edu.jas.application

Class ResidueSolvablePolynomial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

edu.jas.poly.GenSolvablePolynomial<SolvableResidue<C>>

edu.jas.application.ResidueSolvablePolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public class ResidueSolvablePolynomial<C extends GcdRingElem<C>>
extends GenSolvablePolynomial<SolvableResidue<C>>

ResidueSolvablePolynomial generic solvable polynomials with solvable residue coefficients implementing RingElem. n-variate ordered solvable polynomials over solvable residue coefficients. Objects of this class are intended to be immutable. The implementation is based on TreeMap respectively SortedMap from exponents to coefficients by extension of GenPolynomial.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

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

Fields inherited from class edu.jas.poly.GenPolynomial

blen, hash, val

Constructor Summary

Constructors

Modifier	Constructor and Description
	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r) Constructor for zero ResidueSolvablePolynomial.
	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r, ExpVector e) Constructor for ResidueSolvablePolynomial.
	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r, GenSolvablePolynomial<SolvableResidue<C>> S) Constructor for ResidueSolvablePolynomial.
	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r, SolvableResidue<C> c) Constructor for ResidueSolvablePolynomial.
	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r, SolvableResidue<C> c, ExpVector e) Constructor for ResidueSolvablePolynomial.
protected	ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r, java.util.SortedMap<ExpVector,SolvableResidue<C>> v) Constructor for ResidueSolvablePolynomial.

Method Summary

Modifier and Type	Method and Description
ResidueSolvablePolynomial<C>	copy() Clone this ResidueSolvablePolynomial.
boolean	equals(java.lang.Object B) Comparison with any other object.
ResidueSolvablePolynomialRing<C>	factory() Get the corresponding element factory.
ResidueSolvablePolynomial<C>	multiply(ExpVector e) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiply(ExpVector e, ExpVector f) ResidueSolvablePolynomial left and right multiplication.
ResidueSolvablePolynomial<C>	multiply(java.util.Map.Entry<ExpVector,SolvableResidue<C>> m) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiply(ResidueSolvablePolynomial<C> Bp) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiply(ResidueSolvablePolynomial<C> S, ResidueSolvablePolynomial<C> T) ResidueSolvablePolynomial left and right multiplication.
ResidueSolvablePolynomial<C>	multiply(SolvableResidue<C> b) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiply(SolvableResidue<C> b, ExpVector e) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiply(SolvableResidue<C> b, ExpVector e, SolvableResidue<C> c, ExpVector f) ResidueSolvablePolynomial left and right multiplication.
ResidueSolvablePolynomial<C>	multiply(SolvableResidue<C> b, SolvableResidue<C> c) ResidueSolvablePolynomial left and right multiplication.
ResidueSolvablePolynomial<C>	multiplyLeft(ExpVector e) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiplyLeft(java.util.Map.Entry<ExpVector,SolvableResidue<C>> m) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiplyLeft(SolvableResidue<C> b) ResidueSolvablePolynomial multiplication.
ResidueSolvablePolynomial<C>	multiplyLeft(SolvableResidue<C> b, ExpVector e) ResidueSolvablePolynomial multiplication.
protected ResidueSolvablePolynomial<C>	shift(ExpVector f) ResidueSolvablePolynomial multiplication with exponent vector.

Methods inherited from class edu.jas.poly.GenSolvablePolynomial

divide, evalAsRightRecursivePolynomial, isRightRecursivePolynomial, monic, multiply, multiply, quotientRemainder, remainder, rightDivide, rightQuotientRemainder, rightRecursivePolynomial, rightRemainder, scaleSubtractMultiple, scaleSubtractMultiple, scaleSubtractMultiple, subtractMultiple, subtractMultiple

Methods inherited from class edu.jas.poly.GenPolynomial

abs, bitLength, coefficient, coefficientIterator, compareTo, contract, contractCoeff, degree, degree, degreeMin, degreeVector, deHomogenize, deltaExpVectors, deltaExpVectors, divide, divide, doAddTo, doAddTo, doAddTo, doPutToMap, doPutToMap, doRemoveFromMap, egcd, exponentIterator, extend, extendLower, extendUnivariate, gcd, getMap, hashCode, hegcd, homogenize, inflate, inverse, isConstant, isHomogeneous, isONE, isUnit, isWeightHomogeneous, isZERO, iterator, leadingBaseCoefficient, leadingExpVector, leadingFacetPolynomial, leadingMonomial, leadingWeightPolynomial, leftDivideCoeff, length, map, mapOnStream, mapOnStream, maxNorm, modInverse, multiply, negate, negateAlt, numberOfVariables, quotientRemainder, reductum, remainder, reverse, rightDivideCoeff, scaleSubtractMultiple, scaleSubtractMultiple, scaleSubtractMultiple, signum, spliterator, subtract, subtract, subtract, subtract, subtractMultiple, subtractMultiple, sum, sum, sum, sum, sumNorm, toScript, toScriptFactory, toString, toString, totalDegree, trailingBaseCoefficient, trailingExpVector, weightDegree

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface java.lang.Iterable

forEach

Field Detail

ring

public final ResidueSolvablePolynomialRing<C extends GcdRingElem<C>> ring

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

Constructor Detail

ResidueSolvablePolynomial

public ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r)

Constructor for zero ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

ResidueSolvablePolynomial

public ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r,
                                 ExpVector e)

Constructor for ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

e - exponent.

ResidueSolvablePolynomial

public ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r,
                                 SolvableResidue<C> c,
                                 ExpVector e)

Constructor for ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

ResidueSolvablePolynomial

public ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r,
                                 SolvableResidue<C> c)

Constructor for ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

ResidueSolvablePolynomial

public ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r,
                                 GenSolvablePolynomial<SolvableResidue<C>> S)

Constructor for ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

ResidueSolvablePolynomial

protected ResidueSolvablePolynomial(ResidueSolvablePolynomialRing<C> r,
                                    java.util.SortedMap<ExpVector,SolvableResidue<C>> v)

Constructor for ResidueSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

v - the SortedMap of some other (solvable) polynomial.

Method Detail

factory

public ResidueSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<GenPolynomial<SolvableResidue<C extends GcdRingElem<C>>>>

Overrides:

factory in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public ResidueSolvablePolynomial<C> copy()

Clone this ResidueSolvablePolynomial.

Specified by:

copy in interface Element<GenPolynomial<SolvableResidue<C extends GcdRingElem<C>>>>

Overrides:

copy in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<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<SolvableResidue<C extends GcdRingElem<C>>>>

Overrides:

equals in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

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

ResidueSolvablePolynomial multiplication.

Parameters:

Bp - ResidueSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

ResidueSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - ResidueSolvablePolynomial.

T - ResidueSolvablePolynomial.

Returns:

S*this*T.

multiply

public ResidueSolvablePolynomial<C> multiply(SolvableResidue<C> b)

ResidueSolvablePolynomial multiplication. Product with coefficient ring element.

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

Returns:

this*b, where * is coefficient multiplication.

multiply

public ResidueSolvablePolynomial<C> multiply(SolvableResidue<C> b,
                                             SolvableResidue<C> c)

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

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public ResidueSolvablePolynomial<C> multiply(ExpVector e)

ResidueSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

e - exponent.

Returns:

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

multiply

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

ResidueSolvablePolynomial left and right multiplication. Product with exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public ResidueSolvablePolynomial<C> multiply(SolvableResidue<C> b,
                                             ExpVector e)

ResidueSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

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

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

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

e - exponent.

c - coefficient polynomial.

f - exponent.

Returns:

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

multiplyLeft

public ResidueSolvablePolynomial<C> multiplyLeft(SolvableResidue<C> b,
                                                 ExpVector e)

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

Overrides:

multiplyLeft in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public ResidueSolvablePolynomial<C> multiplyLeft(ExpVector e)

ResidueSolvablePolynomial multiplication. Left product with exponent vector.

Overrides:

multiplyLeft in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public ResidueSolvablePolynomial<C> multiplyLeft(SolvableResidue<C> b)

ResidueSolvablePolynomial multiplication. Left product with coefficient ring element.

Overrides:

multiplyLeft in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

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

ResidueSolvablePolynomial multiplication. Left product with 'monomial'.

Overrides:

multiplyLeft in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

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

ResidueSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

multiply in class GenSolvablePolynomial<SolvableResidue<C extends GcdRingElem<C>>>

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

shift

protected ResidueSolvablePolynomial<C> shift(ExpVector f)

ResidueSolvablePolynomial multiplication with exponent vector.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.