edu.jas.poly

Class RecSolvablePolynomial<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

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

edu.jas.poly.RecSolvablePolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

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

RecSolvablePolynomial 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
RecSolvablePolynomialRing<C>	ring The factory for the recursive solvable polynomial ring.

Constructor Summary

Constructors

Constructor and Description
RecSolvablePolynomial(RecSolvablePolynomialRing<C> r) Constructor for zero RecSolvablePolynomial.
RecSolvablePolynomial(RecSolvablePolynomialRing<C> r, ExpVector e) Constructor for RecSolvablePolynomial.
RecSolvablePolynomial(RecSolvablePolynomialRing<C> r, GenPolynomial<C> c) Constructor for RecSolvablePolynomial.
RecSolvablePolynomial(RecSolvablePolynomialRing<C> r, GenPolynomial<C> c, ExpVector e) Constructor for RecSolvablePolynomial.
RecSolvablePolynomial(RecSolvablePolynomialRing<C> r, GenSolvablePolynomial<GenPolynomial<C>> S) Constructor for RecSolvablePolynomial.

Method Summary

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

Methods inherited from class edu.jas.poly.GenSolvablePolynomial

monic, multiply, 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 RecSolvablePolynomialRing<C extends RingElem<C>> ring

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

Constructor Detail

RecSolvablePolynomial

public RecSolvablePolynomial(RecSolvablePolynomialRing<C> r)

Constructor for zero RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

RecSolvablePolynomial

public RecSolvablePolynomial(RecSolvablePolynomialRing<C> r,
                             ExpVector e)

Constructor for RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

e - exponent.

RecSolvablePolynomial

public RecSolvablePolynomial(RecSolvablePolynomialRing<C> r,
                             GenPolynomial<C> c,
                             ExpVector e)

Constructor for RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

RecSolvablePolynomial

public RecSolvablePolynomial(RecSolvablePolynomialRing<C> r,
                             GenPolynomial<C> c)

Constructor for RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

RecSolvablePolynomial

public RecSolvablePolynomial(RecSolvablePolynomialRing<C> r,
                             GenSolvablePolynomial<GenPolynomial<C>> S)

Constructor for RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

Method Detail

factory

public RecSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Overrides:

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

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public RecSolvablePolynomial<C> copy()

Clone this RecSolvablePolynomial.

Specified by:

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

Overrides:

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

Overrides:

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

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

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

RecSolvablePolynomial multiplication.

Parameters:

Bp - RecSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

RecSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - RecSolvablePolynomial.

T - RecSolvablePolynomial.

Returns:

S*this*T.

recMultiply

public RecSolvablePolynomial<C> recMultiply(GenPolynomial<C> b)

RecSolvablePolynomial multiplication. Product with coefficient ring element.

Parameters:

b - coefficient polynomial.

Returns:

this*b, where * is coefficient multiplication.

multiply

public RecSolvablePolynomial<C> multiply(GenPolynomial<C> b,
                                         GenPolynomial<C> c)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public RecSolvablePolynomial<C> multiply(ExpVector e)

RecSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiply

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

RecSolvablePolynomial left and right multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public RecSolvablePolynomial<C> multiply(GenPolynomial<C> b,
                                         ExpVector e)

RecSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

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

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

Overrides:

multiply in class GenSolvablePolynomial<GenPolynomial<C extends RingElem<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 RecSolvablePolynomial<C> multiplyLeft(GenPolynomial<C> b,
                                             ExpVector e)

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

Overrides:

multiplyLeft in class GenSolvablePolynomial<GenPolynomial<C extends RingElem<C>>>

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public RecSolvablePolynomial<C> multiplyLeft(ExpVector e)

RecSolvablePolynomial multiplication. Left product with exponent vector.

Overrides:

multiplyLeft in class GenSolvablePolynomial<GenPolynomial<C extends RingElem<C>>>

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public RecSolvablePolynomial<C> multiplyLeft(GenPolynomial<C> b)

RecSolvablePolynomial multiplication. Left product with coefficient ring element.

Overrides:

multiplyLeft in class GenSolvablePolynomial<GenPolynomial<C extends RingElem<C>>>

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

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

RecSolvablePolynomial multiplication. Left product with 'monomial'.

Overrides:

multiplyLeft in class GenSolvablePolynomial<GenPolynomial<C extends RingElem<C>>>

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

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

RecSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.