num11_p, GiNaC::_num12_p, GiNaC::_num1_p, GiNaC::_num2_p, GiNaC::_num3_p, GiNaC::_num4_p, GiNaC::_num5_p, GiNaC::_num6_p, GiNaC::_num7_p, GiNaC::_num8_p, GiNaC::_num9_p, GiNaC::_num_10_p, GiNaC::_num_11_p, GiNaC::_num_12_p, GiNaC::_num_1_p, GiNaC::_num_2_p, GiNaC::_num_3_p, GiNaC::_num_4_p, GiNaC::_num_5_p, GiNaC::_num_6_p, GiNaC::_num_7_p, GiNaC::_num_8_p, and GiNaC::_num_9_p.

◆ construct_from_ulong()

basic & GiNaC::ex::construct_from_ulong ( unsigned long i )

staticprivate

Definition at line 501 of file ex.cpp.

References GiNaC::_num0_p, GiNaC::_num10_p, GiNaC::_num11_p, GiNaC::_num12_p, GiNaC::_num1_p, GiNaC::_num2_p, GiNaC::_num3_p, GiNaC::_num4_p, GiNaC::_num5_p, GiNaC::_num6_p, GiNaC::_num7_p, GiNaC::_num8_p, and GiNaC::_num9_p.

◆ construct_from_longlong()

basic & GiNaC::ex::construct_from_longlong ( long long i )

staticprivate

Definition at line 535 of file ex.cpp.

References construct_from_int().

◆ construct_from_ulonglong()

basic & GiNaC::ex::construct_from_ulonglong ( unsigned long long i )

staticprivate

Definition at line 544 of file ex.cpp.

References construct_from_uint().

◆ construct_from_double()

basic & GiNaC::ex::construct_from_double ( double d )

staticprivate

Definition at line 553 of file ex.cpp.

◆ construct_from_string_and_lst()

static ptr< basic > GiNaC::ex::construct_from_string_and_lst	(	const std::string &	s,
		const ex &	l
	)

staticprivate

◆ makewriteable()

void GiNaC::ex::makewriteable ( )

private

Make this ex writable (if more than one ex handle the same basic) by unlinking the object and creating an unshared copy of it.

Definition at line 270 of file ex.cpp.

References bp, GiNaC::status_flags::dynallocated, and GINAC_ASSERT.

Referenced by let_op(), operator[](), and operator[]().

◆ share()

void GiNaC::ex::share ( const ex & other ) const

private

Share equal objects between expressions.

See also: ex::compare(const ex &)

Definition at line 279 of file ex.cpp.

References bp, and GiNaC::status_flags::not_shareable.

Referenced by compare(), and is_equal().

Friends And Related Symbol Documentation

◆ archive_node

friend class archive_node

friend

Definition at line 74 of file ex.h.

◆ are_ex_trivially_equal

bool are_ex_trivially_equal	(	const ex &	e1,
		const ex &	e2
	)

friend

Compare two objects of class quickly without doing a deep tree traversal.

Returns: "true" if they are equal "false" if equality cannot be established quickly (e1 and e2 may still be equal, in this case.

Definition at line 700 of file ex.h.

◆ ex_to

template<class T >

const T & ex_to ( const ex & e )

friend

Return a reference to the basic-derived class T object embedded in an expression.

This is fast but unsafe: the result is undefined if the expression does not contain a T object at its top level. Hence, you should generally check the type of e first. Also, you shouldn't cache the returned reference because GiNaC's garbage collector may destroy the referenced object any time it's used in another expression.

Parameters

e	expression

Returns: reference to object of class T

See also: is_exactly_a<class T>()

Definition at line 978 of file ex.h.

◆ is_a

template<class T >

bool is_a ( const ex & obj )

friend

Check if ex is a handle to a T, including base classes.

Definition at line 955 of file ex.h.

◆ is_exactly_a

template<class T >

bool is_exactly_a ( const ex & obj )

friend

Check if ex is a handle to a T, not including base classes.

Definition at line 962 of file ex.h.

Member Data Documentation

◆ bp

ptr<basic> GiNaC::ex::bp

mutableprivate

pointer to basic object managed by this

Definition at line 252 of file ex.h.

Referenced by accept(), GiNaC::archive_node::archive_node(), coeff(), collect(), compare(), conjugate(), construct_from_basic(), dbgprint(), dbgprinttree(), degree(), denom(), diff(), eval(), eval_integ(), eval_ncmul(), evalf(), evalm(), ex(), ex(), ex(), ex(), ex(), ex(), ex(), ex(), ex(), ex(), expand(), get_free_indices(), gethash(), has(), GiNaC::archive_node::has_same_ex_as(), imag_part(), info(), integer_content(), is_equal(), is_polynomial(), ldegree(), let_op(), lhs(), makewriteable(), map(), match(), match(), max_coefficient(), nops(), normal(), numer(), numer_denom(), op(), operator[](), operator[](), operator[](), operator[](), print(), GiNaC::archive_node::printraw(), real_part(), return_type(), return_type_tinfo(), rhs(), series(), share(), smod(), subs(), subs(), subs(), swap(), to_polynomial(), and to_rational().

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

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ ex() [1/10]

◆ ex() [2/10]

◆ ex() [3/10]

◆ ex() [4/10]

◆ ex() [5/10]

◆ ex() [6/10]

◆ ex() [7/10]

◆ ex() [8/10]

◆ ex() [9/10]

◆ ex() [10/10]

Member Function Documentation

◆ swap()

◆ begin()

◆ end()

◆ preorder_begin()

◆ preorder_end()

◆ postorder_begin()

◆ postorder_end()

◆ eval()

◆ evalf()

◆ evalm()

◆ eval_ncmul()

◆ eval_integ()

◆ print()

◆ dbgprint()

◆ dbgprinttree()

◆ info()

◆ nops()

◆ op()

◆ operator[]() [1/4]

◆ operator[]() [2/4]

◆ let_op()

◆ operator[]() [3/4]

◆ operator[]() [4/4]

◆ lhs()

◆ rhs()

◆ conjugate()

◆ real_part()

◆ imag_part()

◆ has()

◆ find()

◆ match() [1/2]

◆ match() [2/2]

◆ subs() [1/3]

◆ subs() [2/3]

◆ subs() [3/3]

◆ map() [1/2]

◆ map() [2/2]

◆ accept()

◆ traverse_preorder()

◆ traverse_postorder()

◆ traverse()

◆ is_polynomial()

◆ degree()

◆ ldegree()

◆ coeff()

◆ lcoeff()

◆ tcoeff()

◆ expand()

◆ collect()

◆ diff()

◆ series()

◆ normal()

◆ to_rational()

◆ to_polynomial()

◆ numer()

◆ denom()

◆ numer_denom()

◆ unit()

◆ content()

◆ integer_content()

◆ primpart() [1/2]

◆ primpart() [2/2]