Package edu.jas.poly

Class GenSolvablePolynomialRing<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomialRing<C>

edu.jas.poly.GenSolvablePolynomialRing<C>

Type Parameters:

C - coefficient type.

All Implemented Interfaces:

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

Direct Known Subclasses:

LocalSolvablePolynomialRing, QLRSolvablePolynomialRing, QuotSolvablePolynomialRing, RecSolvablePolynomialRing, RecSolvableWordPolynomialRing, ResidueSolvablePolynomialRing, ResidueSolvableWordPolynomialRing

public class GenSolvablePolynomialRing<C extends RingElem<C>>
extends GenPolynomialRing<C>

GenSolvablePolynomialRing generic solvable polynomial factory implementing RingFactory and extending GenPolynomialRing factory. Factory for n-variate ordered solvable polynomials over C. The non-commutative multiplication relations are maintained in a 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
GenSolvablePolynomial<C>	ONE	The constant polynomial 1 for this ring.
RelationTable<C>	table	The solvable multiplication relations.
GenSolvablePolynomial<C>	ZERO	The constant polynomial 0 for this ring.

Fields inherited from class edu.jas.poly.GenPolynomialRing

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

Constructor Summary

Constructors

Constructor	Description
GenSolvablePolynomialRing(RingFactory<C> cf, int n)	The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
GenSolvablePolynomialRing(RingFactory<C> cf, int n, RelationTable<C> rt)	The constructor creates a solvable polynomial factory object with the default term order.
GenSolvablePolynomialRing(RingFactory<C> cf, int n, TermOrder t)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
GenSolvablePolynomialRing(RingFactory<C> cf, int n, TermOrder t, RelationTable<C> rt)	The constructor creates a solvable polynomial factory object with the given term order.
GenSolvablePolynomialRing(RingFactory<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.
GenSolvablePolynomialRing(RingFactory<C> cf, int n, TermOrder t, java.lang.String[] v, RelationTable<C> rt)	The constructor creates a solvable polynomial factory object with the given term order.
GenSolvablePolynomialRing(RingFactory<C> cf, GenPolynomialRing 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.
GenSolvablePolynomialRing(RingFactory<C> cf, TermOrder t, java.lang.String[] v)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
GenSolvablePolynomialRing(RingFactory<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
void	addRelations(RelationGenerator<C> rg)	Generate the relation table of the solvable polynomial ring from a relation generator.
void	addRelations(java.util.List<GenPolynomial<C>> rel)	Generate the relation table of the solvable polynomial ring from a polynomial list of relations.
void	addSolvRelations(java.util.List<GenSolvablePolynomial<C>> rel)	Generate the relation table of the solvable polynomial ring from a solvable polynomial list of relations.
GenSolvablePolynomialRing<C>	contract(int i)	Contract variables.
GenSolvablePolynomial<C>	copy(GenSolvablePolynomial<C> c)	Copy polynomial c.
GenSolvablePolynomialRing<C>	distribute()	Distributive representation as polynomial with all main variables.
boolean	equals(java.lang.Object other)	Comparison with any other object.
GenSolvablePolynomialRing<C>	extend(int i)	Extend variables.
GenSolvablePolynomialRing<C>	extend(int i, boolean top)	Extend variables.
GenSolvablePolynomialRing<C>	extend(java.lang.String[] vn)	Extend variables.
GenSolvablePolynomialRing<C>	extend(java.lang.String[] vn, boolean top)	Extend variables.
GenSolvablePolynomial<C>	fromInteger(long a)	Get a (constant) GenSolvablePolynomial<C> element from a long value.
GenSolvablePolynomial<C>	fromInteger(java.math.BigInteger a)	Get a (constant) GenSolvablePolynomial<C> element from a BigInteger value.
GenSolvablePolynomial<C>	getONE()	Get the one element.
GenSolvablePolynomial<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.
GenSolvablePolynomial<C>	parse(java.io.Reader r)	Parse a solvable polynomial with the use of GenPolynomialTokenizer
GenSolvablePolynomial<C>	parse(java.lang.String s)	Parse a solvable polynomial with the use of GenPolynomialTokenizer
GenPolynomialRing<C>	permutation(java.util.List<java.lang.Integer> P)	Permutation of polynomial ring variables.
GenSolvablePolynomial<C>	random(int n)	Random solvable polynomial.
GenSolvablePolynomial<C>	random(int k, int l, int d, float q)	Generate a random solvable polynomial.
GenSolvablePolynomial<C>	random(int k, int l, int d, float q, java.util.Random rnd)	Random solvable polynomial.
GenSolvablePolynomial<C>	random(int n, java.util.Random rnd)	Random solvable polynomial.
GenSolvablePolynomialRing<GenPolynomial<C>>	recursive(int i)	Recursive representation as polynomial ring with i main variables.
GenSolvablePolynomialRing<C>	reverse()	Reverse variables.
GenSolvablePolynomialRing<C>	reverse(boolean partial)	Reverse variables.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation.
GenSolvablePolynomial<C>	univariate(int i)	Generate univariate solvable polynomial in a given variable.
GenSolvablePolynomial<C>	univariate(int modv, int i, long e)	Generate univariate solvable polynomial in a given variable with given exponent.
GenSolvablePolynomial<C>	univariate(int i, long e)	Generate univariate solvable polynomial in a given variable with given exponent.
java.util.List<? extends GenSolvablePolynomial<C>>	univariateList()	Generate list of univariate polynomials in all variables.
java.util.List<? extends GenSolvablePolynomial<C>>	univariateList(int modv)	Generate list of univariate polynomials in all variables.
java.util.List<? extends GenSolvablePolynomial<C>>	univariateList(int modv, long e)	Generate list of univariate polynomials in all variables with given exponent.
GenSolvablePolynomial<C>	valueOf(C a)	Get a (constant) GenPolynomial<C> element from a coefficient value.
GenSolvablePolynomial<C>	valueOf(C a, ExpVector e)	Get a GenPolynomial<C> element from a coeffcient and an exponent vector.
GenSolvablePolynomial<C>	valueOf(ExpVector e)	Get a GenPolynomial<C> element from an exponent vector.

Methods inherited from class edu.jas.poly.GenPolynomialRing

characteristic, copy, copy, copy, extendLower, extendLower, extendLower, fromVector, 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 edu.jas.structure.ElemFactory

valueOf

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

table

public final RelationTable<C extends RingElem<C>> table

The solvable multiplication relations.

ZERO

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

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

ONE

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

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

Constructor Detail

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<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.

GenSolvablePolynomialRing

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

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<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.

GenSolvablePolynomialRing

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

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<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.

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<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.

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<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.

GenSolvablePolynomialRing

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

GenSolvablePolynomialRing

public GenSolvablePolynomialRing(RingFactory<C> cf,
                                 GenPolynomialRing 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

addRelations

public void addRelations(RelationGenerator<C> rg)

Generate the relation table of the solvable polynomial ring from a relation generator.

Parameters:

rg - relation generator.

addRelations

public void addRelations(java.util.List<GenPolynomial<C>> rel)

Generate the relation table of the solvable polynomial ring from a polynomial list of relations.

Parameters:

rel - polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.

addSolvRelations

public void addSolvRelations(java.util.List<GenSolvablePolynomial<C>> rel)

Generate the relation table of the solvable polynomial ring from a solvable polynomial list of relations.

Parameters:

rel - solvable polynomial list of relations [..., ei, fj, pij, ... ] with ei * fj = pij.

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class GenPolynomialRing<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 GenPolynomialRing<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 GenPolynomialRing<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 GenPolynomialRing<C extends RingElem<C>>

See Also:

Object.hashCode()

getZERO

public GenSolvablePolynomial<C> getZERO()

Get the zero element.

Specified by:

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

Overrides:

getZERO in class GenPolynomialRing<C extends RingElem<C>>

Returns:

0 as GenSolvablePolynomial.

getONE

public GenSolvablePolynomial<C> getONE()

Get the one element.

Specified by:

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

Overrides:

getONE in class GenPolynomialRing<C extends RingElem<C>>

Returns:

1 as GenSolvablePolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

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

Overrides:

isCommutative in class GenPolynomialRing<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 define an associative solvable ring.

Specified by:

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

Overrides:

isAssociative in class GenPolynomialRing<C extends RingElem<C>>

Returns:

true, if this ring is associative, else false.

valueOf

public GenSolvablePolynomial<C> valueOf(C a)

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

Overrides:

valueOf in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

a - coefficient.

Returns:

a GenPolynomial<C>.

valueOf

public GenSolvablePolynomial<C> valueOf(ExpVector e)

Get a GenPolynomial<C> element from an exponent vector.

Overrides:

valueOf in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

e - exponent vector.

Returns:

a GenPolynomial<C>.

valueOf

public GenSolvablePolynomial<C> valueOf(C a,
                                        ExpVector e)

Get a GenPolynomial<C> element from a coeffcient and an exponent vector.

Overrides:

valueOf in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a GenPolynomial<C>.

fromInteger

public GenSolvablePolynomial<C> fromInteger(long a)

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

Specified by:

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

Overrides:

fromInteger in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

a - long.

Returns:

a GenSolvablePolynomial<C>.

fromInteger

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

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

Specified by:

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

Overrides:

fromInteger in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

a - BigInteger.

Returns:

a GenSolvablePolynomial<C>.

random

public GenSolvablePolynomial<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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

n - number of terms.

Returns:

a random solvable polynomial.

random

public GenSolvablePolynomial<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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

random

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

Generate a random solvable polynomial.

Overrides:

random in class GenPolynomialRing<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 GenSolvablePolynomial<C> random(int k,
                                       int l,
                                       int d,
                                       float q,
                                       java.util.Random rnd)

Random solvable polynomial.

Overrides:

random in class GenPolynomialRing<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 GenSolvablePolynomial<C> copy(GenSolvablePolynomial<C> c)

Copy polynomial c.

Parameters:

c -

Returns:

a copy of c.

parse

public GenSolvablePolynomial<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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

s - String.

Returns:

GenSolvablePolynomial from s.

parse

public GenSolvablePolynomial<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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

r - Reader.

Returns:

next GenSolvablePolynomial from r.

univariate

public GenSolvablePolynomial<C> univariate(int i)

Generate univariate solvable polynomial in a given variable.

Overrides:

univariate in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

i - the index of the variable.

Returns:

X_i as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenPolynomialRing<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 GenSolvablePolynomial<C> univariate(int modv,
                                           int i,
                                           long e)

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

Overrides:

univariate in class GenPolynomialRing<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<? extends GenSolvablePolynomial<C>> univariateList()

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenPolynomialRing<C extends RingElem<C>>

Returns:

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

univariateList

public java.util.List<? extends GenSolvablePolynomial<C>> univariateList(int modv)

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenPolynomialRing<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<? extends GenSolvablePolynomial<C>> univariateList(int modv,
                                                                         long e)

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

Overrides:

univariateList in class GenPolynomialRing<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 GenSolvablePolynomialRing<C> extend(int i)

Extend variables. Used e.g. in module embedding. Extend number of variables by i. New variables commute with the exiting variables.

Overrides:

extend in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

i - number of variables to extend.

Returns:

extended solvable polynomial ring factory.

extend

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

Extend variables. Used e.g. in module embedding. Extend number of variables by i. New variables commute with the exiting variables.

Overrides:

extend in class GenPolynomialRing<C extends RingElem<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 GenSolvablePolynomialRing<C> extend(java.lang.String[] vn)

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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

vn - names for extended variables.

Returns:

extended polynomial ring factory.

extend

public GenSolvablePolynomialRing<C> extend(java.lang.String[] vn,
                                           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 GenPolynomialRing<C extends RingElem<C>>

Parameters:

vn - names for extended variables.

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

Returns:

extended polynomial ring factory.

contract

public GenSolvablePolynomialRing<C> contract(int i)

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

Overrides:

contract in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

i - number of variables to remove.

Returns:

contracted solvable polynomial ring factory.

reverse

public GenSolvablePolynomialRing<C> reverse()

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

Overrides:

reverse in class GenPolynomialRing<C extends RingElem<C>>

Returns:

solvable polynomial ring factory with reversed variables.

reverse

public GenSolvablePolynomialRing<C> reverse(boolean partial)

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

Overrides:

reverse in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

partial - true for partialy reversed term orders.

Returns:

solvable polynomial ring factory with reversed variables.

recursive

public GenSolvablePolynomialRing<GenPolynomial<C>> recursive(int i)

Recursive representation as polynomial ring with i main variables.

Overrides:

recursive in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

i - number of main variables.

Returns:

recursive polynomial ring factory.

distribute

public GenSolvablePolynomialRing<C> distribute()

Distributive representation as polynomial with all main variables.

Overrides:

distribute in class GenPolynomialRing<C extends RingElem<C>>

Returns:

distributive polynomial ring factory.

permutation

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

Permutation of polynomial ring variables.

Overrides:

permutation in class GenPolynomialRing<C extends RingElem<C>>

Parameters:

P - permutation, must be compatible with the commutator relations.

Returns:

P(this).