edu.jas.application

Class LocalSolvablePolynomial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

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

edu.jas.application.LocalSolvablePolynomial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public class LocalSolvablePolynomial<C extends GcdRingElem<C>>
extends GenSolvablePolynomial<SolvableLocal<C>>

LocalSolvablePolynomial 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. Will be deprecated use QLRSolvablePolynomial.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
LocalSolvablePolynomialRing<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
	LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r) Constructor for zero LocalSolvablePolynomial.
	LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, GenSolvablePolynomial<SolvableLocal<C>> S) Constructor for LocalSolvablePolynomial.
	LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, SolvableLocal<C> c) Constructor for LocalSolvablePolynomial.
	LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, SolvableLocal<C> c, ExpVector e) Constructor for LocalSolvablePolynomial.
protected	LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, java.util.SortedMap<ExpVector,SolvableLocal<C>> v) Constructor for LocalSolvablePolynomial.

Method Summary

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

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

Constructor Detail

LocalSolvablePolynomial

public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r)

Constructor for zero LocalSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

LocalSolvablePolynomial

public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r,
                               SolvableLocal<C> c,
                               ExpVector e)

Constructor for LocalSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

LocalSolvablePolynomial

public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r,
                               SolvableLocal<C> c)

Constructor for LocalSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

LocalSolvablePolynomial

public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r,
                               GenSolvablePolynomial<SolvableLocal<C>> S)

Constructor for LocalSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

LocalSolvablePolynomial

protected LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r,
                                  java.util.SortedMap<ExpVector,SolvableLocal<C>> v)

Constructor for LocalSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

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

Method Detail

factory

public LocalSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Overrides:

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

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public LocalSolvablePolynomial<C> copy()

Clone this LocalSolvablePolynomial.

Specified by:

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

Overrides:

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

Overrides:

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

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

multiply

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

LocalSolvablePolynomial multiplication.

Parameters:

Bp - LocalSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

LocalSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - LocalSolvablePolynomial.

T - LocalSolvablePolynomial.

Returns:

S*this*T.

multiply

public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b)

LocalSolvablePolynomial multiplication. Product with coefficient ring element.

Overrides:

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

Parameters:

b - solvable coefficient.

Returns:

this*b, where * is coefficient multiplication.

multiply

public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b,
                                           SolvableLocal<C> c)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public LocalSolvablePolynomial<C> multiply(ExpVector e)

LocalSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiply

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

LocalSolvablePolynomial left and right multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b,
                                           ExpVector e)

LocalSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

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

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

Overrides:

multiply in class GenSolvablePolynomial<SolvableLocal<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 LocalSolvablePolynomial<C> multiplyLeft(SolvableLocal<C> b,
                                               ExpVector e)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public LocalSolvablePolynomial<C> multiplyLeft(ExpVector e)

LocalSolvablePolynomial multiplication. Left product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public LocalSolvablePolynomial<C> multiplyLeft(SolvableLocal<C> b)

LocalSolvablePolynomial multiplication. Left product with coefficient ring element.

Overrides:

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

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

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

LocalSolvablePolynomial multiplication. Left product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

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

LocalSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

shift

protected LocalSolvablePolynomial<C> shift(ExpVector f)

LocalSolvablePolynomial multiplication. Left product with coefficient ring element.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.