Symbolic integral. More...

#include <integral.h>

Inheritance diagram for GiNaC::integral:

Public Member Functions
	integral (const ex &x_, const ex &a_, const ex &b_, const ex &f_)

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

ex	eval () const override
	Perform automatic non-interruptive term rewriting rules. More...

ex	evalf () const override
	Evaluate object numerically. More...

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

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

ex	eval_ncmul (const exvector &v) const override

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

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

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

unsigned	return_type () const override

return_type_t	return_type_tinfo () const override

ex	conjugate () const override

ex	eval_integ () const override
	Evaluate integrals, if result is known. 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...

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

Static Public Attributes
static int	max_integration_level = 15

static ex	relative_integration_error = 1e-8

Protected Member Functions
ex	derivative (const symbol &s) const override
	Default implementation of ex::diff(). More...

ex	series (const relational &r, int order, unsigned options=0) const override
	Default implementation of ex::series(). More...

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

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

Protected Member Functions inherited from GiNaC::basic
	basic ()

virtual ex	eval_ncmul (const exvector &v) const

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

virtual ex	derivative (const symbol &s) const
	Default implementation of ex::diff(). More...

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

virtual bool	is_equal_same_type (const basic &other) const
	Returns true if two objects of same type are equal. More...

virtual unsigned	calchash () const
	Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so. More...

void	ensure_if_modifiable () const
	Ensure the object may be modified without hurting others, throws if this is not the case. More...

void	do_print (const print_context &c, unsigned level) const
	Default output to stream. More...

void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream. More...

void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream. More...

Private Attributes
ex	x

ex	a

ex	b

ex	f

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

unsigned	hashvalue
	hash value More...

Detailed Description

Symbolic integral.

Definition at line 33 of file integral.h.

Constructor & Destructor Documentation

◆ integral()

GiNaC::integral::integral	(	const ex &	x_,
		const ex &	a_,
		const ex &	b_,
		const ex &	f_
	)

Definition at line 61 of file integral.cpp.

References x.

Referenced by derivative(), expand(), and series().

Member Function Documentation

◆ precedence()

unsigned GiNaC::integral::precedence ( ) const

inlineoverridevirtual

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::basic.

Definition at line 43 of file integral.h.

Referenced by do_print_latex().

◆ eval()

ex GiNaC::integral::eval ( ) const

overridevirtual

Perform automatic non-interruptive term rewriting rules.

Reimplemented from GiNaC::basic.

Definition at line 144 of file integral.cpp.

References GiNaC::_ex0, a, b, GiNaC::status_flags::evaluated, f, GiNaC::basic::flags, GiNaC::ex::has(), GiNaC::haswild(), GiNaC::basic::hold(), and x.

◆ evalf()

ex GiNaC::integral::evalf ( ) const

overridevirtual

Evaluate object numerically.

Reimplemented from GiNaC::basic.

Definition at line 158 of file integral.cpp.

References a, GiNaC::adaptivesimpson(), GiNaC::are_ex_trivially_equal(), b, GiNaC::ex::evalf(), f, GiNaC::ex::subs(), and x.

◆ degree()

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

overridevirtual

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 302 of file integral.cpp.

References a, b, and f.

◆ ldegree()

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

overridevirtual

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 307 of file integral.cpp.

References a, b, and f.

◆ eval_ncmul()

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

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 312 of file integral.cpp.

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

◆ nops()

size_t GiNaC::integral::nops ( ) const

overridevirtual

Number of operands/members.

Reimplemented from GiNaC::basic.

Definition at line 317 of file integral.cpp.

◆ op()

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

overridevirtual

Return operand/member at position i.

Reimplemented from GiNaC::basic.

Definition at line 322 of file integral.cpp.

References a, b, f, GINAC_ASSERT, and x.

◆ let_op()

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

overridevirtual

Return modifiable operand/member at position i.

Reimplemented from GiNaC::basic.

Definition at line 340 of file integral.cpp.

References a, b, GiNaC::basic::ensure_if_modifiable(), f, and x.

◆ expand()

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

overridevirtual

Expand expression, i.e.

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

Reimplemented from GiNaC::basic.

Definition at line 357 of file integral.cpp.

References a, GiNaC::are_ex_trivially_equal(), b, GiNaC::basic::ex, GiNaC::ex::expand(), expand(), GiNaC::status_flags::expanded, f, GiNaC::basic::flags, GiNaC::ex::has(), integral(), GiNaC::ex::nops(), GiNaC::ex::op(), options, GiNaC::basic::setflag(), and x.

Referenced by eval_integ(), and expand().

◆ get_free_indices()

exvector GiNaC::integral::get_free_indices ( ) const

overridevirtual

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 516 of file indexed.cpp.

References a, b, f, and GiNaC::ex::get_free_indices().

◆ return_type()

unsigned GiNaC::integral::return_type ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 406 of file integral.cpp.

References f, and GiNaC::ex::return_type().

◆ return_type_tinfo()

return_type_t GiNaC::integral::return_type_tinfo ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 411 of file integral.cpp.

References f, and GiNaC::ex::return_type_tinfo().

◆ conjugate()

ex GiNaC::integral::conjugate ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 416 of file integral.cpp.

References a, GiNaC::are_ex_trivially_equal(), b, GiNaC::ex::conjugate(), f, GiNaC::ex::subs(), and x.

◆ eval_integ()

ex GiNaC::integral::eval_integ ( ) const

overridevirtual

Evaluate integrals, if result is known.

Reimplemented from GiNaC::basic.

Definition at line 429 of file integral.cpp.

References a, b, GiNaC::ex::eval_integ(), expand(), GiNaC::status_flags::expanded, f, GiNaC::basic::flags, GiNaC::ex::has(), GiNaC::log(), GiNaC::ex::op(), GiNaC::ex::subs(), and x.

◆ archive()

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

overridevirtual

Save (a.k.a.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 82 of file integral.cpp.

References a, b, f, n, and x.

◆ read_archive()

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

overridevirtual

Read (a.k.a.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 73 of file integral.cpp.

References a, b, f, n, and x.

◆ derivative()

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

overrideprotectedvirtual

Default implementation of ex::diff().

It maps the operation on the operands (or returns 0 when the object has no operands).

See also: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 399 of file integral.cpp.

References a, b, GiNaC::ex::diff(), f, integral(), GiNaC::ex::subs(), and x.

◆ series()

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

overrideprotectedvirtual

Default implementation of ex::series().

This performs Taylor expansion.

See also: ex::series

Reimplemented from GiNaC::basic.

Definition at line 1207 of file pseries.cpp.

References GiNaC::_ex1, a, b, f, integral(), GiNaC::is_order_function(), GiNaC::ex::nops(), options, order, r, GiNaC::ex::series(), series(), GiNaC::ex::subs(), and x.

Referenced by series().

◆ do_print()

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

protected

Definition at line 95 of file integral.cpp.

References a, b, c, f, GiNaC::ex::print(), and x.

◆ do_print_latex()

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

protected

Definition at line 108 of file integral.cpp.

References a, b, c, f, precedence(), GiNaC::ex::print(), and x.

Member Data Documentation

◆ max_integration_level

int GiNaC::integral::max_integration_level = 15

static

Definition at line 74 of file integral.h.

Referenced by GiNaC::adaptivesimpson().

◆ relative_integration_error

ex GiNaC::integral::relative_integration_error = 1e-8

static

Definition at line 75 of file integral.h.

◆ x

ex GiNaC::integral::x

private

Definition at line 77 of file integral.h.

Referenced by archive(), conjugate(), derivative(), do_print(), do_print_latex(), eval(), eval_integ(), evalf(), expand(), integral(), let_op(), op(), read_archive(), and series().

◆ a

ex GiNaC::integral::a

private

Definition at line 78 of file integral.h.

Referenced by archive(), conjugate(), degree(), derivative(), do_print(), do_print_latex(), eval(), eval_integ(), evalf(), expand(), get_free_indices(), ldegree(), let_op(), op(), read_archive(), and series().

◆ b

ex GiNaC::integral::b

private

Definition at line 79 of file integral.h.

Referenced by archive(), conjugate(), degree(), derivative(), do_print(), do_print_latex(), eval(), eval_integ(), evalf(), expand(), get_free_indices(), ldegree(), let_op(), op(), read_archive(), and series().

◆ f

ex GiNaC::integral::f

private

Definition at line 80 of file integral.h.

Referenced by archive(), conjugate(), degree(), derivative(), do_print(), do_print_latex(), eval(), eval_integ(), eval_ncmul(), evalf(), expand(), get_free_indices(), ldegree(), let_op(), op(), read_archive(), return_type(), return_type_tinfo(), and series().

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

Public Member Functions

Static Public Attributes

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ integral()

Member Function Documentation

◆ precedence()

◆ eval()

◆ evalf()

◆ degree()

◆ ldegree()

◆ eval_ncmul()

◆ nops()

◆ op()

◆ let_op()

◆ expand()

◆ get_free_indices()

◆ return_type()

◆ return_type_tinfo()

◆ conjugate()

◆ eval_integ()

◆ archive()

◆ read_archive()

◆ derivative()

◆ series()

◆ do_print()

◆ do_print_latex()

Member Data Documentation

◆ max_integration_level

◆ relative_integration_error

◆ x

◆ a

◆ b

◆ f