edu.jas.application

Class ResidueSolvableWordPolynomial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

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

edu.jas.application.ResidueSolvableWordPolynomial<C>

Type Parameters:

C - base coefficient type

All Implemented Interfaces:

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

public class ResidueSolvableWordPolynomial<C extends GcdRingElem<C>>
extends GenSolvablePolynomial<WordResidue<C>>

ResidueSolvableWordPolynomial solvable polynomials with WordResidue coefficients implementing RingElem. n-variate ordered solvable polynomials over non-commutative word 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
ResidueSolvableWordPolynomialRing<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
	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r) Constructor for zero ResidueSolvableWordPolynomial.
	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r, ExpVector e) Constructor for ResidueSolvableWordPolynomial.
	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r, GenSolvablePolynomial<WordResidue<C>> S) Constructor for ResidueSolvableWordPolynomial.
protected	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r, java.util.SortedMap<ExpVector,WordResidue<C>> v) Constructor for ResidueSolvableWordPolynomial.
	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r, WordResidue<C> c) Constructor for ResidueSolvableWordPolynomial.
	ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r, WordResidue<C> c, ExpVector e) Constructor for ResidueSolvableWordPolynomial.

Method Summary

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

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 ResidueSolvableWordPolynomialRing<C extends GcdRingElem<C>> ring

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

Constructor Detail

ResidueSolvableWordPolynomial

public ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r)

Constructor for zero ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

ResidueSolvableWordPolynomial

public ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r,
                                     ExpVector e)

Constructor for ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

e - exponent.

ResidueSolvableWordPolynomial

public ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r,
                                     WordResidue<C> c,
                                     ExpVector e)

Constructor for ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient word residue.

e - exponent.

ResidueSolvableWordPolynomial

public ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r,
                                     WordResidue<C> c)

Constructor for ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient word residue.

ResidueSolvableWordPolynomial

public ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r,
                                     GenSolvablePolynomial<WordResidue<C>> S)

Constructor for ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

ResidueSolvableWordPolynomial

protected ResidueSolvableWordPolynomial(ResidueSolvableWordPolynomialRing<C> r,
                                        java.util.SortedMap<ExpVector,WordResidue<C>> v)

Constructor for ResidueSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

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

Method Detail

factory

public ResidueSolvableWordPolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Overrides:

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

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public ResidueSolvableWordPolynomial<C> copy()

Clone this ResidueSolvableWordPolynomial.

Specified by:

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

Overrides:

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

Overrides:

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

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

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

ResidueSolvableWordPolynomial multiplication.

Parameters:

Bp - ResidueSolvableWordPolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

ResidueSolvableWordPolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - ResidueSolvableWordPolynomial.

T - ResidueSolvableWordPolynomial.

Returns:

S*this*T.

multiply

public ResidueSolvableWordPolynomial<C> multiply(WordResidue<C> b)

ResidueSolvableWordPolynomial multiplication. Product with coefficient ring element.

Overrides:

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

Parameters:

b - coefficient polynomial.

Returns:

this*b, where * is coefficient multiplication.

multiply

public ResidueSolvableWordPolynomial<C> multiply(WordResidue<C> b,
                                                 WordResidue<C> c)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public ResidueSolvableWordPolynomial<C> multiply(ExpVector e)

ResidueSolvableWordPolynomial multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiply

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

ResidueSolvableWordPolynomial left and right multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public ResidueSolvableWordPolynomial<C> multiply(WordResidue<C> b,
                                                 ExpVector e)

ResidueSolvableWordPolynomial multiplication. Product with ring element and exponent vector.

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

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

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

Overrides:

multiply in class GenSolvablePolynomial<WordResidue<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 ResidueSolvableWordPolynomial<C> multiplyLeft(WordResidue<C> b,
                                                     ExpVector e)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public ResidueSolvableWordPolynomial<C> multiplyLeft(ExpVector e)

ResidueSolvableWordPolynomial multiplication. Left product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public ResidueSolvableWordPolynomial<C> multiplyLeft(WordResidue<C> b)

ResidueSolvableWordPolynomial multiplication. Left product with coefficient ring element.

Overrides:

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

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

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

ResidueSolvableWordPolynomial multiplication. Left product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

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

ResidueSolvableWordPolynomial multiplication. Product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

shift

protected ResidueSolvableWordPolynomial<C> shift(ExpVector f)

ResidueSolvableWordPolynomial multiplication. Commutative product with exponent vector.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.