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.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

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

Fields inherited from class edu.jas.poly.GenPolynomial

val

Constructor Summary

Constructors

Modifier	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.
protected	RecSolvablePolynomial(RecSolvablePolynomialRing<C> r, java.util.SortedMap<ExpVector,GenPolynomial<C>> v) 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.
GenSolvablePolynomial<GenPolynomial<C>>	evalAsRightRecursivePolynomial() Evaluate RecSolvablePolynomial as right coefficients polynomial.
RecSolvablePolynomialRing<C>	factory() Get the corresponding element factory.
boolean	isRightRecursivePolynomial(GenSolvablePolynomial<GenPolynomial<C>> R) Test RecSolvablePolynomial right coefficients polynomial.
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.
GenSolvablePolynomial<GenPolynomial<C>>	rightRecursivePolynomial() RecSolvablePolynomial right coefficients from left coefficients.
protected RecSolvablePolynomial<C>	shift(RecSolvablePolynomial<C> B, ExpVector f) RecSolvablePolynomial multiplication.

Methods inherited from class edu.jas.poly.GenSolvablePolynomial

monic, multiply, multiply, multiply, quotientRemainder, scaleSubtractMultiple, scaleSubtractMultiple, scaleSubtractMultiple, subtractMultiple, subtractMultiple

Methods inherited from class edu.jas.poly.GenPolynomial

abs, coefficient, coefficientIterator, compareTo, contract, contractCoeff, degree, degree, degreeVector, deHomogenize, deltaExpVectors, divide, divide, divideAndRemainder, doAddTo, doAddTo, doAddTo, doPutToMap, doPutToMap, doRemoveFromMap, egcd, exponentIterator, extend, extendLower, extendUnivariate, gcd, getMap, hashCode, hegcd, homogenize, inverse, isConstant, isHomogeneous, isONE, isUnit, isWeightHomogeneous, isZERO, iterator, leadingBaseCoefficient, leadingExpVector, leadingMonomial, leadingWeightPolynomial, length, map, maxNorm, modInverse, multiply, negate, numberOfVariables, quotientRemainder, reductum, remainder, reverse, scaleSubtractMultiple, scaleSubtractMultiple, scaleSubtractMultiple, signum, subtract, subtract, subtract, subtractMultiple, subtractMultiple, 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, 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.

RecSolvablePolynomial

protected RecSolvablePolynomial(RecSolvablePolynomialRing<C> r,
                                java.util.SortedMap<ExpVector,GenPolynomial<C>> v)

Constructor for RecSolvablePolynomial.

Parameters:

r - solvable polynomial ring factory.

v - the SortedMap of some other (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.

shift

protected RecSolvablePolynomial<C> shift(RecSolvablePolynomial<C> B,
                                         ExpVector f)

RecSolvablePolynomial multiplication. Commutative product with exponent vector.

Parameters:

B - solvable polynomial.

f - exponent vector.

Returns:

B*f, where * is commutative multiplication.

rightRecursivePolynomial

public GenSolvablePolynomial<GenPolynomial<C>> rightRecursivePolynomial()

RecSolvablePolynomial right coefficients from left coefficients. Note: R is represented as a polynomial with left coefficients, the implementation can at the moment not distinguish between left and right coefficients.

Overrides:

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

Returns:

R = sum( Xⁱ b_i ), with this = sum(a_i Xⁱ ) and eval(sum(Xⁱ b_i)) == sum(a_i Xⁱ)

evalAsRightRecursivePolynomial

public GenSolvablePolynomial<GenPolynomial<C>> evalAsRightRecursivePolynomial()

Evaluate RecSolvablePolynomial as right coefficients polynomial. Note: R is represented as a polynomial with left coefficients, the implementation can at the moment not distinguish between left and right coefficients.

Overrides:

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

Returns:

this as evaluated polynomial R. R = sum( Xⁱ b_i ), this = sum(a_i Xⁱ ) = eval(sum(Xⁱ b_i))

isRightRecursivePolynomial

public boolean isRightRecursivePolynomial(GenSolvablePolynomial<GenPolynomial<C>> R)

Test RecSolvablePolynomial right coefficients polynomial. Note: R is represented as a polynomial with left coefficients, the implementation can at the moment not distinguish between left and right coefficients.

Overrides:

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

Parameters:

R - GenSolvablePolynomial with right coefficients.

Returns:

true, if R is polynomial with right coefficients of this. R = sum( Xⁱ b_i ), with this = sum(a_i Xⁱ ) and eval(sum(Xⁱ b_i)) == sum(a_i Xⁱ)