This class holds a extended truncated power series (positive and negative integer powers). More...

#include <pseries.h>

Inheritance diagram for GiNaC::pseries:

Public Member Functions
	pseries (const ex &rel_, const epvector &ops_)
	Construct pseries from a vector of coefficients and powers.
unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
size_t	nops () const
	Return the number of operands including a possible order term.
ex	op (size_t i) const
	Return the ith term in the series when represented as a sum.
int	degree (const ex &s) const
	Return degree of highest power of the series.
int	ldegree (const ex &s) const
	Return degree of lowest power of the series.
ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in power series if s is the expansion variable.
ex	collect (const ex &s, bool distributed=false) const
	Does nothing.
ex	eval (int level=0) const
	Perform coefficient-wise automatic term rewriting rules in this class.
ex	evalf (int level=0) const
	Evaluate coefficients numerically.
ex	series (const relational &r, int order, unsigned options=0) const
	Re-expansion of a pseries object.
ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions.
ex	normal (exmap &repl, exmap &rev_lookup, int level=0) const
	Implementation of ex::normal() for pseries.
ex	expand (unsigned options=0) const
	Implementation of ex::expand() for a power series.
ex	conjugate () const
ex	real_part () const
ex	imag_part () const
ex	eval_integ () const
	Evaluate integrals, if result is known.
ex	evalm () const
	Evaluate sums, products and integer powers of matrices.
void	archive (archive_node &n) const
	Save (a.k.a.
void	read_archive (const archive_node &n, lst &syms)
	Read (a.k.a.
ex	get_var () const
	Get the expansion variable.
ex	get_point () const
	Get the expansion point.
ex	convert_to_poly (bool no_order=false) const
	Convert the pseries object to an ordinary polynomial.
bool	is_compatible_to (const pseries &other) const
	Check whether series is compatible to another series (expansion variable and point are the same.
bool	is_zero () const
	Check whether series has the value zero.
bool	is_terminating () const
	Returns true if there is no order term, i.e.
ex	coeffop (size_t i) const
	Get coefficients and exponents.
ex	exponop (size_t i) const
ex	add_series (const pseries &other) const
	Add one series object to another, producing a pseries object that represents the sum.
ex	mul_const (const numeric &other) const
	Multiply a pseries object with a numeric constant, producing a pseries object that represents the product.
ex	mul_series (const pseries &other) const
	Multiply one pseries object to another, producing a pseries object that represents the product.
ex	power_const (const numeric &p, int deg) const
	Compute the p-th power of a series.
pseries	shift_exponents (int deg) const
	Return a new pseries object with the powers shifted by deg.
Protected Member Functions
ex	derivative (const symbol &s) const
	Implementation of ex::diff() for a power series.
void	print_series (const print_context &c, const char openbrace, const char closebrace, const char mul_sym, const char pow_sym, unsigned level) const
void	do_print (const print_context &c, unsigned level) const
	Default output to stream.
void	do_print_latex (const print_latex &c, unsigned level) const
void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream.
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.
Protected Attributes
epvector	seq
	Vector of {coefficient, power} pairs.
ex	var
	Series variable (holds a symbol)
ex	point
	Expansion point.

Detailed Description

This class holds a extended truncated power series (positive and negative integer powers).

It consists of expression coefficients (only non-zero coefficients are stored), an expansion variable and an expansion point. Other classes must provide members to convert into this type.

Definition at line 35 of file pseries.h.

Constructor & Destructor Documentation

GiNaC::pseries::pseries	(	const ex &	rel_,
		const epvector &	ops_
	)

Construct pseries from a vector of coefficients and powers.

expair.rest holds the coefficient, expair.coeff holds the power. The powers must be integers (positive or negative) and in ascending order; the last coefficient can be Order(_ex1) to represent a truncated, non-terminating series.

Parameters:

rel_	expansion variable and point (must hold a relational)
ops_	vector of {coefficient, power} pairs (coefficient must not be zero)

Returns:: newly constructed pseries

Definition at line 71 of file pseries.cpp.

References GINAC_ASSERT, GiNaC::ex::lhs(), point, GiNaC::ex::rhs(), and var.

Referenced by add_series(), conjugate(), derivative(), eval(), eval_integ(), evalf(), evalm(), expand(), imag_part(), mul_const(), mul_series(), normal(), power_const(), real_part(), series(), shift_exponents(), and subs().

Member Function Documentation

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

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::basic.

Definition at line 45 of file pseries.h.

Referenced by print_series().

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

Return the number of operands including a possible order term.

Reimplemented from GiNaC::basic.

Definition at line 265 of file pseries.cpp.

References seq.

Referenced by coeffop(), exponop(), and GiNaC::log_series().

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

Return the ith term in the series when represented as a sum.

Reimplemented from GiNaC::basic.

Definition at line 271 of file pseries.cpp.

References coeff(), GiNaC::is_order_function(), point, seq, and var.

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

Return degree of highest power of the series.

This is usually the exponent of the Order term. If s is not the expansion variable of the series, the series is examined termwise.

Reimplemented from GiNaC::basic.

Definition at line 284 of file pseries.cpp.

References coeff(), GiNaC::numeric::degree(), GiNaC::ex::is_equal(), GiNaC::pow(), seq, and var.

Referenced by mul_series(), and series().

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

Return degree of lowest power of the series.

This is usually the exponent of the leading term. If s is not the expansion variable of the series, the series is examined termwise. If s is the expansion variable but the expansion point is not zero the series is not expanded to find the degree. I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0.

Reimplemented from GiNaC::basic.

Definition at line 312 of file pseries.cpp.

References coeff(), GiNaC::ex::is_equal(), GiNaC::numeric::ldegree(), GiNaC::pow(), seq, and var.

Referenced by GiNaC::log_series(), mul_series(), and power_const().

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

Return coefficient of degree n in power series if s is the expansion variable.

If the expansion point is nonzero, by definition the n=1 coefficient in s of a+b*(s-z)+c*(s-z)^2+Order((s-z)^3) is b (assuming the expansion took place in the s in the first place). If s is not the expansion variable, an attempt is made to convert the series to a polynomial and return the corresponding coefficient from there.

Reimplemented from GiNaC::basic.

Definition at line 342 of file pseries.cpp.

References GiNaC::_ex0, GiNaC::ex::coeff(), GiNaC::basic::compare(), convert_to_poly(), GINAC_ASSERT, GiNaC::ex::is_equal(), seq, and var.

Referenced by degree(), ldegree(), GiNaC::log_series(), mul_series(), op(), power_const(), and read_archive().

ex GiNaC::pseries::collect	(	const ex &	s,
		bool	distributed = `false`
	)		const `[virtual]`

Does nothing.

Reimplemented from GiNaC::basic.

Definition at line 374 of file pseries.cpp.

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

Perform coefficient-wise automatic term rewriting rules in this class.

Reimplemented from GiNaC::basic.

Definition at line 380 of file pseries.cpp.

References GiNaC::status_flags::dynallocated, GiNaC::status_flags::evaluated, GiNaC::basic::hold(), GiNaC::max_recursion_level, point, pseries(), seq, and var.

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

Evaluate coefficients numerically.

Reimplemented from GiNaC::basic.

Definition at line 400 of file pseries.cpp.

References GiNaC::status_flags::dynallocated, GiNaC::status_flags::evaluated, GiNaC::max_recursion_level, point, pseries(), seq, and var.

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

Re-expansion of a pseries object.

Reimplemented from GiNaC::basic.

Definition at line 1200 of file pseries.cpp.

References GiNaC::_ex1, convert_to_poly(), degree(), GINAC_ASSERT, GiNaC::ex::is_equal(), GiNaC::relational::lhs(), point, pseries(), GiNaC::relational::rhs(), seq, GiNaC::ex::series(), GiNaC::to_int(), and var.

ex GiNaC::pseries::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 519 of file pseries.cpp.

References convert_to_poly(), GiNaC::status_flags::dynallocated, point, pseries(), seq, GiNaC::basic::setflag(), GiNaC::ex::subs(), and var.

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

Implementation of ex::normal() for pseries.

It normalizes each coefficient and replaces the series by a temporary symbol.

See also:: ex::normal

Reimplemented from GiNaC::basic.

Definition at line 2315 of file normal.cpp.

References GiNaC::_ex1, GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::is_zero(), n, GiNaC::ex::normal(), point, pseries(), GiNaC::replace_with_symbol(), seq, and var.

ex GiNaC::pseries::expand ( unsigned options = 0 ) const [virtual]

Implementation of ex::expand() for a power series.

It expands all the terms individually and returns the resulting series as a new pseries.

Reimplemented from GiNaC::basic.

Definition at line 541 of file pseries.cpp.

References GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::expand(), GiNaC::status_flags::expanded, GiNaC::ex::is_zero(), point, pseries(), seq, and var.

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

Reimplemented from GiNaC::basic.

Definition at line 419 of file pseries.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::ex::conjugate(), GiNaC::conjugateepvector(), GiNaC::status_flags::dynallocated, GiNaC::ex::info(), point, pseries(), GiNaC::info_flags::real, seq, GiNaC::basic::setflag(), and var.

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

Reimplemented from GiNaC::basic.

Definition at line 436 of file pseries.cpp.

References GiNaC::status_flags::dynallocated, GiNaC::ex::info(), point, pseries(), GiNaC::info_flags::real, GiNaC::ex::real_part(), seq, GiNaC::basic::setflag(), and var.

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

Reimplemented from GiNaC::basic.

Definition at line 451 of file pseries.cpp.

References GiNaC::status_flags::dynallocated, GiNaC::ex::info(), point, pseries(), GiNaC::info_flags::real, GiNaC::ex::real_part(), seq, GiNaC::basic::setflag(), and var.

ex GiNaC::pseries::eval_integ ( ) const [virtual]

Evaluate integrals, if result is known.

Reimplemented from GiNaC::basic.

Definition at line 466 of file pseries.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::eval_integ(), point, pseries(), seq, and var.

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

Evaluate sums, products and integer powers of matrices.

Reimplemented from GiNaC::basic.

Definition at line 491 of file pseries.cpp.

References GiNaC::are_ex_trivially_equal(), GiNaC::ex::coeff(), GiNaC::status_flags::dynallocated, GiNaC::ex::evalm(), GiNaC::ex::is_zero(), point, pseries(), seq, and var.

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

Save (a.k.a.

serialize) object into archive.

Reimplemented from GiNaC::basic.

Definition at line 104 of file pseries.cpp.

References GiNaC::archive_node::add_ex(), point, seq, and var.

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

Read (a.k.a.

deserialize) object from archive.

Reimplemented from GiNaC::basic.

Definition at line 84 of file pseries.cpp.

References coeff(), GiNaC::archive_node::find_ex(), GiNaC::archive_node::find_ex_by_loc(), GiNaC::archive_node::find_first(), GiNaC::archive_node::find_last(), last, point, seq, and var.

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

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

See also:: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 557 of file pseries.cpp.

References c, GiNaC::ex::coeff(), GiNaC::is_order_function(), GiNaC::ex::is_zero(), point, pseries(), seq, and var.

ex GiNaC::pseries::get_var ( ) const [inline]

Get the expansion variable.

Definition at line 73 of file pseries.h.

References var.

ex GiNaC::pseries::get_point ( ) const [inline]

Get the expansion point.

Definition at line 76 of file pseries.h.

References point.

ex GiNaC::pseries::convert_to_poly ( bool no_order = false ) const

Convert the pseries object to an ordinary polynomial.

Parameters:

no_order flag: discard higher order terms

Definition at line 593 of file pseries.cpp.

References GiNaC::ex::coeff(), GiNaC::is_order_function(), point, seq, and var.

Referenced by coeff(), series(), and subs().

bool GiNaC::pseries::is_compatible_to ( const pseries & other ) const [inline]

Check whether series is compatible to another series (expansion variable and point are the same.

Definition at line 85 of file pseries.h.

References GiNaC::ex::is_equal(), point, and var.

Referenced by add_series(), and mul_series().

bool GiNaC::pseries::is_zero ( ) const [inline]

Check whether series has the value zero.

Definition at line 88 of file pseries.h.

References seq.

Referenced by power_const().

bool GiNaC::pseries::is_terminating ( ) const

Returns true if there is no order term, i.e.

the series terminates and false otherwise.

Definition at line 609 of file pseries.cpp.

References GiNaC::is_order_function(), and seq.

Referenced by GiNaC::is_terminating(), and GiNaC::log_series().

ex GiNaC::pseries::coeffop ( size_t i ) const

Get coefficients and exponents.

Definition at line 614 of file pseries.cpp.

References nops(), and seq.

ex GiNaC::pseries::exponop ( size_t i ) const

Definition at line 621 of file pseries.cpp.

References nops(), and seq.

ex GiNaC::pseries::add_series ( const pseries & other ) const

Add one series object to another, producing a pseries object that represents the sum.

Parameters:

other pseries object to add with

Returns:: the sum as a pseries

Definition at line 704 of file pseries.cpp.

References GiNaC::_ex0, GiNaC::_ex1, is_compatible_to(), GiNaC::is_order_function(), GiNaC::ex::is_zero(), point, pseries(), seq, GiNaC::to_int(), and var.

Referenced by GiNaC::log_series().

ex GiNaC::pseries::mul_const ( const numeric & other ) const

Multiply a pseries object with a numeric constant, producing a pseries object that represents the product.

Parameters:

other constant to multiply with

Returns:: the product as a pseries

Definition at line 807 of file pseries.cpp.

References GiNaC::numeric::coeff(), GiNaC::is_order_function(), point, pseries(), seq, and var.

Referenced by GiNaC::mul::series().

ex GiNaC::pseries::mul_series ( const pseries & other ) const

Multiply one pseries object to another, producing a pseries object that represents the product.

Parameters:

other pseries object to multiply with

Returns:: the product as a pseries

Definition at line 829 of file pseries.cpp.

References GiNaC::_ex0, GiNaC::_ex1, coeff(), degree(), GiNaC::status_flags::dynallocated, is_compatible_to(), GiNaC::is_order_function(), GiNaC::ex::is_zero(), ldegree(), point, pseries(), seq, GiNaC::basic::setflag(), and var.

ex GiNaC::pseries::power_const	(	const numeric &	p,
		int	deg
	)		const

Compute the p-th power of a series.

Parameters:

p	power to compute
deg	truncation order of series calculation

Definition at line 1000 of file pseries.cpp.

References GiNaC::_ex0, GiNaC::_ex1, c, coeff(), GiNaC::status_flags::dynallocated, GiNaC::is_integer(), GiNaC::numeric::is_negative(), GiNaC::is_order_function(), is_zero(), GiNaC::numeric::is_zero(), ldegree(), point, pseries(), GiNaC::numeric::real(), seq, GiNaC::to_int(), and var.

pseries GiNaC::pseries::shift_exponents ( int deg ) const

Return a new pseries object with the powers shifted by deg.

Definition at line 1088 of file pseries.cpp.

References point, pseries(), seq, and var.

void GiNaC::pseries::print_series	(	const print_context &	c,
		const char *	openbrace,
		const char *	closebrace,
		const char *	mul_sym,
		const char *	pow_sym,
		unsigned	level
	)		const `[protected]`