edu.jas.application

Class ResidueSolvableWordPolynomialRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomialRing<C>

edu.jas.poly.GenSolvablePolynomialRing<WordResidue<C>>

edu.jas.application.ResidueSolvableWordPolynomialRing<C>

Type Parameters:

C - base coefficient type.

All Implemented Interfaces:

AbelianGroupFactory<GenPolynomial<WordResidue<C>>>, ElemFactory<GenPolynomial<WordResidue<C>>>, MonoidFactory<GenPolynomial<WordResidue<C>>>, RingFactory<GenPolynomial<WordResidue<C>>>, java.io.Serializable, java.lang.Iterable<GenPolynomial<WordResidue<C>>>

public class ResidueSolvableWordPolynomialRing<C extends GcdRingElem<C>>
extends GenSolvablePolynomialRing<WordResidue<C>>

ResidueSolvableWordPolynomialRing solvable polynomial with word residue coefficients factory. It implements RingFactory and extends GenSolvablePolynomialRing factory. Factory for n-variate ordered solvable polynomials over non-commutative word residue coefficients. The non-commutative multiplication relations are maintained in a relation table and the non-commutative multiplication relations between the coefficients and the main variables are maintained in a coefficient relation table. Almost immutable object, except variable names and relation table contents.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
ResidueSolvableWordPolynomial<C>	ONE The constant polynomial 1 for this ring.
RecSolvableWordPolynomialRing<C>	polCoeff Recursive solvable polynomial ring with polynomial coefficients.
ResidueSolvableWordPolynomial<C>	ZERO The constant polynomial 0 for this ring.

Fields inherited from class edu.jas.poly.GenSolvablePolynomialRing

table

Fields inherited from class edu.jas.poly.GenPolynomialRing

coFac, evzero, isField, nvar, partial, random, tord, vars

Constructor Summary

Constructors

Constructor and Description
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n) The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n, RelationTable<WordResidue<C>> rt) The constructor creates a solvable polynomial factory object with the default term order.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n, TermOrder t) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n, TermOrder t, RelationTable<WordResidue<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n, TermOrder t, java.lang.String[] v) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, int n, TermOrder t, java.lang.String[] v, RelationTable<WordResidue<C>> rt) The constructor creates a solvable polynomial factory object with the given term order.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, ResidueSolvableWordPolynomialRing o) The constructor creates a solvable polynomial factory object with the the same term order, number of variables and variable names as the given polynomial factory, only the coefficient factories differ and the solvable multiplication relations are empty.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, java.lang.String[] v) The constructor creates a solvable polynomial factory object with the default term order.
ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf, TermOrder t, java.lang.String[] v) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.

Method Summary

Modifier and Type	Method and Description
ResidueSolvableWordPolynomialRing<C>	contract(int i) Contract variables.
ResidueSolvableWordPolynomial<C>	copy(ResidueSolvableWordPolynomial<C> c) Copy polynomial c.
boolean	equals(java.lang.Object other) Comparison with any other object.
ResidueSolvableWordPolynomialRing<C>	extend(int i) Extend variables.
ResidueSolvableWordPolynomialRing<C>	extend(int i, boolean top) Extend variables.
ResidueSolvableWordPolynomialRing<C>	extend(java.lang.String[] vs) Extend variables.
ResidueSolvableWordPolynomialRing<C>	extend(java.lang.String[] vs, boolean top) Extend variables.
ResidueSolvableWordPolynomial<C>	fromInteger(java.math.BigInteger a) Get a (constant) ResidueSolvableWordPolynomial<C> element from a BigInteger value.
ResidueSolvableWordPolynomial<C>	fromInteger(long a) Get a (constant) ResidueSolvableWordPolynomial<C> element from a long value.
ResidueSolvableWordPolynomial<C>	fromPolyCoefficients(GenSolvablePolynomial<GenWordPolynomial<C>> A) Word residue coefficients from integral word polynomial coefficients.
ResidueSolvableWordPolynomial<C>	getONE() Get the one element.
ResidueSolvableWordPolynomial<C>	getZERO() Get the zero element.
int	hashCode() Hash code for this polynomial ring.
boolean	isAssociative() Query if this ring is associative.
boolean	isCommutative() Query if this ring is commutative.
ResidueSolvableWordPolynomial<C>	parse(java.io.Reader r) Parse a solvable polynomial with the use of GenPolynomialTokenizer
ResidueSolvableWordPolynomial<C>	parse(java.lang.String s) Parse a solvable polynomial with the use of GenPolynomialTokenizer
GenSolvablePolynomialRing<WordResidue<C>>	permutation(java.util.List<java.lang.Integer> P) Permutation of polynomial ring variables.
ResidueSolvableWordPolynomial<C>	random(int n) Random solvable polynomial.
ResidueSolvableWordPolynomial<C>	random(int k, int l, int d, float q) Generate a random solvable polynomial.
ResidueSolvableWordPolynomial<C>	random(int k, int l, int d, float q, java.util.Random rnd) Random solvable polynomial.
ResidueSolvableWordPolynomial<C>	random(int n, java.util.Random rnd) Random solvable polynomial.
ResidueSolvableWordPolynomialRing<C>	reverse() Reverse variables.
ResidueSolvableWordPolynomialRing<C>	reverse(boolean partial) Reverse variables.
RecSolvableWordPolynomial<C>	toPolyCoefficients(GenPolynomial<WordResidue<C>> A) Integral word function from word residue coefficients.
RecSolvableWordPolynomial<C>	toPolyCoefficients(ResidueSolvableWordPolynomial<C> A) Integral word function from word residue coefficients.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() Get the String representation.
ResidueSolvableWordPolynomial<C>	univariate(int i) Generate univariate solvable polynomial in a given variable.
ResidueSolvableWordPolynomial<C>	univariate(int modv, int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.
ResidueSolvableWordPolynomial<C>	univariate(int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.
java.util.List<ResidueSolvableWordPolynomial<C>>	univariateList() Generate list of univariate polynomials in all variables.
java.util.List<ResidueSolvableWordPolynomial<C>>	univariateList(int modv) Generate list of univariate polynomials in all variables.
java.util.List<ResidueSolvableWordPolynomial<C>>	univariateList(int modv, long e) Generate list of univariate polynomials in all variables with given exponent.
ResidueSolvableWordPolynomial<C>	valueOf(ExpVector e) Get a ResidueSolvableWordPolynomial<C> element from an ExpVector.
ResidueSolvableWordPolynomial<C>	valueOf(WordResidue<C> a) Get a (constant) ResidueSolvableWordPolynomial<C> element from a coefficient value.
ResidueSolvableWordPolynomial<C>	valueOf(WordResidue<C> a, ExpVector e) Get a ResidueSolvableWordPolynomial<C> element from a coeffcient and an ExpVector.

Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing

addRelations, addRelations, addSolvRelations, copy, distribute, recursive

Methods inherited from class edu.jas.poly.GenPolynomialRing

characteristic, copy, copy, copy, extendLower, extendLower, generators, generators, getComparator, getComparator, getCreations, getGenerators, getONECoefficient, getVars, getZEROCoefficient, isField, isFinite, iterator, newVars, newVars, newVars, newVars, permuteVars, setVars, toScript, univariate, univariate, valueOf, valueOf, varsToString

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

polCoeff

public final RecSolvableWordPolynomialRing<C extends GcdRingElem<C>> polCoeff

Recursive solvable polynomial ring with polynomial coefficients.

ZERO

public final ResidueSolvableWordPolynomial<C extends GcdRingElem<C>> ZERO

The constant polynomial 0 for this ring. Hides super ZERO.

ONE

public final ResidueSolvableWordPolynomial<C extends GcdRingElem<C>> ONE

The constant polynomial 1 for this ring. Hides super ONE.

Constructor Detail

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n)

The constructor creates a solvable polynomial factory object with the default term order and commutative relations.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n,
                                         RelationTable<WordResidue<C>> rt)

The constructor creates a solvable polynomial factory object with the default term order.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

rt - solvable multiplication relations.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n,
                                         TermOrder t)

The constructor creates a solvable polynomial factory object with the given term order and commutative relations.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

t - a term order.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n,
                                         TermOrder t,
                                         RelationTable<WordResidue<C>> rt)

The constructor creates a solvable polynomial factory object with the given term order.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

t - a term order.

rt - solvable multiplication relations.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n,
                                         TermOrder t,
                                         java.lang.String[] v)

The constructor creates a solvable polynomial factory object with the given term order and commutative relations.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

t - a term order.

v - names for the variables.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         TermOrder t,
                                         java.lang.String[] v)

The constructor creates a solvable polynomial factory object with the given term order and commutative relations.

Parameters:

cf - factory for coefficients of type C.

t - a term order.

v - names for the variables.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         java.lang.String[] v)

The constructor creates a solvable polynomial factory object with the default term order.

Parameters:

cf - factory for coefficients of type C.

v - names for the variables.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         int n,
                                         TermOrder t,
                                         java.lang.String[] v,
                                         RelationTable<WordResidue<C>> rt)

The constructor creates a solvable polynomial factory object with the given term order.

Parameters:

cf - factory for coefficients of type C.

n - number of variables.

t - a term order.

v - names for the variables.

rt - solvable multiplication relations.

ResidueSolvableWordPolynomialRing

public ResidueSolvableWordPolynomialRing(RingFactory<WordResidue<C>> cf,
                                         ResidueSolvableWordPolynomialRing o)

The constructor creates a solvable polynomial factory object with the the same term order, number of variables and variable names as the given polynomial factory, only the coefficient factories differ and the solvable multiplication relations are empty.

Parameters:

cf - factory for coefficients of type C.

o - other solvable polynomial ring.

Method Detail

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

toScript in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

equals

public boolean equals(java.lang.Object other)

Comparison with any other object.

Overrides:

equals in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

hashCode in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

See Also:

Object.hashCode()

getZERO

public ResidueSolvableWordPolynomial<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

getZERO in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

0 as ResidueSolvableWordPolynomial.

getONE

public ResidueSolvableWordPolynomial<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

getONE in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

1 as ResidueSolvableWordPolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

isCommutative in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

true if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative. Test if the relations between the mian variables and the coefficient generators define an associative solvable ring.

Specified by:

isAssociative in interface MonoidFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

isAssociative in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

true, if this ring is associative, else false.

valueOf

public ResidueSolvableWordPolynomial<C> valueOf(WordResidue<C> a)

Get a (constant) ResidueSolvableWordPolynomial<C> element from a coefficient value.

Overrides:

valueOf in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

a - coefficient.

Returns:

a ResidueSolvableWordPolynomial<C>.

valueOf

public ResidueSolvableWordPolynomial<C> valueOf(ExpVector e)

Get a ResidueSolvableWordPolynomial<C> element from an ExpVector.

Overrides:

valueOf in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

e - exponent vector.

Returns:

a ResidueSolvableWordPolynomial<C>.

valueOf

public ResidueSolvableWordPolynomial<C> valueOf(WordResidue<C> a,
                                                ExpVector e)

Get a ResidueSolvableWordPolynomial<C> element from a coeffcient and an ExpVector.

Overrides:

valueOf in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a ResidueSolvableWordPolynomial<C>.

fromInteger

public ResidueSolvableWordPolynomial<C> fromInteger(long a)

Get a (constant) ResidueSolvableWordPolynomial<C> element from a long value.

Specified by:

fromInteger in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

a - long.

Returns:

a ResidueSolvableWordPolynomial<C>.

fromInteger

public ResidueSolvableWordPolynomial<C> fromInteger(java.math.BigInteger a)

Get a (constant) ResidueSolvableWordPolynomial<C> element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

a - BigInteger.

Returns:

a ResidueSolvableWordPolynomial<C>.

random

public ResidueSolvableWordPolynomial<C> random(int n)

Random solvable polynomial. Generates a random solvable polynomial with k = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.

Specified by:

random in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

random in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

n - number of terms.

Returns:

a random solvable polynomial.

random

public ResidueSolvableWordPolynomial<C> random(int n,
                                               java.util.Random rnd)

Random solvable polynomial. Generates a random solvable polynomial with k = 5, l = n, d = (nvar == 1) ? n : 3, q = (nvar == 1) ? 0.7 : 0.3.

Specified by:

random in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

random in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

random

public ResidueSolvableWordPolynomial<C> random(int k,
                                               int l,
                                               int d,
                                               float q)

Generate a random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

k - bitsize of random coefficients.

l - number of terms.

d - maximal degree in each variable.

q - density of nozero exponents.

Returns:

a random solvable polynomial.

random

public ResidueSolvableWordPolynomial<C> random(int k,
                                               int l,
                                               int d,
                                               float q,
                                               java.util.Random rnd)

Random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

k - size of random coefficients.

l - number of terms.

d - maximal degree in each variable.

q - density of nozero exponents.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

copy

public ResidueSolvableWordPolynomial<C> copy(ResidueSolvableWordPolynomial<C> c)

Copy polynomial c.

Parameters:

c -

Returns:

a copy of c.

parse

public ResidueSolvableWordPolynomial<C> parse(java.lang.String s)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

parse in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

s - String.

Returns:

ResidueSolvableWordPolynomial from s.

parse

public ResidueSolvableWordPolynomial<C> parse(java.io.Reader r)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<GenPolynomial<WordResidue<C extends GcdRingElem<C>>>>

Overrides:

parse in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

r - Reader.

Returns:

next ResidueSolvableWordPolynomial from r.

univariate

public ResidueSolvableWordPolynomial<C> univariate(int i)

Generate univariate solvable polynomial in a given variable.

Overrides:

univariate in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

i - the index of the variable.

Returns:

X_i as solvable univariate polynomial.

univariate

public ResidueSolvableWordPolynomial<C> univariate(int i,
                                                   long e)

Generate univariate solvable polynomial in a given variable with given exponent.

Overrides:

univariate in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as solvable univariate polynomial.

univariate

public ResidueSolvableWordPolynomial<C> univariate(int modv,
                                                   int i,
                                                   long e)

Generate univariate solvable polynomial in a given variable with given exponent.

Overrides:

univariate in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as solvable univariate polynomial.

univariateList

public java.util.List<ResidueSolvableWordPolynomial<C>> univariateList()

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

List(X_1,...,X_n) a list of univariate polynomials.

univariateList

public java.util.List<ResidueSolvableWordPolynomial<C>> univariateList(int modv)

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

Returns:

List(X_1,...,X_n) a list of univariate polynomials.

univariateList

public java.util.List<ResidueSolvableWordPolynomial<C>> univariateList(int modv,
                                                                       long e)

Generate list of univariate polynomials in all variables with given exponent.

Overrides:

univariateList in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

e - the exponent of the variables.

Returns:

List(X_1^e,...,X_n^e) a list of univariate polynomials.

extend

public ResidueSolvableWordPolynomialRing<C> extend(int i)

Extend variables. Used e.g. in module embedding. Extend number of variables by i.

Overrides:

extend in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

i - number of variables to extend.

Returns:

extended solvable polynomial ring factory.

extend

public ResidueSolvableWordPolynomialRing<C> extend(int i,
                                                   boolean top)

Extend variables. Used e.g. in module embedding. Extend number of variables by i.

Overrides:

extend in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

i - number of variables to extend.

top - true for TOP term order, false for POT term order.

Returns:

extended solvable polynomial ring factory.

extend

public ResidueSolvableWordPolynomialRing<C> extend(java.lang.String[] vs)

Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn). New variables commute with the exiting variables.

Overrides:

extend in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

vs - names for extended variables.

Returns:

extended polynomial ring factory.

extend

public ResidueSolvableWordPolynomialRing<C> extend(java.lang.String[] vs,
                                                   boolean top)

Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn). New variables commute with the exiting variables.

Overrides:

extend in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

vs - names for extended variables.

top - true for TOP term order, false for POT term order.

Returns:

extended polynomial ring factory.

contract

public ResidueSolvableWordPolynomialRing<C> contract(int i)

Contract variables. Used e.g. in module embedding. Contract number of variables by i.

Overrides:

contract in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

i - number of variables to remove.

Returns:

contracted solvable polynomial ring factory.

reverse

public ResidueSolvableWordPolynomialRing<C> reverse()

Reverse variables. Used e.g. in opposite rings.

Overrides:

reverse in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Returns:

solvable polynomial ring factory with reversed variables.

reverse

public ResidueSolvableWordPolynomialRing<C> reverse(boolean partial)

Reverse variables. Used e.g. in opposite rings.

Overrides:

reverse in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

partial - true for partialy reversed term orders.

Returns:

solvable polynomial ring factory with reversed variables.

permutation

public GenSolvablePolynomialRing<WordResidue<C>> permutation(java.util.List<java.lang.Integer> P)

Permutation of polynomial ring variables.

Overrides:

permutation in class GenSolvablePolynomialRing<WordResidue<C extends GcdRingElem<C>>>

Parameters:

P - permutation.

Returns:

P(this).

fromPolyCoefficients

public ResidueSolvableWordPolynomial<C> fromPolyCoefficients(GenSolvablePolynomial<GenWordPolynomial<C>> A)

Word residue coefficients from integral word polynomial coefficients. Represent as polynomial with type WordResidue coefficients.

Parameters:

A - polynomial with integral word polynomial coefficients to be converted.

Returns:

polynomial with type WordResidue coefficients.

toPolyCoefficients

public RecSolvableWordPolynomial<C> toPolyCoefficients(ResidueSolvableWordPolynomial<C> A)

Integral word function from word residue coefficients. Represent as polynomial with type GenWordPolynomial coefficients.

Parameters:

A - polynomial with word residue coefficients to be converted.

Returns:

polynomial with type GenWordPolynomial coefficients.

toPolyCoefficients

public RecSolvableWordPolynomial<C> toPolyCoefficients(GenPolynomial<WordResidue<C>> A)

Integral word function from word residue coefficients. Represent as polynomial with type GenWordPolynomial coefficients.

Parameters:

A - polynomial with word residue coefficients to be converted.

Returns:

polynomial with type GenWordPolynomial coefficients.