Package edu.jas.poly

Class RecSolvableWordPolynomialRing<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomialRing<C>

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

edu.jas.poly.RecSolvableWordPolynomialRing<C>

Type Parameters:

C - base coefficient type.

All Implemented Interfaces:

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

public class RecSolvableWordPolynomialRing<C extends RingElem<C>>
extends GenSolvablePolynomialRing<GenWordPolynomial<C>>

RecSolvableWordPolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory. Factory for n-variate ordered solvable polynomials over non-commutative word polynomial 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	Description
RelationTable<GenWordPolynomial<C>>	coeffTable	The solvable multiplication relations between variables and coefficients.
RecSolvableWordPolynomial<C>	ONE	The constant polynomial 1 for this ring.
RecSolvableWordPolynomial<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	Description
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, int n)	The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, int n, RelationTable<GenWordPolynomial<C>> rt)	The constructor creates a solvable polynomial factory object with the default term order.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, int n, TermOrder t)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, int n, TermOrder t, RelationTable<GenWordPolynomial<C>> rt)	The constructor creates a solvable polynomial factory object with the given term order.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, int n, TermOrder t, java.lang.String[] v, RelationTable<GenWordPolynomial<C>> rt)	The constructor creates a solvable polynomial factory object with the given term order.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, RecSolvableWordPolynomialRing 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.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, TermOrder t, java.lang.String[] v)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf, java.lang.String[] v)	The constructor creates a solvable polynomial factory object with the default term order.

Method Summary

Modifier and Type	Method	Description
RecSolvableWordPolynomialRing<C>	contract(int i)	Contract variables.
RecSolvableWordPolynomial<C>	copy(RecSolvableWordPolynomial<C> c)	Copy polynomial c.
boolean	equals(java.lang.Object other)	Comparison with any other object.
RecSolvableWordPolynomialRing<C>	extend(int i)	Extend variables.
RecSolvableWordPolynomialRing<C>	extend(java.lang.String[] vs)	Extend variables.
RecSolvableWordPolynomial<C>	fromInteger(long a)	Get a (constant) RecSolvableWordPolynomial<C> element from a long value.
RecSolvableWordPolynomial<C>	fromInteger(java.math.BigInteger a)	Get a (constant) RecSolvableWordPolynomial<C> element from a BigInteger value.
RecSolvableWordPolynomial<C>	getONE()	Get the one element.
RecSolvableWordPolynomial<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.
RecSolvableWordPolynomial<C>	parse(java.io.Reader r)	Parse a solvable polynomial with the use of GenPolynomialTokenizer
RecSolvableWordPolynomial<C>	parse(java.lang.String s)	Parse a solvable polynomial with the use of GenPolynomialTokenizer
GenSolvablePolynomialRing<GenWordPolynomial<C>>	permutation(java.util.List<java.lang.Integer> P)	Permutation of polynomial ring variables.
RecSolvableWordPolynomial<C>	random(int n)	Random solvable polynomial.
RecSolvableWordPolynomial<C>	random(int k, int l, int d, float q)	Generate a random solvable polynomial.
RecSolvableWordPolynomial<C>	random(int k, int l, int d, float q, java.util.Random rnd)	Random solvable polynomial.
RecSolvableWordPolynomial<C>	random(int n, java.util.Random rnd)	Random solvable polynomial.
RecSolvableWordPolynomialRing<C>	reverse()	Reverse variables.
RecSolvableWordPolynomialRing<C>	reverse(boolean partial)	Reverse variables.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation.
RecSolvableWordPolynomial<C>	univariate(int i)	Generate univariate solvable polynomial in a given variable.
RecSolvableWordPolynomial<C>	univariate(int modv, int i, long e)	Generate univariate solvable polynomial in a given variable with given exponent.
RecSolvableWordPolynomial<C>	univariate(int i, long e)	Generate univariate solvable polynomial in a given variable with given exponent.
java.util.List<RecSolvableWordPolynomial<C>>	univariateList()	Generate list of univariate polynomials in all variables.
java.util.List<RecSolvableWordPolynomial<C>>	univariateList(int modv)	Generate list of univariate polynomials in all variables.
java.util.List<RecSolvableWordPolynomial<C>>	univariateList(int modv, long e)	Generate list of univariate polynomials in all variables with given exponent.
RecSolvableWordPolynomial<C>	valueOf(ExpVector e)	Get a RecSolvableWordPolynomial<C> element from an ExpVector.
RecSolvableWordPolynomial<C>	valueOf(GenWordPolynomial<C> a)	Get a (constant) RecSolvableWordPolynomial<C> element from a coefficient value.
RecSolvableWordPolynomial<C>	valueOf(GenWordPolynomial<C> a, ExpVector e)	Get a RecSolvableWordPolynomial<C> element from a coefficient and an ExpVector.

Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing

addRelations, addRelations, addSolvRelations, copy, distribute, extend, extend, recursive

Methods inherited from class edu.jas.poly.GenPolynomialRing

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

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

coeffTable

public final RelationTable<GenWordPolynomial<C extends RingElem<C>>> coeffTable

The solvable multiplication relations between variables and coefficients.

ZERO

public final RecSolvableWordPolynomial<C extends RingElem<C>> ZERO

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

ONE

public final RecSolvableWordPolynomial<C extends RingElem<C>> ONE

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

Constructor Detail

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf,
                                     int n,
                                     RelationTable<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf,
                                     int n,
                                     TermOrder t,
                                     RelationTable<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf,
                                     int n,
                                     TermOrder t,
                                     java.lang.String[] v,
                                     RelationTable<GenWordPolynomial<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.

RecSolvableWordPolynomialRing

public RecSolvableWordPolynomialRing(RingFactory<GenWordPolynomial<C>> cf,
                                     RecSolvableWordPolynomialRing 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<GenWordPolynomial<C extends RingElem<C>>>

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<C extends RingElem<C>>

Overrides:

toScript in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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<GenWordPolynomial<C extends RingElem<C>>>

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

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

See Also:

Object.hashCode()

getZERO

public RecSolvableWordPolynomial<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<C extends RingElem<C>>

Overrides:

getZERO in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Returns:

0 as RecSolvableWordPolynomial.

getONE

public RecSolvableWordPolynomial<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<C extends RingElem<C>>

Overrides:

getONE in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Returns:

1 as RecSolvableWordPolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<C extends RingElem<C>>

Overrides:

isCommutative in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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<C extends RingElem<C>>

Overrides:

isAssociative in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Returns:

true, if this ring is associative, else false.

valueOf

public RecSolvableWordPolynomial<C> valueOf(GenWordPolynomial<C> a)

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

Overrides:

valueOf in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

a - coefficient.

Returns:

a RecSolvableWordPolynomial<C>.

valueOf

public RecSolvableWordPolynomial<C> valueOf(ExpVector e)

Get a RecSolvableWordPolynomial<C> element from an ExpVector.

Overrides:

valueOf in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

e - exponent vector.

Returns:

a RecSolvableWordPolynomial<C>.

valueOf

public RecSolvableWordPolynomial<C> valueOf(GenWordPolynomial<C> a,
                                            ExpVector e)

Get a RecSolvableWordPolynomial<C> element from a coefficient and an ExpVector.

Overrides:

valueOf in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a RecSolvableWordPolynomial<C>.

fromInteger

public RecSolvableWordPolynomial<C> fromInteger(long a)

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

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

a - long.

Returns:

a RecSolvableWordPolynomial<C>.

fromInteger

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

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

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

a - BigInteger.

Returns:

a RecSolvableWordPolynomial<C>.

random

public RecSolvableWordPolynomial<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<C extends RingElem<C>>

Overrides:

random in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

n - number of terms.

Returns:

a random solvable polynomial.

random

public RecSolvableWordPolynomial<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<C extends RingElem<C>>

Overrides:

random in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

random

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

Generate a random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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 RecSolvableWordPolynomial<C> random(int k,
                                           int l,
                                           int d,
                                           float q,
                                           java.util.Random rnd)

Random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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 RecSolvableWordPolynomial<C> copy(RecSolvableWordPolynomial<C> c)

Copy polynomial c.

Parameters:

c -

Returns:

a copy of c.

parse

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

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Overrides:

parse in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

s - String.

Returns:

RecSolvableWordPolynomial from s.

parse

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

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Overrides:

parse in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

r - Reader.

Returns:

next RecSolvableWordPolynomial from r.

univariate

public RecSolvableWordPolynomial<C> univariate(int i)

Generate univariate solvable polynomial in a given variable.

Overrides:

univariate in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

i - the index of the variable.

Returns:

X_i as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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<RecSolvableWordPolynomial<C>> univariateList()

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Returns:

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

univariateList

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

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

modv - number of module variables.

Returns:

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

univariateList

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

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

Overrides:

univariateList in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<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 RecSolvableWordPolynomialRing<C> extend(int i)

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

Overrides:

extend in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

i - number of variables to extend.

Returns:

extended solvable polynomial ring factory.

extend

public RecSolvableWordPolynomialRing<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<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

vs - names for extended variables.

Returns:

extended polynomial ring factory.

contract

public RecSolvableWordPolynomialRing<C> contract(int i)

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

Overrides:

contract in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

i - number of variables to remove.

Returns:

contracted solvable polynomial ring factory.

reverse

public RecSolvableWordPolynomialRing<C> reverse()

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

Overrides:

reverse in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Returns:

solvable polynomial ring factory with reversed variables.

reverse

public RecSolvableWordPolynomialRing<C> reverse(boolean partial)

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

Overrides:

reverse in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

partial - true for partially reversed term orders.

Returns:

solvable polynomial ring factory with reversed variables.

permutation

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

Permutation of polynomial ring variables.

Overrides:

permutation in class GenSolvablePolynomialRing<GenWordPolynomial<C extends RingElem<C>>>

Parameters:

P - permutation.

Returns:

P(this).