This class is a wrapper around CLN-numbers within the GiNaC class hierarchy. More...

#include <numeric.h>

Inheritance diagram for GiNaC::numeric:

Public Member Functions
	numeric (int i)

	numeric (unsigned int i)

	numeric (long i)

	numeric (unsigned long i)

	numeric (long long i)

	numeric (unsigned long long i)

	numeric (long numer, long denom)
	Constructor for rational numerics a/b. More...

	numeric (double d)

	numeric (const char *)
	ctor from C-style string. More...

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

bool	info (unsigned inf) const override
	Information about the object. More...

bool	is_polynomial (const ex &var) const override
	Check whether this is a polynomial in the given variables. 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	coeff (const ex &s, int n=1) const override
	Return coefficient of degree n in object s. More...

bool	has (const ex &other, unsigned options=0) const override
	Disassemble real part and imaginary part to scan for the occurrence of a single number. More...

ex	eval () const override
	Evaluation of numbers doesn't do anything at all. More...

ex	evalf () const override
	Cast numeric into a floating-point object. More...

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

ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const override
	Implementation of ex::normal() for a numeric. More...

ex	to_rational (exmap &repl) const override
	Implementation of ex::to_rational() for a numeric. More...

ex	to_polynomial (exmap &repl) const override
	Implementation of ex::to_polynomial() for a numeric. More...

numeric	integer_content () const override

ex	smod (const numeric &xi) const override
	Apply symmetric modular homomorphism to an expanded multivariate polynomial. More...

numeric	max_coefficient () const override
	Implementation ex::max_coefficient(). More...

ex	conjugate () const override

ex	real_part () const override

ex	imag_part () const override

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...

const numeric	add (const numeric &other) const
	Numerical addition method. More...

const numeric	sub (const numeric &other) const
	Numerical subtraction method. More...

const numeric	mul (const numeric &other) const
	Numerical multiplication method. More...

const numeric	div (const numeric &other) const
	Numerical division method. More...

const numeric	power (const numeric &other) const
	Numerical exponentiation. More...

const numeric &	add_dyn (const numeric &other) const
	Numerical addition method. More...

const numeric &	sub_dyn (const numeric &other) const
	Numerical subtraction method. More...

const numeric &	mul_dyn (const numeric &other) const
	Numerical multiplication method. More...

const numeric &	div_dyn (const numeric &other) const
	Numerical division method. More...

const numeric &	power_dyn (const numeric &other) const
	Numerical exponentiation. More...

const numeric &	operator= (int i)

const numeric &	operator= (unsigned int i)

const numeric &	operator= (long i)

const numeric &	operator= (unsigned long i)

const numeric &	operator= (double d)

const numeric &	operator= (const char *s)

const numeric	inverse () const
	Inverse of a number. More...

numeric	step () const
	Return the step function of a numeric. More...

int	csgn () const
	Return the complex half-plane (left or right) in which the number lies. More...

int	compare (const numeric &other) const
	This method establishes a canonical order on all numbers. More...

bool	is_equal (const numeric &other) const

bool	is_zero () const
	True if object is zero. More...

bool	is_positive () const
	True if object is not complex and greater than zero. More...

bool	is_negative () const
	True if object is not complex and less than zero. More...

bool	is_integer () const
	True if object is a non-complex integer. More...

bool	is_pos_integer () const
	True if object is an exact integer greater than zero. More...

bool	is_nonneg_integer () const
	True if object is an exact integer greater or equal zero. More...

bool	is_even () const
	True if object is an exact even integer. More...

bool	is_odd () const
	True if object is an exact odd integer. More...

bool	is_prime () const
	Probabilistic primality test. More...

bool	is_rational () const
	True if object is an exact rational number, may even be complex (denominator may be unity). More...

bool	is_real () const
	True if object is a real integer, rational or float (but not complex). More...

bool	is_cinteger () const
	True if object is element of the domain of integers extended by I, i.e. More...

bool	is_crational () const
	True if object is an exact rational number, may even be complex (denominator may be unity). More...

bool	operator== (const numeric &other) const

bool	operator!= (const numeric &other) const

bool	operator< (const numeric &other) const
	Numerical comparison: less. More...

bool	operator<= (const numeric &other) const
	Numerical comparison: less or equal. More...

bool	operator> (const numeric &other) const
	Numerical comparison: greater. More...

bool	operator>= (const numeric &other) const
	Numerical comparison: greater or equal. More...

int	to_int () const
	Converts numeric types to machine's int. More...

long	to_long () const
	Converts numeric types to machine's long. More...

double	to_double () const
	Converts numeric types to machine's double. More...

cln::cl_N	to_cl_N () const
	Returns a new CLN object of type cl_N, representing the value of *this. More...

const numeric	real () const
	Real part of a number. More...

const numeric	imag () const
	Imaginary part of a number. More...

const numeric	numer () const
	Numerator. More...

const numeric	denom () const
	Denominator. More...

int	int_length () const
	Size in binary notation. More...

	numeric (const cln::cl_N &z)
	Ctor from CLN types. More...

Public Member Functions inherited from GiNaC::basic
virtual	~basic ()
	basic destructor, virtual because class ex will delete objects of derived classes via a basic*. More...

	basic (const basic &other)

const basic &	operator= (const basic &other)
	basic assignment operator: the other object might be of a derived class. More...

virtual basic *	duplicate () const
	Create a clone of this object on the heap. More...

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

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

virtual ex	evalm () const
	Evaluate sums, products and integer powers of matrices. More...

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

virtual ex	eval_indexed (const basic &i) const
	Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression. More...

virtual void	print (const print_context &c, unsigned level=0) const
	Output to stream. More...

virtual void	dbgprint () const
	Little wrapper around print to be called within a debugger. More...

virtual void	dbgprinttree () const
	Little wrapper around printtree to be called within a debugger. More...

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

virtual bool	info (unsigned inf) const
	Information about the object. More...

virtual size_t	nops () const
	Number of operands/members. More...

virtual ex	op (size_t i) const
	Return operand/member at position i. More...

virtual ex	operator[] (const ex &index) const

virtual ex	operator[] (size_t i) const

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

virtual ex &	operator[] (const ex &index)

virtual ex &	operator[] (size_t i)

virtual bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern. More...

virtual bool	match (const ex &pattern, exmap &repls) const
	Check whether the expression matches a given pattern. More...

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

virtual ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively). More...

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

virtual bool	is_polynomial (const ex &var) const
	Check whether this is a polynomial in the given variables. More...

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

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

virtual ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s. More...

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

virtual ex	collect (const ex &s, bool distributed=false) const
	Sort expanded expression in terms of powers of some object(s). More...

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

virtual ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const
	Default implementation of ex::normal(). More...

virtual ex	to_rational (exmap &repl) const
	Default implementation of ex::to_rational(). More...

virtual ex	to_polynomial (exmap &repl) const

virtual numeric	integer_content () const

virtual ex	smod (const numeric &xi) const
	Apply symmetric modular homomorphism to an expanded multivariate polynomial. More...

virtual numeric	max_coefficient () const
	Implementation ex::max_coefficient(). More...

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

virtual ex	add_indexed (const ex &self, const ex &other) const
	Add two indexed expressions. More...

virtual ex	scalar_mul_indexed (const ex &self, const numeric &other) const
	Multiply an indexed expression with a scalar. More...

virtual bool	contract_with (exvector::iterator self, exvector::iterator other, exvector &v) const
	Try to contract two indexed expressions that appear in the same product. More...

virtual unsigned	return_type () const

virtual return_type_t	return_type_tinfo () const

virtual ex	conjugate () const

virtual ex	real_part () const

virtual ex	imag_part () const

template<class T >
void	print_dispatch (const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class. More...

void	print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class. More...

virtual void	archive (archive_node &n) const
	Save (serialize) the object into archive node. More...

virtual void	read_archive (const archive_node &n, lst &syms)
	Load (deserialize) the object from an archive node. More...

ex	subs_one_level (const exmap &m, unsigned options) const
	Helper function for subs(). More...

ex	diff (const symbol &s, unsigned nth=1) const
	Default interface of nth derivative ex::diff(s, n). More...

int	compare (const basic &other) const
	Compare objects syntactically to establish canonical ordering. More...

bool	is_equal (const basic &other) const
	Test for syntactic equality. More...

const basic &	hold () const
	Stop further evaluation. More...

unsigned	gethash () const

const basic &	setflag (unsigned f) const
	Set some status_flags. More...

const basic &	clearflag (unsigned f) const
	Clear some status_flags. More...

Public Member Functions inherited from GiNaC::refcounted
	refcounted () noexcept

unsigned int	add_reference () noexcept

unsigned int	remove_reference () noexcept

unsigned int	get_refcount () const noexcept

void	set_refcount (unsigned int r) noexcept

Protected Member Functions
ex	derivative (const symbol &s) const override
	Implementation of ex::diff for a numeric always returns 0. More...

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

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

void	print_numeric (const print_context &c, const char par_open, const char par_close, const char imag_sym, const char mul_sym, unsigned level) const

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

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

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

void	do_print_csrc_cl_N (const print_csrc_cl_N &c, unsigned level) const

void	do_print_tree (const print_tree &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
cln::cl_N	value

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

unsigned	hashvalue
	hash value More...

Detailed Description

This class is a wrapper around CLN-numbers within the GiNaC class hierarchy.

Objects of this type may directly be created by the user.

Definition at line 81 of file numeric.h.

Constructor & Destructor Documentation

◆ numeric() [1/10]

GiNaC::numeric::numeric ( int i )

Definition at line 85 of file numeric.cpp.

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

Referenced by add(), conjugate(), denom(), div(), evalf(), imag(), imag_part(), inverse(), mul(), numer(), operator=(), power(), real(), real_part(), step(), and sub().

◆ numeric() [2/10]

GiNaC::numeric::numeric ( unsigned int i )

Definition at line 106 of file numeric.cpp.

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

◆ numeric() [3/10]

GiNaC::numeric::numeric ( long i )

Definition at line 127 of file numeric.cpp.

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

◆ numeric() [4/10]

GiNaC::numeric::numeric ( unsigned long i )

Definition at line 134 of file numeric.cpp.

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

◆ numeric() [5/10]

GiNaC::numeric::numeric ( long long i )

Definition at line 140 of file numeric.cpp.

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

◆ numeric() [6/10]

GiNaC::numeric::numeric ( unsigned long long i )

Definition at line 146 of file numeric.cpp.

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

◆ numeric() [7/10]

GiNaC::numeric::numeric	(	long	numer,
		long	denom
	)

Constructor for rational numerics a/b.

Exceptions

overflow_error (division by zero)

Definition at line 155 of file numeric.cpp.

References denom(), GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, numer(), GiNaC::basic::setflag(), and value.

◆ numeric() [8/10]

GiNaC::numeric::numeric ( double d )

Definition at line 164 of file numeric.cpp.

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

◆ numeric() [9/10]

GiNaC::numeric::numeric ( const char * s )

ctor from C-style string.

It also accepts complex numbers in GiNaC notation like "2+5*I".

Definition at line 176 of file numeric.cpp.

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

◆ numeric() [10/10]

GiNaC::numeric::numeric ( const cln::cl_N & z )

explicit

Ctor from CLN types.

This is for the initiated user or internal use only.

Definition at line 255 of file numeric.cpp.

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

Member Function Documentation

◆ precedence()

unsigned GiNaC::numeric::precedence ( ) const

inlineoverridevirtual

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::basic.

Definition at line 101 of file numeric.h.

Referenced by print_numeric().

◆ info()

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

overridevirtual

Information about the object.

See also: class info_flags

Reimplemented from GiNaC::basic.

Definition at line 684 of file numeric.cpp.

Referenced by GiNaC::abs_power(), GiNaC::csgn_power(), and GiNaC::zeta1_eval().

◆ is_polynomial()

bool GiNaC::numeric::is_polynomial ( const ex & var ) const

overridevirtual

Check whether this is a polynomial in the given variables.

Reimplemented from GiNaC::basic.

Definition at line 728 of file numeric.cpp.

◆ degree()

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

overridevirtual

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 733 of file numeric.cpp.

◆ ldegree()

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

overridevirtual

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 738 of file numeric.cpp.

◆ coeff()

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

overridevirtual

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 743 of file numeric.cpp.

References GiNaC::_ex0, and n.

Referenced by GiNaC::pseries::mul_const().

◆ has()

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

overridevirtual

Disassemble real part and imaginary part to scan for the occurrence of a single number.

Also handles the imaginary unit. It ignores the sign on both this and the argument, which may lead to what might appear as funny results: (2+I).has(-2) -> true. But this is consistent, since we also would like to have (-2+I).has(2) -> true and we want to think about the sign as a multiplicative factor.

Reimplemented from GiNaC::basic.

Definition at line 754 of file numeric.cpp.

References GiNaC::_num0_p, GiNaC::I, imag(), is_equal(), is_real(), is_zero(), and real().

◆ eval()

ex GiNaC::numeric::eval ( ) const

overridevirtual

Evaluation of numbers doesn't do anything at all.

Reimplemented from GiNaC::basic.

Definition at line 783 of file numeric.cpp.

References GiNaC::basic::hold().

◆ evalf()

ex GiNaC::numeric::evalf ( ) const

overridevirtual

Cast numeric into a floating-point object.

For example exact numeric(1) is returned as a 1.0000000000000000000000 and so on according to how Digits is currently set. In case the object already was a floating point number the precision is trimmed to match the currently set default.

Returns: an ex-handle to a numeric.

Reimplemented from GiNaC::basic.

Definition at line 795 of file numeric.cpp.

References numeric(), and value.

◆ subs()

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

inlineoverridevirtual

Substitute a set of objects by arbitrary expressions.

The ex returned will already be evaluated.

Reimplemented from GiNaC::basic.

Definition at line 110 of file numeric.h.

References m, options, and GiNaC::basic::subs_one_level().

◆ normal()

ex GiNaC::numeric::normal	(	exmap &	repl,
		exmap &	rev_lookup,
		lst &	modifier
	)		const

overridevirtual

Implementation of ex::normal() for a numeric.

It splits complex numbers into re+I*im and replaces I and non-rational real numbers with a temporary symbol.

See also: ex::normal

Reimplemented from GiNaC::basic.

Definition at line 2252 of file normal.cpp.

References denom(), GiNaC::I, imag(), is_integer(), is_rational(), is_real(), numer(), real(), and GiNaC::replace_with_symbol().

◆ to_rational()

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

overridevirtual

Implementation of ex::to_rational() for a numeric.

It splits complex numbers into re+I*im and replaces I and non-rational real numbers with a temporary symbol.

Reimplemented from GiNaC::basic.

Definition at line 2668 of file normal.cpp.

References GiNaC::I, imag(), is_rational(), is_real(), real(), and GiNaC::replace_with_symbol().

◆ to_polynomial()

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

overridevirtual

Implementation of ex::to_polynomial() for a numeric.

It splits complex numbers into re+I*im and replaces I and non-integer real numbers with a temporary symbol.

Reimplemented from GiNaC::basic.

Definition at line 2686 of file normal.cpp.

References GiNaC::I, imag(), is_integer(), is_real(), real(), and GiNaC::replace_with_symbol().

◆ integer_content()

numeric GiNaC::numeric::integer_content ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 328 of file normal.cpp.

References GiNaC::abs().

◆ smod()

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

overridevirtual

Apply symmetric modular homomorphism to an expanded multivariate polynomial.

This function is usually used internally by heur_gcd().

Parameters

xi modulus

Returns: mapped polynomial

See also: heur_gcd

Reimplemented from GiNaC::basic.

Definition at line 1208 of file normal.cpp.

References GiNaC::smod().

◆ max_coefficient()

numeric GiNaC::numeric::max_coefficient ( ) const

overridevirtual

Implementation ex::max_coefficient().

See also: heur_gcd

Reimplemented from GiNaC::basic.

Definition at line 1166 of file normal.cpp.

References GiNaC::abs().

◆ conjugate()

ex GiNaC::numeric::conjugate ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 800 of file numeric.cpp.

References GiNaC::conjugate(), is_real(), numeric(), and value.

◆ real_part()

ex GiNaC::numeric::real_part ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 808 of file numeric.cpp.

References numeric(), and value.

◆ imag_part()

ex GiNaC::numeric::imag_part ( ) const

overridevirtual

Reimplemented from GiNaC::basic.

Definition at line 813 of file numeric.cpp.

References numeric(), and value.

◆ archive()

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

overridevirtual

Save (a.k.a.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 344 of file numeric.cpp.

References n, value, and GiNaC::write_real_float().

◆ read_archive()

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

overridevirtual

Read (a.k.a.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 289 of file numeric.cpp.

References c, GiNaC::status_flags::evaluated, GiNaC::status_flags::expanded, n, GiNaC::read_real_float(), GiNaC::basic::setflag(), and value.

◆ derivative()

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

inlineoverrideprotectedvirtual

Implementation of ex::diff for a numeric always returns 0.

See also: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 127 of file numeric.h.

◆ is_equal_same_type()

bool GiNaC::numeric::is_equal_same_type ( const basic & other ) const

overrideprotectedvirtual

Returns true if two objects of same type are equal.

Normally needs not be reimplemented as long as it wasn't overwritten by some parent class, since it just calls compare_same_type(). The reason why this function exists is that sometimes it is easier to determine equality than an order relation and then it can be overridden.

Reimplemented from GiNaC::basic.

Definition at line 829 of file numeric.cpp.

References GINAC_ASSERT, and is_equal().

◆ calchash()

unsigned GiNaC::numeric::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 838 of file numeric.cpp.

References GiNaC::golden_ratio_hash(), GiNaC::status_flags::hash_calculated, GiNaC::basic::hashvalue, GiNaC::basic::setflag(), and value.

◆ add()

const numeric GiNaC::numeric::add ( const numeric & other ) const

Numerical addition method.

Adds argument to *this and returns result as a numeric object.

Definition at line 864 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::operator+(), GiNaC::operator++(), GiNaC::operator+=(), and GiNaC::operator--().

◆ sub()

const numeric GiNaC::numeric::sub ( const numeric & other ) const

Numerical subtraction method.

Subtracts argument from *this and returns result as a numeric object.

Definition at line 872 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::operator-(), and GiNaC::operator-=().

◆ mul()

const numeric GiNaC::numeric::mul ( const numeric & other ) const

Numerical multiplication method.

Multiplies *this and argument and returns result as a numeric object.

Definition at line 880 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::mul::expand(), GiNaC::power::expand_add_2(), GiNaC::lcm(), GiNaC::operator*(), GiNaC::operator*=(), and GiNaC::operator-().

◆ div()

const numeric GiNaC::numeric::div ( const numeric & other ) const

Numerical division method.

Divides *this by argument and returns result as a numeric object.

Exceptions

overflow_error (division by zero)

Definition at line 890 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::multinomial_coefficient(), GiNaC::operator/(), GiNaC::operator/=(), GiNaC::basic::series(), and GiNaC::tgamma_eval().

◆ power()

const numeric GiNaC::numeric::power ( const numeric & other ) const

Numerical exponentiation.

Raises *this to the power given as argument and returns result as a numeric object.

Definition at line 900 of file numeric.cpp.

References GiNaC::_num0_p, GiNaC::_num1_p, numeric(), and value.

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

◆ add_dyn()

const numeric & GiNaC::numeric::add_dyn ( const numeric & other ) const

Numerical addition method.

Adds argument to *this and returns result as a numeric object on the heap. Use internally only for direct wrapping into an ex object, where the result would end up on the heap anyways.

Definition at line 925 of file numeric.cpp.

References GiNaC::_num0_p, and value.

◆ sub_dyn()

const numeric & GiNaC::numeric::sub_dyn ( const numeric & other ) const

Numerical subtraction method.

Subtracts argument from *this and returns result as a numeric object on the heap. Use internally only for direct wrapping into an ex object, where the result would end up on the heap anyways.

Definition at line 942 of file numeric.cpp.

References GiNaC::_num0_p, and value.

◆ mul_dyn()

const numeric & GiNaC::numeric::mul_dyn ( const numeric & other ) const

Numerical multiplication method.

Multiplies *this and argument and returns result as a numeric object on the heap. Use internally only for direct wrapping into an ex object, where the result would end up on the heap anyways.

Definition at line 957 of file numeric.cpp.

References GiNaC::_num1_p, and value.

Referenced by GiNaC::power::expand_add_2().

◆ div_dyn()

const numeric & GiNaC::numeric::div_dyn ( const numeric & other ) const

Numerical division method.

Divides *this by argument and returns result as a numeric object on the heap. Use internally only for direct wrapping into an ex object, where the result would end up on the heap anyways.

Exceptions

overflow_error (division by zero)

Definition at line 976 of file numeric.cpp.

References GiNaC::_num1_p, and value.

◆ power_dyn()

const numeric & GiNaC::numeric::power_dyn ( const numeric & other ) const

Numerical exponentiation.

Raises *this to the power given as argument and returns result as a numeric object on the heap. Use internally only for direct wrapping into an ex object, where the result would end up on the heap anyways.

Definition at line 993 of file numeric.cpp.

References GiNaC::_num0_p, GiNaC::_num1_p, and value.

◆ operator=() [1/6]

const numeric & GiNaC::numeric::operator= ( int i )

Definition at line 1016 of file numeric.cpp.

References numeric(), and operator=().

Referenced by operator=().

◆ operator=() [2/6]

const numeric & GiNaC::numeric::operator= ( unsigned int i )

Definition at line 1022 of file numeric.cpp.

References numeric(), and operator=().

◆ operator=() [3/6]

const numeric & GiNaC::numeric::operator= ( long i )

Definition at line 1028 of file numeric.cpp.

References numeric(), and operator=().

◆ operator=() [4/6]

const numeric & GiNaC::numeric::operator= ( unsigned long i )

Definition at line 1034 of file numeric.cpp.

References numeric(), and operator=().

◆ operator=() [5/6]

const numeric & GiNaC::numeric::operator= ( double d )

Definition at line 1040 of file numeric.cpp.

References numeric(), and operator=().

◆ operator=() [6/6]

const numeric & GiNaC::numeric::operator= ( const char * s )

Definition at line 1046 of file numeric.cpp.

References numeric(), and operator=().

◆ inverse()

const numeric GiNaC::numeric::inverse ( ) const

Inverse of a number.

Definition at line 1053 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::divide_in_z(), GiNaC::power::eval(), GiNaC::heur_gcd_z(), GiNaC::interpolate(), and GiNaC::psi1_eval().

◆ step()

numeric GiNaC::numeric::step ( ) const

Return the step function of a numeric.

The imaginary part of it is ignored because the step function is generally considered real but a numeric may develop a small imaginary part due to rounding errors.

Definition at line 1064 of file numeric.cpp.

References numeric(), r, and value.

◆ csgn()

int GiNaC::numeric::csgn ( ) const

Return the complex half-plane (left or right) in which the number lies.

csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0, csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.

See also: numeric::compare(const numeric &other)

Definition at line 1078 of file numeric.cpp.

References r, and value.

◆ compare()

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

This method establishes a canonical order on all numbers.

For complex numbers this is not possible in a mathematically consistent way but we need to establish some order and it ought to be fast. So we simply define it to be compatible with our method csgn.

Returns: csgn(*this-other)

See also: numeric::csgn()

Definition at line 1104 of file numeric.cpp.

References value.

Referenced by GiNaC::power::eval().

◆ is_equal()

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

Definition at line 1122 of file numeric.cpp.

References value.

Referenced by GiNaC::atan(), GiNaC::cos_eval(), GiNaC::power::eval(), GiNaC::exp_eval(), has(), is_equal_same_type(), GiNaC::psi2_eval(), GiNaC::sin_eval(), GiNaC::tan_eval(), and GiNaC::zeta1_eval().

◆ is_zero()

bool GiNaC::numeric::is_zero ( ) const

True if object is zero.

Definition at line 1129 of file numeric.cpp.

References value.

Referenced by GiNaC::asinh_conjugate(), GiNaC::atan(), GiNaC::atan_conjugate(), GiNaC::expairseq::construct_from_2_expairseq(), GiNaC::expairseq::construct_from_expairseq_ex(), GiNaC::csgn_eval(), GiNaC::power::eval(), GiNaC::fsolve(), GiNaC::gcd(), has(), info(), GiNaC::iquo(), GiNaC::irem(), GiNaC::matrix::pivot(), GiNaC::matrix::pow(), GiNaC::pseries::power_const(), GiNaC::step_eval(), and GiNaC::zeta1_eval().

◆ is_positive()

bool GiNaC::numeric::is_positive ( ) const

True if object is not complex and greater than zero.

Definition at line 1136 of file numeric.cpp.

References value.

Referenced by GiNaC::power::eval(), info(), GiNaC::psi1_eval(), GiNaC::psi2_eval(), and GiNaC::tgamma_eval().

◆ is_negative()

bool GiNaC::numeric::is_negative ( ) const

True if object is not complex and less than zero.

Definition at line 1145 of file numeric.cpp.

References value.

Referenced by GiNaC::bernoulli(), GiNaC::beta_eval(), GiNaC::eta_eval(), GiNaC::eta_evalf(), info(), and GiNaC::pseries::power_const().

◆ is_integer()

bool GiNaC::numeric::is_integer ( ) const

True if object is a non-complex integer.

Definition at line 1154 of file numeric.cpp.

References value.

Referenced by GiNaC::bernoulli(), GiNaC::beta_eval(), GiNaC::binomial_sym(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::gcd(), info(), GiNaC::iquo(), GiNaC::irem(), GiNaC::lcm(), GiNaC::mod(), normal(), GiNaC::psi1_eval(), GiNaC::psi2_eval(), GiNaC::smod(), GiNaC::tgamma_eval(), to_int(), to_long(), to_polynomial(), and GiNaC::zeta1_eval().

◆ is_pos_integer()

bool GiNaC::numeric::is_pos_integer ( ) const

True if object is an exact integer greater than zero.

Definition at line 1161 of file numeric.cpp.

References value.

Referenced by GiNaC::mul::eval(), GiNaC::power::eval(), info(), and GiNaC::pseries::power_const().

◆ is_nonneg_integer()

bool GiNaC::numeric::is_nonneg_integer ( ) const

True if object is an exact integer greater or equal zero.

Definition at line 1168 of file numeric.cpp.

References value.

Referenced by GiNaC::binomial_sym(), info(), and print_numeric().

◆ is_even()

bool GiNaC::numeric::is_even ( ) const

True if object is an exact even integer.

Definition at line 1175 of file numeric.cpp.

References value.

Referenced by info(), GiNaC::kronecker_symbol(), and GiNaC::tgamma_eval().

◆ is_odd()

bool GiNaC::numeric::is_odd ( ) const

True if object is an exact odd integer.

Definition at line 1182 of file numeric.cpp.

References value.

Referenced by info(), GiNaC::is_discriminant_of_quadratic_number_field(), and GiNaC::matrix::pow().

◆ is_prime()

bool GiNaC::numeric::is_prime ( ) const

Probabilistic primality test.

Returns: true if object is exact integer and prime.

Definition at line 1191 of file numeric.cpp.

References value.

Referenced by info().

◆ is_rational()

bool GiNaC::numeric::is_rational ( ) const

True if object is an exact rational number, may even be complex (denominator may be unity).

Definition at line 1201 of file numeric.cpp.

References value.

Referenced by GiNaC::power::eval(), info(), GiNaC::multiply_lcm(), normal(), and to_rational().

◆ is_real()

bool GiNaC::numeric::is_real ( ) const

True if object is a real integer, rational or float (but not complex).

Definition at line 1208 of file numeric.cpp.

References value.

Referenced by GiNaC::atan(), GiNaC::beta_eval(), conjugate(), GiNaC::csgn_eval(), denom(), do_print_csrc(), do_print_csrc_cl_N(), GiNaC::eta_eval(), GiNaC::eta_evalf(), GiNaC::power::eval(), GiNaC::fsolve(), has(), info(), is_cinteger(), is_crational(), normal(), numer(), operator<(), operator<=(), operator>(), operator>=(), GiNaC::step_eval(), to_double(), to_polynomial(), and to_rational().

◆ is_cinteger()

bool GiNaC::numeric::is_cinteger ( ) const

True if object is element of the domain of integers extended by I, i.e.

is of the form a+b*I, where a and b are integers.

Definition at line 1228 of file numeric.cpp.

References is_real(), and value.

Referenced by info().

◆ is_crational()

bool GiNaC::numeric::is_crational ( ) const

True if object is an exact rational number, may even be complex (denominator may be unity).

Definition at line 1243 of file numeric.cpp.

References is_real(), and value.

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

◆ operator==()

bool GiNaC::numeric::operator== ( const numeric & other ) const

Definition at line 1214 of file numeric.cpp.

References value.

◆ operator!=()

bool GiNaC::numeric::operator!= ( const numeric & other ) const

Definition at line 1220 of file numeric.cpp.

References value.

◆ operator<()

bool GiNaC::numeric::operator< ( const numeric & other ) const

Numerical comparison: less.

Exceptions

invalid_argument (complex inequality)

Definition at line 1259 of file numeric.cpp.

References is_real(), and value.

◆ operator<=()

bool GiNaC::numeric::operator<= ( const numeric & other ) const

Numerical comparison: less or equal.

Exceptions

invalid_argument (complex inequality)

Definition at line 1270 of file numeric.cpp.

References is_real(), and value.

◆ operator>()

bool GiNaC::numeric::operator> ( const numeric & other ) const

Numerical comparison: greater.

Exceptions

invalid_argument (complex inequality)

Definition at line 1281 of file numeric.cpp.

References is_real(), and value.

◆ operator>=()

bool GiNaC::numeric::operator>= ( const numeric & other ) const

Numerical comparison: greater or equal.

Exceptions

invalid_argument (complex inequality)

Definition at line 1292 of file numeric.cpp.

References is_real(), and value.

◆ to_int()

int GiNaC::numeric::to_int ( ) const

Converts numeric types to machine's int.

You should check with is_integer() if the number is really an integer before calling this method. You may also consider checking the range first.

Definition at line 1303 of file numeric.cpp.

References GINAC_ASSERT, is_integer(), and value.

Referenced by GiNaC::bernoulli(), GiNaC::binomial_sym(), GiNaC::power::do_print_csrc(), GiNaC::power::eval(), GiNaC::power::expand(), GiNaC::Li_eval(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), and GiNaC::Kronecker_dz_kernel::series_coeff_impl().

◆ to_long()

long GiNaC::numeric::to_long ( ) const

Converts numeric types to machine's long.

You should check with is_integer() if the number is really an integer before calling this method. You may also consider checking the range first.

Definition at line 1313 of file numeric.cpp.

References GINAC_ASSERT, is_integer(), and value.

Referenced by GiNaC::power::expand(), and GiNaC::power::expand_add().

◆ to_double()

double GiNaC::numeric::to_double ( ) const

Converts numeric types to machine's double.

You should check with is_real() if the number is really not complex before calling this method.

Definition at line 1322 of file numeric.cpp.

References GINAC_ASSERT, is_real(), and value.

◆ to_cl_N()

cln::cl_N GiNaC::numeric::to_cl_N ( ) const

Returns a new CLN object of type cl_N, representing the value of *this.

This method may be used when mixing GiNaC and CLN in one project.

Definition at line 1332 of file numeric.cpp.

References value.

Referenced by GiNaC::atan(), GiNaC::gcd(), GiNaC::iquo(), GiNaC::irem(), GiNaC::lcm(), GiNaC::mod(), GiNaC::Kronecker_dtau_kernel::series_coeff_impl(), and GiNaC::smod().

◆ real()

const numeric GiNaC::numeric::real ( ) const

Real part of a number.

Definition at line 1339 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::csgn_eval(), GiNaC::power::eval(), has(), normal(), GiNaC::pseries::power_const(), GiNaC::step_eval(), to_polynomial(), and to_rational().

◆ imag()

const numeric GiNaC::numeric::imag ( ) const

Imaginary part of a number.

Definition at line 1346 of file numeric.cpp.

References numeric(), and value.

Referenced by GiNaC::csgn_eval(), has(), normal(), GiNaC::step_eval(), to_polynomial(), and to_rational().

◆ numer()

const numeric GiNaC::numeric::numer ( ) const

Numerator.

Computes the numerator of rational numbers, rationalized numerator of complex if real and imaginary part are both rational numbers (i.e numer(4/3+5/6*I) == 8+5*I), the number carrying the sign in all other cases.

Definition at line 1356 of file numeric.cpp.

References is_real(), GiNaC::lcm(), numeric(), r, and value.

Referenced by GiNaC::power::eval(), GiNaC::frac_cancel(), normal(), and numeric().

◆ denom()

const numeric GiNaC::numeric::denom ( ) const

Denominator.

Computes the denominator of rational numbers, common integer denominator of complex if real and imaginary part are both rational numbers (i.e denom(4/3+5/6*I) == 6), one in all other cases.

Definition at line 1387 of file numeric.cpp.

References GiNaC::_num1_p, is_real(), GiNaC::lcm(), numeric(), r, and value.

Referenced by GiNaC::power::eval(), GiNaC::frac_cancel(), normal(), and numeric().

◆ int_length()

int GiNaC::numeric::int_length ( ) const

Size in binary notation.

For integers, this is the smallest n >= 0 such that -2^n <= x < 2^n. If x > 0, this is the unique n > 0 such that 2^(n-1) <= x < 2^n.

Returns: number of bits (excluding sign) needed to represent that number in two's complement if it is an integer, 0 otherwise.

Definition at line 1418 of file numeric.cpp.

References value.

Referenced by GiNaC::heur_gcd_z().

◆ print_numeric()

void GiNaC::numeric::print_numeric	(	const print_context &	c,
		const char *	par_open,
		const char *	par_close,
		const char *	imag_sym,
		const char *	mul_sym,
		unsigned	level
	)		const

protected

Definition at line 542 of file numeric.cpp.

References c, is_nonneg_integer(), precedence(), GiNaC::print_real_number(), r, GiNaC::print_context::s, and value.

Referenced by do_print(), do_print_latex(), and do_print_python_repr().

◆ do_print()

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

protected

Definition at line 605 of file numeric.cpp.

References c, and print_numeric().

◆ do_print_latex()

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

protected

Definition at line 610 of file numeric.cpp.

References c, and print_numeric().

◆ do_print_csrc()

void GiNaC::numeric::do_print_csrc	(	const print_csrc &	c,
		unsigned	level
	)		const

protected

Definition at line 615 of file numeric.cpp.

References c, is_real(), GiNaC::print_real_csrc(), and value.

◆ do_print_csrc_cl_N()

void GiNaC::numeric::do_print_csrc_cl_N	(	const print_csrc_cl_N &	c,
		unsigned	level
	)		const

protected

Definition at line 651 of file numeric.cpp.

References c, is_real(), GiNaC::print_real_cl_N(), and value.

◆ do_print_tree()

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

protected

Definition at line 669 of file numeric.cpp.

References c, GiNaC::basic::flags, GiNaC::basic::hashvalue, and value.

◆ do_print_python_repr()

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

protected

Definition at line 677 of file numeric.cpp.

References c, and print_numeric().

Member Data Documentation

◆ value

cln::cl_N GiNaC::numeric::value

protected

Definition at line 200 of file numeric.h.

Referenced by add(), add_dyn(), archive(), calchash(), compare(), conjugate(), csgn(), denom(), div(), div_dyn(), do_print_csrc(), do_print_csrc_cl_N(), do_print_tree(), evalf(), GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(), imag(), imag_part(), int_length(), inverse(), is_cinteger(), is_crational(), is_equal(), is_even(), is_integer(), is_negative(), is_nonneg_integer(), is_odd(), is_pos_integer(), is_positive(), is_prime(), is_rational(), is_real(), is_zero(), mul(), mul_dyn(), numer(), numeric(), operator!=(), operator<(), operator<=(), operator==(), operator>(), operator>=(), power(), power_dyn(), print_numeric(), read_archive(), real(), real_part(), step(), sub(), sub_dyn(), to_cl_N(), to_double(), to_int(), and to_long().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ numeric() [1/10]

◆ numeric() [2/10]

◆ numeric() [3/10]

◆ numeric() [4/10]

◆ numeric() [5/10]

◆ numeric() [6/10]

◆ numeric() [7/10]

◆ numeric() [8/10]

◆ numeric() [9/10]

◆ numeric() [10/10]

Member Function Documentation

◆ precedence()

◆ info()

◆ is_polynomial()

◆ degree()

◆ ldegree()

◆ coeff()

◆ has()

◆ eval()

◆ evalf()

◆ subs()

◆ normal()

◆ to_rational()

◆ to_polynomial()

◆ integer_content()

◆ smod()

◆ max_coefficient()

◆ conjugate()

◆ real_part()

◆ imag_part()

◆ archive()

◆ read_archive()

◆ derivative()

◆ is_equal_same_type()

◆ calchash()

◆ add()

◆ sub()

◆ mul()

◆ div()

◆ power()

◆ add_dyn()

◆ sub_dyn()

◆ mul_dyn()

◆ div_dyn()

◆ power_dyn()

◆ operator=() [1/6]

◆ operator=() [2/6]

◆ operator=() [3/6]

◆ operator=() [4/6]

◆ operator=() [5/6]

◆ operator=() [6/6]

◆ inverse()

◆ step()

◆ csgn()

◆ compare()

◆ is_equal()

◆ is_zero()

◆ is_positive()

◆ is_negative()

◆ is_integer()

◆ is_pos_integer()

◆ is_nonneg_integer()

◆ is_even()

◆ is_odd()

◆ is_prime()

◆ is_rational()

◆ is_real()

◆ is_cinteger()

◆ is_crational()

◆ operator==()

◆ operator!=()

◆ operator<()

◆ operator<=()

◆ operator>()

◆ operator>=()