This class holds a two-component object, a basis and and exponent representing exponentiation. More...

#include <power.h>

Inheritance diagram for GiNaC::power:

Public Member Functions
	power (const ex &lh, const ex &rh)
template<typename T >
	power (const ex &lh, const T &rh)
unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
bool	info (unsigned inf) const
	Information about the object.
size_t	nops () const
	Number of operands/members.
ex	op (size_t i) const
	Return operand/member at position i.
ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively).
bool	is_polynomial (const ex &var) const
	Check whether this is a polynomial in the given variables.
int	degree (const ex &s) const
	Return degree of highest power in object s.
int	ldegree (const ex &s) const
	Return degree of lowest power in object s.
ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s.
ex	eval (int level=0) const
	Perform automatic term rewriting rules in this class.
ex	evalf (int level=0) const
	Evaluate object numerically.
ex	evalm () const
	Evaluate sums, products and integer powers of matrices.
ex	series (const relational &s, int order, unsigned options=0) const
	Implementation of ex::series() for powers.
ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions.
bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern.
ex	normal (exmap &repl, exmap &rev_lookup, int level=0) const
	Implementation of ex::normal([B) for powers.
ex	to_rational (exmap &repl) const
	Implementation of ex::to_rational() for powers.
ex	to_polynomial (exmap &repl) const
	Implementation of ex::to_polynomial() for powers.
ex	conjugate () const
ex	real_part () const
ex	imag_part () const
void	archive (archive_node &n) const
	Save (a.k.a.
void	read_archive (const archive_node &n, lst &syms)
	Read (a.k.a.
Protected Member Functions
ex	derivative (const symbol &s) const
	Implementation of ex::diff() for a power.
ex	eval_ncmul (const exvector &v) const
unsigned	return_type () const
return_type_t	return_type_tinfo () const
ex	expand (unsigned options=0) const
	Expand expression, i.e.
void	print_power (const print_context &c, const char powersymbol, const char openbrace, const char *closebrace, unsigned level) const
void	do_print_dflt (const print_dflt &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_python (const print_python &c, unsigned level) const
void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream.
void	do_print_csrc_cl_N (const print_csrc_cl_N &c, unsigned level) const
ex	expand_add (const add &a, int n, unsigned options) const
	expand a^n where a is an add and n is a positive integer.
ex	expand_add_2 (const add &a, unsigned options) const
	Special case of power::expand_add.
ex	expand_mul (const mul &m, const numeric &n, unsigned options, bool from_expand=false) const
	Expand factors of m in m^n where m is a mul and n is an integer.
Protected Attributes
ex	basis
ex	exponent
Friends
class	mul

Detailed Description

This class holds a two-component object, a basis and and exponent representing exponentiation.

Definition at line 38 of file power.h.

Constructor & Destructor Documentation

GiNaC::power::power	(	const ex &	lh,
		const ex &	rh
	)		`[inline]`

Definition at line 48 of file power.h.

Referenced by conjugate(), derivative(), do_print_latex(), eval(), evalf(), evalm(), expand(), expand_add(), expand_add_2(), imag_part(), map(), normal(), real_part(), subs(), to_polynomial(), and to_rational().

template<typename T >

GiNaC::power::power	(	const ex &	lh,
		const T &	rh
	)		`[inline]`

Definition at line 49 of file power.h.

Member Function Documentation

unsigned GiNaC::power::precedence ( ) const [inline, virtual]

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::basic.

Definition at line 53 of file power.h.

Referenced by print_power().

bool GiNaC::power::info ( unsigned inf ) const [virtual]

Information about the object.

See also:: class info_flags

Reimplemented from GiNaC::basic.

Definition at line 225 of file power.cpp.

size_t GiNaC::power::nops ( ) const [virtual]

Number of operands/members.

Reimplemented from GiNaC::basic.

Definition at line 264 of file power.cpp.

ex GiNaC::power::op ( size_t i ) const [virtual]

Return operand/member at position i.

Reimplemented from GiNaC::basic.

Definition at line 269 of file power.cpp.

References basis, exponent, and GINAC_ASSERT.

ex GiNaC::power::map ( map_function & f ) const [virtual]

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

Reimplemented from GiNaC::basic.

Definition at line 276 of file power.cpp.

References GiNaC::are_ex_trivially_equal(), basis, GiNaC::status_flags::dynallocated, exponent, and power().

bool GiNaC::power::is_polynomial ( const ex & var ) const [virtual]

Check whether this is a polynomial in the given variables.

Reimplemented from GiNaC::basic.

Definition at line 288 of file power.cpp.

References basis, exponent, GiNaC::ex::has(), GiNaC::ex::info(), GiNaC::ex::is_polynomial(), and GiNaC::info_flags::nonnegint.

int GiNaC::power::degree ( const ex & s ) const [virtual]

Return degree of highest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 297 of file power.cpp.

References basis, GiNaC::ex::degree(), exponent, GiNaC::ex::has(), GiNaC::ex::is_equal(), GiNaC::basic::is_equal(), GiNaC::is_integer(), and GiNaC::to_int().

int GiNaC::power::ldegree ( const ex & s ) const [virtual]

Return degree of lowest power in object s.

Reimplemented from GiNaC::basic.

Definition at line 312 of file power.cpp.

References basis, exponent, GiNaC::ex::has(), GiNaC::ex::is_equal(), GiNaC::basic::is_equal(), GiNaC::is_integer(), GiNaC::ex::ldegree(), and GiNaC::to_int().

ex GiNaC::power::coeff	(	const ex &	s,
		int	n = `1`
	)		const `[virtual]`

Return coefficient of degree n in object s.

Reimplemented from GiNaC::basic.

Definition at line 327 of file power.cpp.

References GiNaC::_ex0, GiNaC::_ex1, basis, exponent, GiNaC::ex::is_equal(), GiNaC::basic::is_equal(), GiNaC::is_integer(), and GiNaC::to_int().

ex GiNaC::power::eval ( int level = 0 ) const [virtual]

Perform automatic term rewriting rules in this class.

In the following x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2... stand for such expressions that contain a plain number.

^(x,0) -> 1 (also handles ^(0,0))
^(x,1) -> x
^(0,c) -> 0 or exception (depending on the real part of c)
^(1,x) -> 1
^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
^(^(x,c1),c2) -> ^(x,c1*c2) if x is positive and c1 is real.
^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)

Parameters:

level cut-off in recursive evaluation

Reimplemented from GiNaC::basic.

Definition at line 371 of file power.cpp.

ex GiNaC::power::evalf ( int level = 0 ) const [virtual]

Evaluate object numerically.

Reimplemented from GiNaC::basic.

Definition at line 579 of file power.cpp.

References basis, GiNaC::ex::evalf(), exponent, GiNaC::max_recursion_level, and power().

ex GiNaC::power::evalm ( ) const [virtual]

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 600 of file power.cpp.

References basis, GiNaC::status_flags::dynallocated, GiNaC::ex::evalm(), exponent, GiNaC::pow(), and power().

ex GiNaC::power::series	(	const relational &	r,
		int	order,
		unsigned	options = `0`
	)		const `[virtual]`

Implementation of ex::series() for powers.

This performs Laurent expansion of reciprocals of series at singularities.

See also:: ex::series

Reimplemented from GiNaC::basic.

Definition at line 1103 of file pseries.cpp.

References GiNaC::_ex1, basis, GiNaC::exp(), GiNaC::ex::expand(), exponent, GiNaC::ex::info(), GiNaC::ex::is_equal(), GiNaC::is_integer(), GiNaC::ex::is_zero(), GiNaC::ex::ldegree(), GiNaC::relational::lhs(), GiNaC::log(), GiNaC::info_flags::negint, GiNaC::subs_options::no_pattern, GiNaC::info_flags::rational_function, GiNaC::relational::rhs(), GiNaC::ex::series(), GiNaC::basic::series(), GiNaC::ex::subs(), and GiNaC::to_int().

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

Substitute a set of objects by arbitrary expressions.

The ex returned will already be evaluated.

Reimplemented from GiNaC::basic.

Definition at line 639 of file power.cpp.

References GiNaC::subs_options::algebraic, GiNaC::are_ex_trivially_equal(), basis, exponent, GiNaC::subs_options::no_pattern, power(), GiNaC::ex::subs(), GiNaC::basic::subs_one_level(), and GiNaC::tryfactsubs().

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

Test for occurrence of a pattern.

An object 'has' a pattern if it matches the pattern itself or one of the children 'has' it. As a consequence (according to the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y) is false.

Reimplemented from GiNaC::basic.

Definition at line 612 of file power.cpp.

References GiNaC::has_options::algebraic, basis, exponent, GiNaC::basic::has(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::match(), GiNaC::info_flags::negint, GiNaC::ex::op(), GiNaC::info_flags::posint, and GiNaC::to_int().

ex GiNaC::power::normal	(	exmap &	repl,
		exmap &	rev_lookup,
		int	level = `0`
	)		const `[virtual]`

Implementation of ex::normal([B) for powers.

It normalizes the basis, distributes integer exponents to numerator and denominator, and replaces non-integer powers by temporary symbols.

See also:: ex::normal

Reimplemented from GiNaC::basic.

Definition at line 2260 of file normal.cpp.

References GiNaC::_ex1, basis, GiNaC::status_flags::dynallocated, exponent, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::ex::is_equal(), GiNaC::max_recursion_level, GiNaC::info_flags::negative, GiNaC::ex::op(), GiNaC::info_flags::positive, power(), GiNaC::replace_with_symbol(), and GiNaC::basic::setflag().

ex GiNaC::power::to_rational ( exmap & repl ) const [virtual]

Implementation of ex::to_rational() for powers.

It replaces non-integer powers by temporary symbols.

Reimplemented from GiNaC::basic.

Definition at line 2544 of file normal.cpp.

References basis, exponent, GiNaC::ex::info(), GiNaC::info_flags::integer, power(), GiNaC::replace_with_symbol(), and GiNaC::ex::to_rational().

ex GiNaC::power::to_polynomial ( exmap & repl ) const [virtual]

Implementation of ex::to_polynomial() for powers.

It replaces non-posint powers by temporary symbols.

Reimplemented from GiNaC::basic.

Definition at line 2554 of file normal.cpp.

References GiNaC::_ex_1, basis, GiNaC::collect_common_factors(), exponent, GiNaC::ex::info(), GiNaC::info_flags::negint, GiNaC::info_flags::posint, power(), GiNaC::replace_with_symbol(), GiNaC::ex::to_polynomial(), and GiNaC::ex::to_rational().

ex GiNaC::power::conjugate ( ) const [virtual]

Reimplemented from GiNaC::basic.

Definition at line 670 of file power.cpp.

References GiNaC::are_ex_trivially_equal(), basis, GiNaC::ex::conjugate(), GiNaC::status_flags::dynallocated, exponent, GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::info_flags::positive, and power().

ex GiNaC::power::real_part ( ) const [virtual]

Reimplemented from GiNaC::basic.

Definition at line 691 of file power.cpp.

References GiNaC::abs(), basis, c, GiNaC::cos(), GiNaC::exp(), GiNaC::ex::expand(), exponent, GiNaC::I, GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::log(), GiNaC::info_flags::posint, power(), GiNaC::ex::real_part(), and GiNaC::ex::subs().

ex GiNaC::power::imag_part ( ) const [virtual]

Reimplemented from GiNaC::basic.

Definition at line 716 of file power.cpp.

References GiNaC::abs(), basis, c, GiNaC::exp(), GiNaC::ex::expand(), exponent, GiNaC::I, GiNaC::ex::imag_part(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::log(), GiNaC::info_flags::posint, power(), GiNaC::ex::real_part(), GiNaC::sin(), and GiNaC::ex::subs().

void GiNaC::power::archive ( archive_node & n ) const [virtual]

Save (a.k.a.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 81 of file power.cpp.

References GiNaC::archive_node::add_ex(), basis, and exponent.

void GiNaC::power::read_archive	(	const archive_node &	n,
		lst &	syms
	)		`[virtual]`

Read (a.k.a.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 74 of file power.cpp.

References basis, exponent, and GiNaC::archive_node::find_ex().

ex GiNaC::power::derivative ( const symbol & s ) const [protected, virtual]

Implementation of ex::diff() for a power.

See also:: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 747 of file power.cpp.

References GiNaC::_ex1, GiNaC::_ex_1, basis, GiNaC::ex::diff(), exponent, GiNaC::log(), mul, and power().

ex GiNaC::power::eval_ncmul ( const exvector & v ) const [protected, virtual]

Reimplemented from GiNaC::basic.

Definition at line 665 of file power.cpp.

unsigned GiNaC::power::return_type ( ) const [protected, virtual]

Reimplemented from GiNaC::basic.

Definition at line 776 of file power.cpp.

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

return_type_t GiNaC::power::return_type_tinfo ( ) const [protected, virtual]

Reimplemented from GiNaC::basic.

Definition at line 781 of file power.cpp.

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

ex GiNaC::power::expand ( unsigned options = 0 ) const [protected, virtual]

Expand expression, i.e.

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

Reimplemented from GiNaC::basic.

Definition at line 786 of file power.cpp.

References GiNaC::are_ex_trivially_equal(), basis, GiNaC::status_flags::dynallocated, GiNaC::ex::expand(), expand_add(), expand_mul(), GiNaC::status_flags::expanded, exponent, GiNaC::basic::hold(), GiNaC::ex::info(), GiNaC::info_flags::integer, GiNaC::is_integer(), last, mul, GiNaC::expairseq::overall_coeff, power(), r, GiNaC::add::recombine_pair_to_ex(), GiNaC::expairseq::seq, GiNaC::basic::setflag(), and GiNaC::numeric::to_int().

Referenced by expand_add().

void GiNaC::power::print_power	(	const print_context &	c,
		const char *	powersymbol,
		const char *	openbrace,
		const char *	closebrace,
		unsigned	level
	)		const `[protected]`