edu.jas.gbmod

Class QuotSolvablePolynomial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

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

edu.jas.gbmod.QuotSolvablePolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public class QuotSolvablePolynomial<C extends GcdRingElem<C>>
extends GenSolvablePolynomial<SolvableQuotient<C>>

QuotSolvablePolynomial generic recursive solvable polynomials implementing RingElem. n-variate ordered solvable polynomials over solvable polynomial 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.

See Also:

Serialized Form

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor and Description
QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r) Constructor for zero QuotSolvablePolynomial.
QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r, GenSolvablePolynomial<SolvableQuotient<C>> S) Constructor for QuotSolvablePolynomial.
QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r, SolvableQuotient<C> c) Constructor for QuotSolvablePolynomial.
QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r, SolvableQuotient<C> c, ExpVector e) Constructor for QuotSolvablePolynomial.

Method Summary

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

Methods inherited from class edu.jas.poly.GenSolvablePolynomial

monic, multiply, multiply, quotientRemainder

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 QuotSolvablePolynomialRing<C extends GcdRingElem<C>> ring

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

Constructor Detail

QuotSolvablePolynomial

public QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r)

Constructor for zero QuotSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

QuotSolvablePolynomial

public QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r,
                              SolvableQuotient<C> c,
                              ExpVector e)

Constructor for QuotSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

QuotSolvablePolynomial

public QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r,
                              SolvableQuotient<C> c)

Constructor for QuotSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

QuotSolvablePolynomial

public QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r,
                              GenSolvablePolynomial<SolvableQuotient<C>> S)

Constructor for QuotSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

Method Detail

factory

public QuotSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Overrides:

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

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public QuotSolvablePolynomial<C> copy()

Clone this QuotSolvablePolynomial.

Specified by:

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

Overrides:

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

Overrides:

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

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

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

QuotSolvablePolynomial multiplication.

Parameters:

Bp - QuotSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

QuotSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - QuotSolvablePolynomial.

T - QuotSolvablePolynomial.

Returns:

S*this*T.

multiply

public QuotSolvablePolynomial<C> multiply(SolvableQuotient<C> b)

QuotSolvablePolynomial multiplication. Product with coefficient ring element.

Overrides:

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

Parameters:

b - solvable coefficient.

Returns:

this*b, where * is coefficient multiplication.

multiply

public QuotSolvablePolynomial<C> multiply(SolvableQuotient<C> b,
                                          SolvableQuotient<C> c)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public QuotSolvablePolynomial<C> multiply(ExpVector e)

QuotSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiply

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

QuotSolvablePolynomial left and right multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public QuotSolvablePolynomial<C> multiply(SolvableQuotient<C> b,
                                          ExpVector e)

QuotSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

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

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

Overrides:

multiply in class GenSolvablePolynomial<SolvableQuotient<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 QuotSolvablePolynomial<C> multiplyLeft(SolvableQuotient<C> b,
                                              ExpVector e)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public QuotSolvablePolynomial<C> multiplyLeft(ExpVector e)

QuotSolvablePolynomial multiplication. Left product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public QuotSolvablePolynomial<C> multiplyLeft(SolvableQuotient<C> b)

QuotSolvablePolynomial multiplication. Left product with coefficient ring element.

Overrides:

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

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

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

QuotSolvablePolynomial multiplication. Left product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

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

QuotSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.