A class for a univariate polynomial providing everything what a GiNaC expression of type polynomial is and in addition, stores the single main variable of the polynomial. More...

#include <UnivariatePolynomial.h>

Inheritance diagram for GiNaCRA::UnivariatePolynomial:

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Collaboration diagram for GiNaCRA::UnivariatePolynomial:

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Public Types
enum	subresultantStrategy { GENERIC_SUBRESULTANTSTRATEGY, LAZARDS_SUBRESULTANTSTRATEGY, DUCOS_SUBRESULTANTSTRATEGY }
	Predefined flags for different solving strategies in `UnivariatePolynomial::subresultants`. More...
Public Member Functions
	UnivariatePolynomial ()
	Constructs a univariate polynomial consisting of the standard variable defined in constants.h.
	UnivariatePolynomial (const numeric &n)
	Constructs a univariate polynomial with exactly the specified root.
	UnivariatePolynomial (const ex &p, const symbol &s, bool enableCheck=true) throw ( invalid_argument )
	Constructs a univariate polynomial.
	UnivariatePolynomial (const UnivariatePolynomial &p)
	Constructs a univariate polynomial as copy of another one.
const symbol	variable () const
	Selects the main variable of the polynomial.
const bool	enabledPolynomialCheck () const
	Selects the flag for the is_rational_polynomial check.
UnivariatePolynomial	inVariable (const symbol &x) const
const UnivariatePolynomial &	operator= (const UnivariatePolynomial &)
	This polynomial gets all values of the other.
const UnivariatePolynomial &	operator= (const ex &)
	This polynomial gets all values of the other expression, using the current main variable.
ex	coeff (int i) const
ex	lcoeff () const
ex	tcoeff () const
ex	content () const
UnivariatePolynomial	diff (unsigned nth=1) const
UnivariatePolynomial	trunc () const
	Removes the leading term.
bool	isZero () const
	Returns true if the univariate polynomial is the zero polynomial, otherwise false.
const bool	hasZeroRoot () const
int	degree () const
int	ldegree () const
	The low-degree is the smallest exponent at the main variable occuring.
UnivariatePolynomial	primpart () const
UnivariatePolynomial	primpart (const ex &content) const
UnivariatePolynomial	sepapart () const
	Computes a polynomial being decomposed into linear factors of multiplicity 1 with the same set of zeros as this polynomial.
UnivariatePolynomial	nonzeropart () const
	Eliminates the root 0 from the polynomial by dividing the polynomial by a power of the main variable.
bool	isCompatible (const UnivariatePolynomial &o) const
	Compares univariate polynomials for compatibility regarding common computations.
bool	isConstant () const
	Returns true if the univariate polynomial is constant in the respective variable, otherwise false.
ex	evaluateAt (const ex &a) const
	Evaluation of the univariate polynomial at the specified expression, yielding a term in the coefficients only.
const UnivariatePolynomial	rem (const UnivariatePolynomial &o) const
	Compute the remainder of `o` modulo the given polynomial in this variable.
const UnivariatePolynomial	quo (const UnivariatePolynomial &o) const
	Compute the quotient of division by `o` in this variable.
const UnivariatePolynomial	add (const UnivariatePolynomial &o) const
	Compute the sum of this and `o` in this variable.
const UnivariatePolynomial	mul (const UnivariatePolynomial &o) const
	Compute the product of this and `o` in this variable.
const UnivariatePolynomial	sub (const UnivariatePolynomial &o) const
	Compute the subtraction of this by `o` in this variable.
UnivariatePolynomial	square () const
	Calculates the square.
const UnivariatePolynomial	gcd (const UnivariatePolynomial &o) const
	Computes the greatest common divisor of this polynomial and the given by Euclid's algorithm.
const UnivariatePolynomial	resultant (const UnivariatePolynomial &o) const
	Compute the resultant of `o` and the given polynomial in this variable.
const bool	isEqual (const UnivariatePolynomial &o) const
void	do_print (const print_context &c, unsigned level=0) const
Static Public Member Functions
static list< UnivariatePolynomial >	standardSturmSequence (const UnivariatePolynomial &a, const UnivariatePolynomial &b) throw ( invalid_argument )
	Generates a standard Sturm sequence by generating an additively inverted polynomial remainder sequence.
static bool	univariatePolynomialIsLess (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static bool	univariatePolynomialIsLessLowDeg (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static bool	univariatePolynomialIsLessOddDeg (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static bool	univariatePolynomialIsLessOddLowDeg (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static bool	univariatePolynomialIsLessEvenDeg (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static bool	univariatePolynomialIsLessEvenLowDeg (const UnivariatePolynomial &a, const UnivariatePolynomial &b)
	Compares two univariate polynomials.
static const list < UnivariatePolynomial >	subresultants (const UnivariatePolynomial &a, const UnivariatePolynomial &b, const subresultantStrategy strategy=GENERIC_SUBRESULTANTSTRATEGY)
	Computes the subresultant sequence according to the algorithm in [Lionel Ducos.
static const vector< ex >	subresultantCoefficients (const UnivariatePolynomial &a, const UnivariatePolynomial &b, const subresultantStrategy strategy=GENERIC_SUBRESULTANTSTRATEGY)
	Returns the leading coefficients of the subresultants of a and b.
static const vector< ex >	principalSubresultantCoefficients (const UnivariatePolynomial &a, const UnivariatePolynomial &b, const subresultantStrategy strategy=GENERIC_SUBRESULTANTSTRATEGY)
	Returns the i-th coefficients of the i-th subresultant of a and b at the i-th position of the result vector.
Protected Attributes
symbol	mVariable
bool	mEnabledPolynomialCheck

Detailed Description

A class for a univariate polynomial providing everything what a GiNaC expression of type polynomial is and in addition, stores the single main variable of the polynomial.

Author:: Ulrich Loup

Since:: 2010-08-03

Version:: 2012-05-19

See also:: ISBN 0-387-94090-1 and ISBN-13: 978-3642069642

Definition at line 51 of file UnivariatePolynomial.h.

Member Enumeration Documentation

enum GiNaCRA::UnivariatePolynomial::subresultantStrategy

Predefined flags for different solving strategies in UnivariatePolynomial::subresultants.

Enumerator:

GENERIC_SUBRESULTANTSTRATEGY
LAZARDS_SUBRESULTANTSTRATEGY
DUCOS_SUBRESULTANTSTRATEGY

Definition at line 461 of file UnivariatePolynomial.h.

Constructor & Destructor Documentation

GiNaCRA::UnivariatePolynomial::UnivariatePolynomial ( ) [inline]

Constructs a univariate polynomial consisting of the standard variable defined in constants.h.

Definition at line 63 of file UnivariatePolynomial.h.

Referenced by add(), diff(), evaluateAt(), gcd(), inVariable(), mul(), nonzeropart(), primpart(), quo(), rem(), resultant(), sepapart(), square(), sub(), subresultants(), and trunc().

GiNaCRA::UnivariatePolynomial::UnivariatePolynomial ( const numeric & n ) [inline]

Constructs a univariate polynomial with exactly the specified root.

Parameters:

n	root to-be

Definition at line 73 of file UnivariatePolynomial.h.

GiNaCRA::UnivariatePolynomial::UnivariatePolynomial	(	const ex &	p,
		const symbol &	s,
		bool	enableCheck = `true`
	)		throw ( invalid_argument )

Constructs a univariate polynomial.

Parameters:

p	polynomial
s	main variable of the univariate polynomial p
enableCheck	if set to `true` (default), the polynomial is checked for being a proper polynomial by GiNaC::ex::is_polynomial. Otherwise no check will be performed.

Definition at line 49 of file UnivariatePolynomial.cpp.

GiNaCRA::UnivariatePolynomial::UnivariatePolynomial ( const UnivariatePolynomial & p ) [inline]

Constructs a univariate polynomial as copy of another one.

Parameters:

p	univariate polynomial

Definition at line 91 of file UnivariatePolynomial.h.

Member Function Documentation

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::add ( const UnivariatePolynomial & o ) const [inline]

Compute the sum of this and o in this variable.

Parameters:

o	other polynomial

Returns:

Definition at line 311 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::operator+().

ex GiNaCRA::UnivariatePolynomial::coeff ( int i ) const [inline]

Parameters:

i	degree of which the coefficient shall be returned

Returns:: the i-th coefficient of this polynomial

Reimplemented in GiNaCRA::RationalUnivariatePolynomial.

Definition at line 148 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::RationalUnivariatePolynomial::cauchyBound(), and nonzeropart().

ex GiNaCRA::UnivariatePolynomial::content ( ) const [inline]

Returns:: the content of this polynomial

Definition at line 172 of file UnivariatePolynomial.h.

References mVariable.

int GiNaCRA::UnivariatePolynomial::degree ( ) const [inline]

Returns:: degree of the univariate polynomial in its respective symbol

Definition at line 212 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::RationalUnivariatePolynomial::cauchyBound(), GiNaCRA::RealAlgebraicNumberFactory::commonRealRoots(), GiNaCRA::RationalUnivariatePolynomial::evaluateAt(), GiNaCRA::RealAlgebraicNumberIR::inverse(), isConstant(), GiNaCRA::RationalUnivariatePolynomial::maximumNorm(), nonzeropart(), GiNaCRA::RationalUnivariatePolynomial::oneNorm(), subresultants(), GiNaCRA::RationalUnivariatePolynomial::twoNorm(), univariatePolynomialIsLessEvenDeg(), univariatePolynomialIsLessEvenLowDeg(), univariatePolynomialIsLessLowDeg(), univariatePolynomialIsLessOddDeg(), and univariatePolynomialIsLessOddLowDeg().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::diff ( unsigned nth = 1 ) const [inline]

Parameters:

nth

Returns:: nth derivative of the univariate polynomial in the given symbol

Definition at line 181 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::RealAlgebraicNumberIR::add(), GiNaCRA::RationalUnivariatePolynomial::approximateRealRoot(), GiNaCRA::RationalUnivariatePolynomial::calculateRemainderTarskiQuery(), GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::CAD::elimination(), GiNaCRA::RealAlgebraicNumberFactory::evaluateIR(), GiNaCRA::RealAlgebraicNumberIR::mul(), GiNaCRA::RealAlgebraicNumberFactory::realRoots(), GiNaCRA::RealAlgebraicNumberFactory::realRootsEval(), sepapart(), and GiNaCRA::RealAlgebraicNumberIR::sgn().

void GiNaCRA::UnivariatePolynomial::do_print	(	const print_context &	c,
		unsigned	level = `0`
	)		const

Definition at line 62 of file UnivariatePolynomial.cpp.

References mVariable.

const bool GiNaCRA::UnivariatePolynomial::enabledPolynomialCheck ( ) const [inline]

Selects the flag for the is_rational_polynomial check.

Returns:: flag for the is_rational_polynomial check

Definition at line 114 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck.

Referenced by GiNaCRA::operator-().

ex GiNaCRA::UnivariatePolynomial::evaluateAt ( const ex & a ) const [inline]

Evaluation of the univariate polynomial at the specified expression, yielding a term in the coefficients only.

Parameters:

a	an expression for evaluation

Returns:: value of the univariate polynomial at the specified numeric.

Definition at line 277 of file UnivariatePolynomial.h.

References mVariable, and UnivariatePolynomial().

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::gcd ( const UnivariatePolynomial & o ) const [inline]

Computes the greatest common divisor of this polynomial and the given by Euclid's algorithm.

Parameters:

o

Returns:: the greatest common divisor of this polynomial and the given

Definition at line 351 of file UnivariatePolynomial.h.

References GiNaC::gcd(), mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by sepapart().

const bool GiNaCRA::UnivariatePolynomial::hasZeroRoot ( ) const [inline]

Returns:: true in case the polynomial's lowest degree is not 0

Definition at line 204 of file UnivariatePolynomial.h.

References ldegree().

Referenced by GiNaCRA::RealAlgebraicNumberFactory::realRoots(), and GiNaCRA::RealAlgebraicNumberFactory::realRootsEval().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::inVariable ( const symbol & x ) const [inline]

Definition at line 123 of file UnivariatePolynomial.h.

References mVariable, and UnivariatePolynomial().

bool GiNaCRA::UnivariatePolynomial::isCompatible ( const UnivariatePolynomial & o ) const [inline]

Compares univariate polynomials for compatibility regarding common computations.

Returns:: true in case the other UnivariatePolynomial has the same symbol as this.

Definition at line 259 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::RealAlgebraicNumberIR::sgn(), and subresultants().

bool GiNaCRA::UnivariatePolynomial::isConstant ( ) const [inline]

Returns true if the univariate polynomial is constant in the respective variable, otherwise false.

Returns:: true if the univariate polynomial is constant in the respective variable, otherwise false.

Definition at line 268 of file UnivariatePolynomial.h.

References degree(), and mVariable.

Referenced by GiNaCRA::RealAlgebraicNumberFactory::realRoots(), sepapart(), and GiNaCRA::CAD::truncation().

const bool GiNaCRA::UnivariatePolynomial::isEqual ( const UnivariatePolynomial & o ) const [inline]

Parameters:

o

Returns:: true in case the other univariate polynomial equals this

Definition at line 378 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::operator!=(), GiNaCRA::UnivariatePolynomialSetEquals::operator()(), GiNaCRA::operator==(), and univariatePolynomialIsLess().

bool GiNaCRA::UnivariatePolynomial::isZero ( ) const [inline]

Returns true if the univariate polynomial is the zero polynomial, otherwise false.

Returns:: true if the univariate polynomial is the zero polynomial, otherwise false.

Definition at line 196 of file UnivariatePolynomial.h.

Referenced by GiNaCRA::CAD::elimination(), and subresultants().

ex GiNaCRA::UnivariatePolynomial::lcoeff ( ) const [inline]

Returns:: the leading coefficient of this polynomial

Reimplemented in GiNaCRA::RationalUnivariatePolynomial.

Definition at line 156 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::RationalUnivariatePolynomial::cauchyBound(), and subresultants().

int GiNaCRA::UnivariatePolynomial::ldegree ( ) const [inline]

The low-degree is the smallest exponent at the main variable occuring.

Returns:: low-degree of the univariate polynomial in its respective symbol

Definition at line 220 of file UnivariatePolynomial.h.

References mVariable.

Referenced by GiNaCRA::RationalUnivariatePolynomial::cauchyBound(), hasZeroRoot(), GiNaCRA::RationalUnivariatePolynomial::maximumNorm(), nonzeropart(), GiNaCRA::RationalUnivariatePolynomial::oneNorm(), and GiNaCRA::RationalUnivariatePolynomial::twoNorm().

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::mul ( const UnivariatePolynomial & o ) const [inline]

Compute the product of this and o in this variable.

Parameters:

o	other polynomial

Returns:

Definition at line 321 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::operator*().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::nonzeropart ( ) const

Eliminates the root 0 from the polynomial by dividing the polynomial by a power of the main variable.

Runtime complexity:: linear in degree()

Definition at line 111 of file UnivariatePolynomial.cpp.

References coeff(), degree(), ldegree(), mVariable, UnivariatePolynomial(), and variable().

Referenced by GiNaCRA::RealAlgebraicNumberFactory::realRoots(), and GiNaCRA::RealAlgebraicNumberFactory::realRootsEval().

const UnivariatePolynomial & GiNaCRA::UnivariatePolynomial::operator= ( const UnivariatePolynomial & o )

This polynomial gets all values of the other.

Definition at line 73 of file UnivariatePolynomial.cpp.

References mEnabledPolynomialCheck, and mVariable.

Referenced by operator=().

const UnivariatePolynomial & GiNaCRA::UnivariatePolynomial::operator= ( const ex & o )

This polynomial gets all values of the other expression, using the current main variable.

Definition at line 81 of file UnivariatePolynomial.cpp.

References operator=().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::primpart ( ) const [inline]

Returns:: primitive part of the univariate polynomial

Definition at line 228 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::RealAlgebraicNumberIR::add(), GiNaCRA::RealAlgebraicNumberIR::mul(), and sepapart().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::primpart ( const ex & content ) const [inline]

Parameters:

content precomputed content of this polynomial

Returns:: primitive part of the univariate polynomial

Definition at line 237 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

const vector< ex > GiNaCRA::UnivariatePolynomial::principalSubresultantCoefficients	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b,
		const subresultantStrategy	strategy = `GENERIC_SUBRESULTANTSTRATEGY`
	)		`[static]`

Returns the i-th coefficients of the i-th subresultant of a and b at the i-th position of the result vector.

Parameters:

a	the first Polynomial
b	the second Polynomial
strategy	choice of optimization. Standard is none, other possibilities are due to the sections 2 and 3 of the paper.

See also:: UnivariatePolynomial::subresultants

Returns:: vector containing at the i-th position the i-th subresultant coefficient

Definition at line 228 of file UnivariatePolynomial.cpp.

References subresultants().

Referenced by GiNaCRA::CAD::elimination().

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::quo ( const UnivariatePolynomial & o ) const [inline]

Compute the quotient of division by o in this variable.

Parameters:

o	other polynomial

Returns:

Definition at line 301 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::operator/(), and sepapart().

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::rem ( const UnivariatePolynomial & o ) const [inline]

Compute the remainder of o modulo the given polynomial in this variable.

Parameters:

o	other polynomial

Returns:

Definition at line 291 of file UnivariatePolynomial.h.

References mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::operator%().

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::resultant ( const UnivariatePolynomial & o ) const [inline]

Compute the resultant of o and the given polynomial in this variable.

The resultant ist the subresultant of lowest degree.

Parameters:

o	other polynomial

Returns:: the resultant of this polynomial and o

See also:: subresultants, GiNaC::resultant

Definition at line 364 of file UnivariatePolynomial.h.

References mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::RealAlgebraicNumberFactory::evaluateIR().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::sepapart ( ) const

Computes a polynomial being decomposed into linear factors of multiplicity 1 with the same set of zeros as this polynomial.

This is also referred to as the square-free part.

Returns:: separable part of the univariate polynomial, or zero in case the polynomial was constant

Definition at line 103 of file UnivariatePolynomial.cpp.

References diff(), gcd(), isConstant(), mEnabledPolynomialCheck, mVariable, primpart(), quo(), and UnivariatePolynomial().

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::square ( ) const [inline]

Calculates the square.

Returns:: this polynomial squared

Definition at line 340 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

list< UnivariatePolynomial > GiNaCRA::UnivariatePolynomial::standardSturmSequence	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		throw ( invalid_argument ) `[static]`

Generates a standard Sturm sequence by generating an additively inverted polynomial remainder sequence.

Convention: If one polynomial is zero, the corresponding Sturm sequence is zero followed by the other polynomial.

Parameters:

a
b

Returns:: Vector of pointers to the elements of the standard Sturm sequence

Definition at line 254 of file UnivariatePolynomial.cpp.

const UnivariatePolynomial GiNaCRA::UnivariatePolynomial::sub ( const UnivariatePolynomial & o ) const [inline]

Compute the subtraction of this by o in this variable.

Parameters:

o	other polynomial

Returns:

Definition at line 331 of file UnivariatePolynomial.h.

References mEnabledPolynomialCheck, mVariable, and UnivariatePolynomial().

Referenced by GiNaCRA::operator-().

const vector< ex > GiNaCRA::UnivariatePolynomial::subresultantCoefficients	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b,
		const subresultantStrategy	strategy = `GENERIC_SUBRESULTANTSTRATEGY`
	)		`[static]`

Returns the leading coefficients of the subresultants of a and b.

Parameters:

a	the first Polynomial
b	the second Polynomial
strategy	choice of optimization. Standard is none, other possibilities are due to the sections 2 and 3 of the paper.

See also:: UnivariatePolynomial::subresultants

Returns:: vector containing at the i-th position the i-th subresultant coefficient

Definition at line 217 of file UnivariatePolynomial.cpp.

References subresultants().

const list< UnivariatePolynomial > GiNaCRA::UnivariatePolynomial::subresultants	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b,
		const subresultantStrategy	strategy = `GENERIC_SUBRESULTANTSTRATEGY`
	)		`[static]`

Computes the subresultant sequence according to the algorithm in [Lionel Ducos.

Optimizations of the subresultant algorithm. Journal of Pure and Applied Algebra 145 (2000) 149–163]

Marginal cases: Let the degree of a be smaller or equal than the degree of b. if deg(b) is less than 2, then only a, b are returned.

Parameters:

a	the first Polynomial
b	the second Polynomial
strategy	choice of optimization. Standard is none, other possibilities are due to the sections 2 and 3 of the paper.

Returns:: the subresultant sequence in descending order of degree.

Runtime complexity:: O( deg(a)*deg(b) )

Todo:: implement using page 151 of the above mentioned article

Todo:: implement using page 154 of the above mentioned article

Todo:: implement using page 151 of the above mentioned article

Todo:: implement using page 154 of the above mentioned article

Definition at line 125 of file UnivariatePolynomial.cpp.

References degree(), DUCOS_SUBRESULTANTSTRATEGY, GENERIC_SUBRESULTANTSTRATEGY, isCompatible(), isZero(), LAZARDS_SUBRESULTANTSTRATEGY, lcoeff(), mVariable, UnivariatePolynomial(), and variable().

Referenced by principalSubresultantCoefficients(), and subresultantCoefficients().

ex GiNaCRA::UnivariatePolynomial::tcoeff ( ) const [inline]

Returns:: the trailing coefficient of this polynomial

Reimplemented in GiNaCRA::RationalUnivariatePolynomial.

Definition at line 164 of file UnivariatePolynomial.h.

References mVariable.

UnivariatePolynomial GiNaCRA::UnivariatePolynomial::trunc ( ) const

Removes the leading term.

Returns:: the polynomial without leading term

Definition at line 93 of file UnivariatePolynomial.cpp.

References mEnabledPolynomialCheck, UnivariatePolynomial(), and variable().

Referenced by GiNaCRA::CAD::truncation().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLess	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to GiNaC::ex_is_less( a, b ).

Parameters:

a
b

Returns:: true if a < b, false otherwise

Definition at line 273 of file UnivariatePolynomial.cpp.

References isEqual().

Referenced by univariatePolynomialIsLessEvenDeg(), univariatePolynomialIsLessEvenLowDeg(), univariatePolynomialIsLessLowDeg(), univariatePolynomialIsLessOddDeg(), and univariatePolynomialIsLessOddLowDeg().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLessEvenDeg	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to a.degree() even or a.degree() >= b.degree() and GiNaC::ex_is_less( a, b ).

Parameters:

a
b

Returns:: true if a < b, false otherwise

Definition at line 295 of file UnivariatePolynomial.cpp.

References degree(), and univariatePolynomialIsLess().

Referenced by GiNaCRA::CADSettings::getSettings().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLessEvenLowDeg	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to a.degree() even and a.degree() < b.degree() or a.degree() >= b.degree() and GiNaC::ex_is_less( a, b ).

Parameters:

a
b

Returns:: true if a < b, false otherwise

Definition at line 300 of file UnivariatePolynomial.cpp.

References degree(), and univariatePolynomialIsLess().

Referenced by GiNaCRA::CADSettings::getSettings().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLessLowDeg	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to a.degree() < b.degree() or a.degree() >= b.degree() and GiNaC::ex_is_less( a, b ).

Parameters:

a
b

Returns:: true if a < b, false otherwise

Definition at line 278 of file UnivariatePolynomial.cpp.

References degree(), and univariatePolynomialIsLess().

Referenced by GiNaCRA::CADSettings::getSettings().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLessOddDeg	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to a.degree() odd or a.degree() >= b.degree() and GiNaC::ex_is_less( a, b ).

Parameters:

a
b

Returns:: true if a < b, false otherwise

Definition at line 283 of file UnivariatePolynomial.cpp.

References degree(), and univariatePolynomialIsLess().

Referenced by GiNaCRA::CADSettings::getSettings().

bool GiNaCRA::UnivariatePolynomial::univariatePolynomialIsLessOddLowDeg	(	const UnivariatePolynomial &	a,
		const UnivariatePolynomial &	b
	)		`[static]`

Compares two univariate polynomials.

The behavior of this function is equivalent to a.degree() odd and a.degree() < b.degree() or a.degree() >= b.degree() and GiNaC::ex_is_less( a, b ).

Parameters: