Package edu.jas.poly

Class QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

edu.jas.poly.GenSolvablePolynomial<C>

edu.jas.poly.QLRSolvablePolynomial<C,D>

Type Parameters:

C - polynomial coefficient type

D - quotient coefficient type

All Implemented Interfaces:

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

public class QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>
extends GenSolvablePolynomial<C>

QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem. n-variate ordered solvable polynomials over solvable quotient, local and local-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	Description
QLRSolvablePolynomialRing<C,D>	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	Description
	QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r)	Constructor for zero QLRSolvablePolynomial.
	QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r, C c)	Constructor for QLRSolvablePolynomial.
	QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r, C c, ExpVector e)	Constructor for QLRSolvablePolynomial.
	QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r, GenSolvablePolynomial<C> S)	Constructor for QLRSolvablePolynomial.
protected	QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r, java.util.SortedMap<ExpVector,C> v)	Constructor for QLRSolvablePolynomial.

Method Summary

Modifier and Type	Method	Description
QLRSolvablePolynomial<C,D>	copy()	Clone this QLRSolvablePolynomial.
boolean	equals(java.lang.Object B)	Comparison with any other object.
QLRSolvablePolynomialRing<C,D>	factory()	Get the corresponding element factory.
int	hashCode()	Hash code for this polynomial.
QLRSolvablePolynomial<C,D>	multiply(C b)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiply(C b, C c)	QLRSolvablePolynomial left and right multiplication.
QLRSolvablePolynomial<C,D>	multiply(C b, ExpVector e)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiply(C b, ExpVector e, C c, ExpVector f)	QLRSolvablePolynomial left and right multiplication.
QLRSolvablePolynomial<C,D>	multiply(ExpVector e)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiply(ExpVector e, ExpVector f)	QLRSolvablePolynomial left and right multiplication.
QLRSolvablePolynomial<C,D>	multiply(QLRSolvablePolynomial<C,D> Bp)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiply(QLRSolvablePolynomial<C,D> S, QLRSolvablePolynomial<C,D> T)	QLRSolvablePolynomial left and right multiplication.
QLRSolvablePolynomial<C,D>	multiply(java.util.Map.Entry<ExpVector,C> m)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiplyLeft(C b)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiplyLeft(C b, ExpVector e)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiplyLeft(ExpVector e)	QLRSolvablePolynomial multiplication.
QLRSolvablePolynomial<C,D>	multiplyLeft(java.util.Map.Entry<ExpVector,C> m)	QLRSolvablePolynomial multiplication.
protected QLRSolvablePolynomial<C,D>	shift(ExpVector f)	QLRSolvablePolynomial 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, 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, squareNorm, 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 java.lang.Iterable

forEach

Methods inherited from interface edu.jas.structure.MonoidElem

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

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Field Detail

ring

public final QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>> ring

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

Constructor Detail

QLRSolvablePolynomial

public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r)

Constructor for zero QLRSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

QLRSolvablePolynomial

public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r,
                             C c,
                             ExpVector e)

Constructor for QLRSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

QLRSolvablePolynomial

public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r,
                             C c)

Constructor for QLRSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

QLRSolvablePolynomial

public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r,
                             GenSolvablePolynomial<C> S)

Constructor for QLRSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

QLRSolvablePolynomial

protected QLRSolvablePolynomial(QLRSolvablePolynomialRing<C,D> r,
                                java.util.SortedMap<ExpVector,C> v)

Constructor for QLRSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

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

Method Detail

factory

public QLRSolvablePolynomialRing<C,D> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Overrides:

factory in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public QLRSolvablePolynomial<C,D> copy()

Clone this QLRSolvablePolynomial.

Specified by:

copy in interface Element<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Overrides:

copy in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Overrides:

equals in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial.

Specified by:

hashCode in interface Element<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Overrides:

hashCode in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

the hashCode.

See Also:

Object.hashCode()

multiply

public QLRSolvablePolynomial<C,D> multiply(QLRSolvablePolynomial<C,D> Bp)

QLRSolvablePolynomial multiplication.

Parameters:

Bp - QLRSolvablePolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

public QLRSolvablePolynomial<C,D> multiply(QLRSolvablePolynomial<C,D> S,
                                                 QLRSolvablePolynomial<C,D> T)

QLRSolvablePolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - QLRSolvablePolynomial.

T - QLRSolvablePolynomial.

Returns:

S*this*T.

multiply

public QLRSolvablePolynomial<C,D> multiply(C b)

QLRSolvablePolynomial multiplication. Product with coefficient ring element.

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

b - solvable coefficient.

Returns:

this*b, where * is coefficient multiplication.

multiply

public QLRSolvablePolynomial<C,D> multiply(C b,
                                                 C c)

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

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public QLRSolvablePolynomial<C,D> multiply(ExpVector e)

QLRSolvablePolynomial multiplication. Product with exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

e - exponent.

Returns:

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

multiply

public QLRSolvablePolynomial<C,D> multiply(ExpVector e,
                                                 ExpVector f)

QLRSolvablePolynomial left and right multiplication. Product with exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public QLRSolvablePolynomial<C,D> multiply(C b,
                                                 ExpVector e)

QLRSolvablePolynomial multiplication. Product with ring element and exponent vector.

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

public QLRSolvablePolynomial<C,D> multiply(C b,
                                                 ExpVector e,
                                                 C c,
                                                 ExpVector f)

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

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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 QLRSolvablePolynomial<C,D> multiplyLeft(C b,
                                                     ExpVector e)

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

Overrides:

multiplyLeft in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public QLRSolvablePolynomial<C,D> multiplyLeft(ExpVector e)

QLRSolvablePolynomial multiplication. Left product with exponent vector.

Overrides:

multiplyLeft in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public QLRSolvablePolynomial<C,D> multiplyLeft(C b)

QLRSolvablePolynomial multiplication. Left product with coefficient ring element.

Overrides:

multiplyLeft in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

public QLRSolvablePolynomial<C,D> multiplyLeft(java.util.Map.Entry<ExpVector,C> m)

QLRSolvablePolynomial multiplication. Left product with 'monomial'.

Overrides:

multiplyLeft in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

public QLRSolvablePolynomial<C,D> multiply(java.util.Map.Entry<ExpVector,C> m)

QLRSolvablePolynomial multiplication. Product with 'monomial'.

Overrides:

multiply in class GenSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

shift

protected QLRSolvablePolynomial<C,D> shift(ExpVector f)

QLRSolvablePolynomial multiplication with exponent vector.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.