An abstract class defining the interface of a univariate polynomial over an arbitrary BPASRing. More...

#include <BPASUnivarPolynomial.hpp>

Simplified semantic inheritance diagram for BPASUnivariatePolynomial< Ring, Derived >:

Full inheritance diagram for BPASUnivariatePolynomial< Ring, Derived >:

Public Member Functions
virtual void	differentiate ()=0
	Differentiate this polynomial, setting itself to its derivative.

virtual void	differentiate (int k)=0
	Differentiate this polynomial k times, setting itself to the final derivative. More...

virtual Derived	derivative () const =0
	Obtain the derivative of this polynomial. More...

virtual Derived	derivative (int) const =0
	Obtain the kth derivative of this polynomial. More...

virtual Ring	evaluate (const Ring &r) const =0
	Evaluate this polynomial by substituting the input ring element r for the indeterminate. More...

virtual Derived	monicDivide (const Derived &d)=0
	Divide this polynomial by the monic polynomial d, setting this polynomial to be the remainder. More...

virtual Derived	monicDivide (const Derived &d, Derived *q=NULL) const =0
	Divide this polynomial by the monic polynomial d. More...

virtual Derived	lazyPseudoDivide (const Derived &d, Ring h1, Ring h2)=0
	Perform a lazy pseudo-divison, also known as sparse pseudo-division. More...

virtual Derived	lazyPseudoDivide (const Derived &d, Derived q, Ring h1, Ring *h2) const =0
	Perform a lazy pseudo-divison, also known as sparse pseudo-division. More...

virtual Derived	pseudoDivide (const Derived &d, Ring *he)=0
	Perform a pseudo-divison, specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to deg(this) - deg(d) + 1 Return the quotient and this becomes the remainder. More...

virtual Derived	pseudoDivide (const Derived &d, Derived q, Ring he) const =0
	Perform a pseudo-divison, specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to deg(this) - deg(d) + 1 Return the quotient and this becomes the remainder. More...

virtual Ring	coefficient (int d) const =0
	Get the coefficient of the monomial with degree d. More...

virtual void	setCoefficient (int d, const Ring &r)=0
	Set the coefficient of the monomial with degree d to be the Ring element r. More...

virtual void	setVariableName (const Symbol &sym)=0
	Set the indeterminate of this polynomial to be the input symbol. More...

virtual Symbol	variable () const =0
	Get the indeterminate of this polynomial. More...

virtual Derived	operator<< (int i) const =0
	Shift this polynomial left i times, that is, multiply by x^i, where x is this polynomial's indeterminate. More...

virtual Derived &	operator<<= (int i)=0
	Shift this polynomial left i times, that is, multiply by x^i, where x is this polynomial's indeterminate, and set this polynomial to the result. More...

virtual Derived	operator>> (int) const =0
	Shift this polynomial right i times, that is, divide by x^i, where x is this polynomial's indeterminate,. More...

virtual Derived &	operator>>= (int)=0
	Shift this polynomial right i times, that is, divide by x^i, where x is this polynomial's indeterminate, and set this polynomial to the result. More...

Detailed Description

template<class Ring, class Derived>
class BPASUnivariatePolynomial< Ring, Derived >

An abstract class defining the interface of a univariate polynomial over an arbitrary BPASRing.

Depending on the specialization of the template Ring parameter, this class might form a Euclidean domain, and if so, fulfills the Euclidean domain interface also.

Derived should be the conrete class being implemented, following the Curiously Recurring Template Pattern.

Member Function Documentation

◆ coefficient()

template<class Ring, class Derived>

virtual Ring BPASUnivariatePolynomial< Ring, Derived >::coefficient ( int d ) const

pure virtual

Get the coefficient of the monomial with degree d.

Parameters

d	the degree of the monomial.

Returns: the coefficient of that monomial.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

◆ derivative() [1/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::derivative ( ) const

pure virtual

Obtain the derivative of this polynomial.

Returns: the derivative.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ derivative() [2/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::derivative ( int ) const

pure virtual

Obtain the kth derivative of this polynomial.

Parameters

k	the number of times to differentiate.

Returns: the kth derivative.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ differentiate()

template<class Ring, class Derived>

virtual void BPASUnivariatePolynomial< Ring, Derived >::differentiate ( int k )

pure virtual

Differentiate this polynomial k times, setting itself to the final derivative.

Parameters

k	the number of times to differentiate.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ evaluate()

template<class Ring, class Derived>

virtual Ring BPASUnivariatePolynomial< Ring, Derived >::evaluate ( const Ring & r ) const

pure virtual

Evaluate this polynomial by substituting the input ring element r for the indeterminate.

Parameters

r	the input ring element

Returns: the evaluation of this polynomial at r.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ lazyPseudoDivide() [1/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::lazyPseudoDivide	(	const Derived &	d,
		Ring *	h1,
		Ring *	h2
	)

pure virtual

Perform a lazy pseudo-divison, also known as sparse pseudo-division.

Specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to the number of division steps performed. Return the quotient and this becomes the remainder.

Parameters

	d	the divisor.
[out]	h1	The leading coefficient of b to the power e
[out]	h2	h to the power deg(a) - deg(b) + 1 - e

Returns: the quotient.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ lazyPseudoDivide() [2/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::lazyPseudoDivide	(	const Derived &	d,
		Derived *	q,
		Ring *	h1,
		Ring *	h2
	)		const

pure virtual

Perform a lazy pseudo-divison, also known as sparse pseudo-division.

Specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to the number of division steps performed. Return the quotient and this becomes the remainder.

Parameters

	d	the divisor.
[out]	q	a pointer to the quotient to output.
[out]	h1	The leading coefficient of b to the power e
[out]	h2	h to the power deg(this) - deg(d) + 1 - e

Returns: the remainder.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ monicDivide() [1/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::monicDivide ( const Derived & d )

pure virtual

Divide this polynomial by the monic polynomial d, setting this polynomial to be the remainder.

Parameters

d	the monic divison.

Returns: the quotient.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ monicDivide() [2/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::monicDivide	(	const Derived &	d,
		Derived *	q = `NULL`
	)		const

pure virtual

Divide this polynomial by the monic polynomial d.

The remainder is returned and the quotient returned via pointer q.

Parameters

	d	the monic divisor.
[out]	q	a pointer to the quotient to return.

Returns: the remainder.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ operator<<()

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::operator<< ( int i ) const

pure virtual

Shift this polynomial left i times, that is, multiply by x^i, where x is this polynomial's indeterminate.

Returns: the shifted polynomial.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariateRationalPolynomial, DenseUnivariatePolynomial< Field >, and DenseUnivariateIntegerPolynomial.

◆ operator<<=()

template<class Ring, class Derived>

virtual Derived& BPASUnivariatePolynomial< Ring, Derived >::operator<<= ( int i )

pure virtual

Shift this polynomial left i times, that is, multiply by x^i, where x is this polynomial's indeterminate, and set this polynomial to the result.

Returns: a reference to this polynomial after shifting.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariateRationalPolynomial, DenseUnivariateIntegerPolynomial, and DenseUnivariatePolynomial< Field >.

◆ operator>>()

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::operator>> ( int ) const

pure virtual

Shift this polynomial right i times, that is, divide by x^i, where x is this polynomial's indeterminate,.

Returns: the shifted polynomial.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

◆ operator>>=()

template<class Ring, class Derived>

virtual Derived& BPASUnivariatePolynomial< Ring, Derived >::operator>>= ( int )

pure virtual

Shift this polynomial right i times, that is, divide by x^i, where x is this polynomial's indeterminate, and set this polynomial to the result.

Returns: a reference to this polynomial after shifting.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

◆ pseudoDivide() [1/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::pseudoDivide	(	const Derived &	d,
		Ring *	he
	)

pure virtual

Perform a pseudo-divison, specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to deg(this) - deg(d) + 1 Return the quotient and this becomes the remainder.

Parameters

	d	the divisor.
[out]	he	h to the power deg(this) - deg(d) + 1

Returns: the quotient.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ pseudoDivide() [2/2]

template<class Ring, class Derived>

virtual Derived BPASUnivariatePolynomial< Ring, Derived >::pseudoDivide	(	const Derived &	d,
		Derived *	q,
		Ring *	he
	)		const

pure virtual

Perform a pseudo-divison, specifically, determine q and r, as in division, but satisfying h^e * this = q*d + r, where h is the leading coefficient of d and e is a positive integer equal to deg(this) - deg(d) + 1 Return the quotient and this becomes the remainder.

Parameters

	d	the divisor.
[out]	q	a pointer to the quotient to output.
[out]	he	h to the power deg(this) - deg(d) + 1

Returns: the remainder.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateIntegerPolynomial, and DenseUnivariateRationalPolynomial.

◆ setCoefficient()

template<class Ring, class Derived>

virtual void BPASUnivariatePolynomial< Ring, Derived >::setCoefficient	(	int	d,
		const Ring &	r
	)

pure virtual

Set the coefficient of the monomial with degree d to be the Ring element r.

Parameters

d	the degree of the monomial.
r	the ring element

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

◆ setVariableName()

template<class Ring, class Derived>

virtual void BPASUnivariatePolynomial< Ring, Derived >::setVariableName ( const Symbol & sym )

pure virtual

Set the indeterminate of this polynomial to be the input symbol.

Parameters

sym	the new symbol for the indeterminate.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

◆ variable()

template<class Ring, class Derived>

virtual Symbol BPASUnivariatePolynomial< Ring, Derived >::variable ( ) const

pure virtual

Get the indeterminate of this polynomial.

Returns: this polynomial's indeterminate.

Implemented in SparseUnivariateTempPoly< Ring, Derived >, SparseUnivariateTempPoly< Field, Derived >, DenseUnivariatePolynomial< Field >, DenseUnivariateRationalPolynomial, and DenseUnivariateIntegerPolynomial.

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

include/Polynomial/BPASUnivarPolynomial.hpp

Public Member Functions

Detailed Description

template<class Ring, class Derived> class BPASUnivariatePolynomial< Ring, Derived >

Member Function Documentation

◆ coefficient()

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ differentiate()

◆ evaluate()

◆ lazyPseudoDivide() [1/2]

◆ lazyPseudoDivide() [2/2]

◆ monicDivide() [1/2]

◆ monicDivide() [2/2]

◆ operator<<()

◆ operator<<=()

◆ operator>>()

◆ operator>>=()

◆ pseudoDivide() [1/2]

◆ pseudoDivide() [2/2]

◆ setCoefficient()

◆ setVariableName()

◆ variable()

template<class Ring, class Derived>
class BPASUnivariatePolynomial< Ring, Derived >