Class RecSolvableWordPolynomial<C extends RingElem<C>>

java.lang.Object

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

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

edu.jas.poly.RecSolvableWordPolynomial<C>

Type Parameters:

C - base coefficient type

All Implemented Interfaces:

AbelianGroupElem<GenPolynomial<GenWordPolynomial<C>>>, Element<GenPolynomial<GenWordPolynomial<C>>>, MonoidElem<GenPolynomial<GenWordPolynomial<C>>>, RingElem<GenPolynomial<GenWordPolynomial<C>>>, Serializable, Comparable<GenPolynomial<GenWordPolynomial<C>>>, Iterable<Monomial<GenWordPolynomial<C>>>

public class RecSolvableWordPolynomial<C extends RingElem<C>>
extends GenSolvablePolynomial<GenWordPolynomial<C>>

RecSolvableWordPolynomial generic recursive solvable polynomials implementing RingElem. n-variate ordered solvable polynomials over non-commutative word 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.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

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

Fields inherited from class GenPolynomial

blen, hash, val

Constructor Summary

Constructors

Modifier	Constructor	Description
	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r)	Constructor for zero RecSolvableWordPolynomial.
	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r, ExpVector e)	Constructor for RecSolvableWordPolynomial.
	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r, GenSolvablePolynomial<GenWordPolynomial<C>> S)	Constructor for RecSolvableWordPolynomial.
	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r, GenWordPolynomial<C> c)	Constructor for RecSolvableWordPolynomial.
	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r, GenWordPolynomial<C> c, ExpVector e)	Constructor for RecSolvableWordPolynomial.
protected	RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r, SortedMap<ExpVector, GenWordPolynomial<C>> v)	Constructor for RecSolvableWordPolynomial.

Method Summary

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

Methods inherited from class GenSolvablePolynomial

divide, evalAsRightRecursivePolynomial, isRightRecursivePolynomial, leftMonic, monic, multiply, multiply, multiply, quotientRemainder, remainder, rightDivide, rightMonic, rightQuotientRemainder, rightRecursivePolynomial, rightRemainder, scaleSubtractMultiple, scaleSubtractMultiple, scaleSubtractMultiple, subtractMultiple, subtractMultiple

Methods inherited from class GenPolynomial

abs, bitLength, coefficient, coefficientIterator, coeffPrimitivePart, 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, monicRight, multiply, negate, negateAlt, numberOfVariables, quotientRemainder, reductum, remainder, reverse, rightDivideCoeff, rightGcd, 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 Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface Iterable

forEach

Methods inherited from interface MonoidElem

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

Methods inherited from interface RingElem

leftGcd

Field Details

ring

public final RecSolvableWordPolynomialRing<C extends RingElem<C>> ring

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

Constructor Details

RecSolvableWordPolynomial

public RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r)

Constructor for zero RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

RecSolvableWordPolynomial

public RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r,
 ExpVector e)

Constructor for RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

e - exponent.

RecSolvableWordPolynomial

public RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r,
 GenWordPolynomial<C> c,
 ExpVector e)

Constructor for RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

e - exponent.

RecSolvableWordPolynomial

public RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r,
 GenWordPolynomial<C> c)

Constructor for RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

c - coefficient polynomial.

RecSolvableWordPolynomial

public RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r,
 GenSolvablePolynomial<GenWordPolynomial<C>> S)

Constructor for RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

S - solvable polynomial.

RecSolvableWordPolynomial

protected RecSolvableWordPolynomial(RecSolvableWordPolynomialRing<C> r,
 SortedMap<ExpVector, GenWordPolynomial<C>> v)

Constructor for RecSolvableWordPolynomial.

Parameters:

r - solvable polynomial ring factory.

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

Method Details

factory

public RecSolvableWordPolynomialRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Overrides:

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

Returns:

factory for this Element.

See Also:

• Element.factory()

copy

public RecSolvableWordPolynomial<C> copy()

Clone this RecSolvableWordPolynomial.

Specified by:

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

Overrides:

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

Returns:

copy of this.

See Also:

• Object.clone()

equals

public boolean equals(Object B)

Comparison with any other object.

Specified by:

equals in interface Element<C extends RingElem<C>>

Overrides:

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

Parameters:

B -

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 RingElem<C>>

Overrides:

hashCode in class GenSolvablePolynomial<GenWordPolynomial<C extends RingElem<C>>>

Returns:

the hashCode.

See Also:

• Object.hashCode()

multiply

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

RecSolvableWordPolynomial multiplication.

Parameters:

Bp - RecSolvableWordPolynomial.

Returns:

this*Bp, where * denotes solvable multiplication.

multiply

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

RecSolvableWordPolynomial left and right multiplication. Product with two polynomials.

Parameters:

S - RecSolvableWordPolynomial.

T - RecSolvableWordPolynomial.

Returns:

S*this*T.

recMultiply

public RecSolvableWordPolynomial<C> recMultiply(GenWordPolynomial<C> b)

RecSolvableWordPolynomial multiplication. Product with coefficient ring element.

Parameters:

b - coefficient polynomial.

Returns:

this*b, where * is coefficient multiplication.

multiply

public RecSolvableWordPolynomial<C> multiply(GenWordPolynomial<C> b,
 GenWordPolynomial<C> c)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

c - coefficient polynomial.

Returns:

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

multiply

public RecSolvableWordPolynomial<C> multiply(ExpVector e)

RecSolvableWordPolynomial multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiply

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

RecSolvableWordPolynomial left and right multiplication. Product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

f - exponent.

Returns:

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

multiply

public RecSolvableWordPolynomial<C> multiply(GenWordPolynomial<C> b,
 ExpVector e)

RecSolvableWordPolynomial multiplication. Product with ring element and exponent vector.

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiply

public RecSolvableWordPolynomial<C> multiply(GenWordPolynomial<C> b,
 ExpVector e,
 GenWordPolynomial<C> c,
 ExpVector f)

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

Overrides:

multiply in class GenSolvablePolynomial<GenWordPolynomial<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 RecSolvableWordPolynomial<C> multiplyLeft(GenWordPolynomial<C> b,
 ExpVector e)

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

Overrides:

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

Parameters:

b - coefficient polynomial.

e - exponent.

Returns:

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

multiplyLeft

public RecSolvableWordPolynomial<C> multiplyLeft(ExpVector e)

RecSolvableWordPolynomial multiplication. Left product with exponent vector.

Overrides:

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

Parameters:

e - exponent.

Returns:

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

multiplyLeft

public RecSolvableWordPolynomial<C> multiplyLeft(GenWordPolynomial<C> b)

RecSolvableWordPolynomial multiplication. Left product with coefficient ring element.

Overrides:

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

Parameters:

b - coefficient polynomial.

Returns:

b*this, where * is coefficient multiplication.

multiplyLeft

public RecSolvableWordPolynomial<C> multiplyLeft(Map.Entry<ExpVector, GenWordPolynomial<C>> m)

RecSolvableWordPolynomial multiplication. Left product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

m * this, where * denotes solvable multiplication.

multiply

public RecSolvableWordPolynomial<C> multiply(Map.Entry<ExpVector, GenWordPolynomial<C>> m)

RecSolvableWordPolynomial multiplication. Product with 'monomial'.

Overrides:

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

Parameters:

m - 'monomial'.

Returns:

this * m, where * denotes solvable multiplication.

shift

protected RecSolvableWordPolynomial<C> shift(ExpVector f)

RecSolvableWordPolynomial multiplication. Commutative product with exponent vector.

Parameters:

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.