Package edu.jas.fd

Class QuotSolvablePolynomial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomial<C>

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

edu.jas.fd.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. Will be deprecated use QLRSolvablePolynomial.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

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

Method Summary

Modifier and Type	Method	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.
int	hashCode()	Hash code for this polynomial.
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, SolvableQuotient<C> c)	QuotSolvablePolynomial left and right 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(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>	multiplyLeft(SolvableQuotient<C> b)	QuotSolvablePolynomial multiplication.
QuotSolvablePolynomial<C>	multiplyLeft(SolvableQuotient<C> b, ExpVector e)	QuotSolvablePolynomial multiplication.
QuotSolvablePolynomial<C>	multiplyLeft(ExpVector e)	QuotSolvablePolynomial multiplication.
QuotSolvablePolynomial<C>	multiplyLeft(java.util.Map.Entry<ExpVector,SolvableQuotient<C>> m)	QuotSolvablePolynomial multiplication.
protected QuotSolvablePolynomial<C>	shift(ExpVector f)	QuotSolvablePolynomial 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, 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 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.

QuotSolvablePolynomial

protected QuotSolvablePolynomial(QuotSolvablePolynomialRing<C> r,
                                 java.util.SortedMap<ExpVector,SolvableQuotient<C>> v)

Constructor for QuotSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

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

Method Detail

factory

public QuotSolvablePolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<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<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<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)

hashCode

public int hashCode()

Hash code for this polynomial.

Specified by:

hashCode in interface Element<C extends GcdRingElem<C>>

Overrides:

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

Returns:

the hashCode.

See Also:

Object.hashCode()

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.

shift

protected QuotSolvablePolynomial<C> shift(ExpVector f)

QuotSolvablePolynomial multiplication. Left product with coefficient ring element.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.