edu.jas.poly

Class GenSolvablePolynomial<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

edu.jas.poly.GenSolvablePolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

AbelianGroupElem<GenPolynomial<C>>, Element<GenPolynomial<C>>, MonoidElem<GenPolynomial<C>>, RingElem<GenPolynomial<C>>, java.io.Serializable, java.lang.Comparable<GenPolynomial<C>>, java.lang.Iterable<Monomial<C>>

Direct Known Subclasses:

LocalSolvablePolynomial, QLRSolvablePolynomial, QuotSolvablePolynomial, RecSolvablePolynomial, ResidueSolvablePolynomial

public class GenSolvablePolynomial<C extends RingElem<C>>
extends GenPolynomial<C>

GenSolvablePolynomial generic solvable polynomials implementing RingElem. n-variate ordered solvable polynomials over C. Objects of this class are intended to be immutable. The implementation is based on TreeMap respectively SortedMap from exponents to coefficients by extension of GenPolybomial. Only the coefficients are modeled with generic types, the exponents are fixed to ExpVector with long entries (this will eventually be changed in the future).

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
GenSolvablePolynomialRing<C>	ring The factory for the solvable polynomial ring.

Constructor Summary

Constructors

Constructor and Description
GenSolvablePolynomial(GenSolvablePolynomialRing<C> r) Constructor for zero GenSolvablePolynomial.
GenSolvablePolynomial(GenSolvablePolynomialRing<C> r, C c) Constructor for GenSolvablePolynomial.
GenSolvablePolynomial(GenSolvablePolynomialRing<C> r, C c, ExpVector e) Constructor for GenSolvablePolynomial.

Method Summary

Modifier and Type	Method and Description
GenSolvablePolynomial<C>	copy() Clone this GenSolvablePolynomial.
boolean	equals(java.lang.Object B) Comparison with any other object.
GenSolvablePolynomialRing<C>	factory() Get the corresponding element factory.
GenSolvablePolynomial<C>	monic() GenSolvablePolynomial monic, i.e.
GenSolvablePolynomial<C>	multiply(C b) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiply(C b, C c) GenSolvablePolynomial left and right multiplication.
GenSolvablePolynomial<C>	multiply(C b, ExpVector e) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiply(C b, ExpVector e, C c, ExpVector f) GenSolvablePolynomial left and right multiplication.
GenSolvablePolynomial<C>	multiply(ExpVector e) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiply(ExpVector e, ExpVector f) GenSolvablePolynomial left and right multiplication.
GenSolvablePolynomial<C>	multiply(GenSolvablePolynomial<C> Bp) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiply(GenSolvablePolynomial<C> S, GenSolvablePolynomial<C> T) GenSolvablePolynomial left and right multiplication.
GenSolvablePolynomial<C>	multiply(java.util.Map.Entry<ExpVector,C> m) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiplyLeft(C b) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiplyLeft(C b, ExpVector e) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiplyLeft(ExpVector e) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>	multiplyLeft(java.util.Map.Entry<ExpVector,C> m) GenSolvablePolynomial multiplication.
GenSolvablePolynomial<C>[]	quotientRemainder(GenSolvablePolynomial<C> S) GenSolvablePolynomial left division with remainder.

Methods inherited from class edu.jas.poly.GenPolynomial

abs, coefficient, coefficientIterator, compareTo, contract, contractCoeff, degree, degree, degreeVector, deHomogenize, divide, divide, divideAndRemainder, doPutToMap, doPutToMap, doRemoveFromMap, egcd, exponentIterator, extend, extendLower, extendUnivariate, gcd, getMap, hashCode, hegcd, homogenize, inverse, isConstant, isHomogeneous, isONE, isUnit, isZERO, iterator, leadingBaseCoefficient, leadingExpVector, leadingMonomial, length, map, maxNorm, modInverse, multiply, negate, numberOfVariables, quotientRemainder, reductum, remainder, reverse, scaleSubtractMultiple, scaleSubtractMultiple, signum, subtract, subtract, subtract, subtractMultiple, subtractMultiple, sum, sum, sum, sumNorm, toScript, toScriptFactory, toString, toString, totalDegree, trailingBaseCoefficient, trailingExpVector

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

ring

public final GenSolvablePolynomialRing<C extends RingElem<C>> ring

The factory for the solvable polynomial ring. Hides super.ring.

Constructor Detail

GenSolvablePolynomial

public GenSolvablePolynomial(GenSolvablePolynomialRing<C> r)

Constructor for zero GenSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

GenSolvablePolynomial

public GenSolvablePolynomial(GenSolvablePolynomialRing<C> r,
                             C c,
                             ExpVector e)

Constructor for GenSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient.

e - exponent.

GenSolvablePolynomial

public GenSolvablePolynomial(GenSolvablePolynomialRing<C> r,
                             C c)

Constructor for GenSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient.

Method Detail

factory

public GenSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<GenPolynomial<C extends RingElem<C>>>

Overrides:

factory in class GenPolynomial<C extends RingElem<C>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public GenSolvablePolynomial<C> copy()

Clone this GenSolvablePolynomial.

Specified by:

copy in interface Element<GenPolynomial<C extends RingElem<C>>>

Overrides:

copy in class GenPolynomial<C extends RingElem<C>>

Returns:

copy of this.

See Also:

Object.clone()

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

Specified by:

equals in interface Element<GenPolynomial<C extends RingElem<C>>>

Overrides:

equals in class GenPolynomial<C extends RingElem<C>>

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

public GenSolvablePolynomial<C> multiply(GenSolvablePolynomial<C> Bp)

GenSolvablePolynomial multiplication.

Parameters:

Bp - GenSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

public GenSolvablePolynomial<C> multiply(GenSolvablePolynomial<C> S,
                                         GenSolvablePolynomial<C> T)

GenSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - GenSolvablePolynomial.

T - GenSolvablePolynomial.

Returns:

S*this*T.

multiply

public GenSolvablePolynomial<C> multiply(C b)

GenSolvablePolynomial multiplication. Product with coefficient ring element.

Overrides:

multiply in class GenPolynomial<C extends RingElem<C>>

Parameters:

b - coefficient.

Returns:

this*b, where * is coefficient multiplication.

multiply

public GenSolvablePolynomial<C> multiply(C b,
                                         C c)

GenSolvablePolynomial left and right multiplication. Product with coefficient ring element.

Parameters:

b - coefficient.

c - coefficient.

Returns:

b*this*c, where * is coefficient multiplication.

multiply

public GenSolvablePolynomial<C> multiply(ExpVector e)

GenSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

multiply in class GenPolynomial<C extends RingElem<C>>

Parameters:

e - exponent.

Returns:

this * x^e, where * denotes solvable multiplication.

multiply

public GenSolvablePolynomial<C> multiply(ExpVector e,
                                         ExpVector f)

GenSolvablePolynomial left and right multiplication. Product with exponent vector.

Parameters:

e - exponent.

f - exponent.

Returns:

x^e * this * x^f, where * denotes solvable multiplication.

multiply

public GenSolvablePolynomial<C> multiply(C b,
                                         ExpVector e)

GenSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

multiply in class GenPolynomial<C extends RingElem<C>>

Parameters:

b - coefficient.

e - exponent.

Returns:

this * b x^e, where * denotes solvable multiplication.

multiply

public GenSolvablePolynomial<C> multiply(C b,
                                         ExpVector e,
                                         C c,
                                         ExpVector f)

GenSolvablePolynomial left and right multiplication. Product with ring element and exponent vector.

Parameters:

b - coefficient.

e - exponent.

c - coefficient.

f - exponent.

Returns:

b x^e * this * c x^f, where * denotes solvable multiplication.

multiplyLeft

public GenSolvablePolynomial<C> multiplyLeft(C b,
                                             ExpVector e)

GenSolvablePolynomial multiplication. Left product with ring element and exponent vector.

Parameters:

b - coefficient.

e - exponent.

Returns:

b x^e * this, where * denotes solvable multiplication.

multiplyLeft

public GenSolvablePolynomial<C> multiplyLeft(ExpVector e)

GenSolvablePolynomial multiplication. Left product with exponent vector.

Parameters:

e - exponent.

Returns:

x^e * this, where * denotes solvable multiplication.

multiplyLeft

public GenSolvablePolynomial<C> multiplyLeft(C b)

GenSolvablePolynomial multiplication. Left product with coefficient ring element.

Parameters:

b - coefficient.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

public GenSolvablePolynomial<C> multiplyLeft(java.util.Map.Entry<ExpVector,C> m)

GenSolvablePolynomial multiplication. Left product with 'monomial'.

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

public GenSolvablePolynomial<C> multiply(java.util.Map.Entry<ExpVector,C> m)

GenSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

multiply in class GenPolynomial<C extends RingElem<C>>

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

monic

public GenSolvablePolynomial<C> monic()

GenSolvablePolynomial monic, i.e. leadingCoefficient == 1. If leadingCoefficient is not invertible returns this unmodified.

Overrides:

monic in class GenPolynomial<C extends RingElem<C>>

Returns:

monic(this).

quotientRemainder

public GenSolvablePolynomial<C>[] quotientRemainder(GenSolvablePolynomial<C> S)

GenSolvablePolynomial left division with remainder. Fails, if exact division by leading base coefficient is not possible. Meaningful only for univariate polynomials over fields, but works in any case.

Parameters:

S - nonzero GenSolvablePolynomial with invertible leading coefficient.

Returns:

[ quotient , remainder ] with this = quotient * S + remainder and deg(remainder) < deg(S) or remiander = 0.

See Also:

PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial).