Package edu.jas.poly

Class GenWordPolynomialRing<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenWordPolynomialRing<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public final class GenWordPolynomialRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<GenWordPolynomial<C>>

GenWordPolynomialRing generic polynomial factory implementing RingFactory; Factory for non-commutative string polynomials over C.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
WordFactory	alphabet	The factory for the alphabet.
RingFactory<C>	coFac	The factory for the coefficients.
GenWordPolynomial<C>	ONE	The constant polynomial 1 for this ring.
Word	wone	The constant empty word exponent for this ring.
GenWordPolynomial<C>	ZERO	The constant polynomial 0 for this ring.

Constructor Summary

Constructors

Constructor	Description
GenWordPolynomialRing(GenPolynomialRing<C> fac)	The constructor creates a polynomial factory object.
GenWordPolynomialRing(RingFactory<C> cf, GenWordPolynomialRing o)	The constructor creates a polynomial factory object.
GenWordPolynomialRing(RingFactory<C> cf, WordFactory wf)	The constructor creates a polynomial factory object with the default term order.
GenWordPolynomialRing(RingFactory<C> cf, java.lang.String s)	The constructor creates a polynomial factory object.
GenWordPolynomialRing(RingFactory<C> cf, java.lang.String[] s)	The constructor creates a polynomial factory object.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
java.util.List<GenWordPolynomial<C>>	commute()	Generate commute polynomials for all variables.
java.util.List<GenWordPolynomial<C>>	commute(int i)	Generate commute polynomials for given variable.
GenWordPolynomial<C>	commute(int i, int j)	Generate commute polynomial in two variables.
GenWordPolynomialRing<C>	copy()	Copy this factory.
GenWordPolynomial<C>	copy(GenWordPolynomial<C> c)	Copy polynomial c.
boolean	equals(java.lang.Object other)	Comparison with any other object.
GenWordPolynomialRing<C>	extend(int i)	Extend variables.
GenWordPolynomialRing<C>	extend(java.lang.String[] vn)	Extend variables.
GenWordPolynomial<C>	fromInteger(long a)	Get a (constant) GenWordPolynomial<C> element from a long value.
GenWordPolynomial<C>	fromInteger(java.math.BigInteger a)	Get a (constant) GenWordPolynomial<C> element from a BigInteger value.
java.util.List<GenWordPolynomial<C>>	generators()	Get a list of all generating elements.
java.util.List<GenWordPolynomial<C>>	getGenerators()	Get the generating elements excluding the generators for the coefficient ring.
GenWordPolynomial<C>	getONE()	Get the one element.
C	getONECoefficient()	Get the one element from the coefficients.
java.lang.String[]	getVars()	Get the variable names.
GenWordPolynomial<C>	getZERO()	Get the zero element.
C	getZEROCoefficient()	Get the zero element from the coefficients.
int	hashCode()	Hash code for this polynomial ring.
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Query if this ring is commutative.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
GenWordPolynomial<C>	parse(java.io.Reader r)	Parse a polynomial with the use of GenWordPolynomialTokenizer.
GenWordPolynomial<C>	parse(java.lang.String s)	Parse a polynomial with the use of GenWordPolynomialTokenizer.
GenWordPolynomial<C>	random(int n)	Random polynomial.
GenWordPolynomial<C>	random(int k, int l, int d)	Generate a random polynomial.
GenWordPolynomial<C>	random(int k, int l, int d, java.util.Random rnd)	Generate a random polynomial.
GenWordPolynomial<C>	random(int n, java.util.Random rnd)	Random polynomial.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation.
GenWordPolynomial<C>	univariate(int i)	Generate univariate polynomial in a given variable.
java.util.List<GenWordPolynomial<C>>	univariateList()	Generate list of univariate polynomials in all variables.
GenWordPolynomial<C>	valueOf(C a)	Get a (constant) GenWordPolynomial<C> element from a coefficient value.
GenWordPolynomial<C>	valueOf(C a, ExpVector e)	Get a GenWordPolynomial<C> element from a coefficient and an ExpVector.
GenWordPolynomial<C>	valueOf(C a, Word e)	Get a GenWordPolynomial<C> element from a coefficient and a word.
GenWordPolynomial<C>	valueOf(ExpVector e)	Get a GenWordPolynomial<C> element from an ExpVector.
GenWordPolynomial<C>	valueOf(GenPolynomial<C> a)	Get a GenWordPolynomial<C> element from a GenPolynomial<C>.
GenWordPolynomial<C>	valueOf(GenWordPolynomial<C> a)	Get a GenWordPolynomial<C> element from a GenWordPolynomial<C>.
GenWordPolynomial<C>	valueOf(Word e)	Get a GenWordPolynomial<C> element from a word.
java.util.List<GenWordPolynomial<C>>	valueOf(java.util.List<GenPolynomial<C>> A)	Get a list of GenWordPolynomial<C> element from a list of GenPolynomial<C>.

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Field Detail

coFac

public final RingFactory<C extends RingElem<C>> coFac

The factory for the coefficients.

alphabet

public final WordFactory alphabet

The factory for the alphabet.

ZERO

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

The constant polynomial 0 for this ring.

ONE

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

The constant polynomial 1 for this ring.

wone

public final Word wone

The constant empty word exponent for this ring.

Constructor Detail

GenWordPolynomialRing

public GenWordPolynomialRing(RingFactory<C> cf,
                             WordFactory wf)

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

Parameters:

cf - factory for coefficients of type C.

wf - factory for strings.

GenWordPolynomialRing

public GenWordPolynomialRing(RingFactory<C> cf,
                             java.lang.String[] s)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

s - array of variable names.

GenWordPolynomialRing

public GenWordPolynomialRing(RingFactory<C> cf,
                             java.lang.String s)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

s - string of single letter variable names.

GenWordPolynomialRing

public GenWordPolynomialRing(RingFactory<C> cf,
                             GenWordPolynomialRing o)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

o - other polynomial ring.

GenWordPolynomialRing

public GenWordPolynomialRing(GenPolynomialRing<C> fac)

The constructor creates a polynomial factory object.

Parameters:

fac - polynomial ring.

Method Detail

copy

public GenWordPolynomialRing<C> copy()

Copy this factory.

Returns:

a clone of this.

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

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>>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

extend

public GenWordPolynomialRing<C> extend(int i)

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

Parameters:

i - number of variables to extend.

Returns:

extended word polynomial ring factory.

extend

public GenWordPolynomialRing<C> extend(java.lang.String[] vn)

Extend variables. Extend number of variables by length(vn).

Parameters:

vn - names for extended variables.

Returns:

extended polynomial ring factory.

equals

public boolean equals(java.lang.Object other)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

getVars

public java.lang.String[] getVars()

Get the variable names.

Returns:

vars.

getZEROCoefficient

public C getZEROCoefficient()

Get the zero element from the coefficients.

Returns:

0 as C.

getONECoefficient

public C getONECoefficient()

Get the one element from the coefficients.

Returns:

1 as C.

getZERO

public GenWordPolynomial<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as GenWordPolynomial.

getONE

public GenWordPolynomial<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as GenWordPolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

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

Returns:

true if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

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

Returns:

true if this ring is associative, else false.

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

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

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<C extends RingElem<C>>

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<C extends RingElem<C>>

Returns:

characteristic of this ring.

valueOf

public GenWordPolynomial<C> valueOf(C a)

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

Parameters:

a - coefficient.

Returns:

a GenWordPolynomial<C>.

valueOf

public GenWordPolynomial<C> valueOf(Word e)

Get a GenWordPolynomial<C> element from a word.

Parameters:

e - word.

Returns:

a GenWordPolynomial<C>.

valueOf

public GenWordPolynomial<C> valueOf(ExpVector e)

Get a GenWordPolynomial<C> element from an ExpVector.

Parameters:

e - exponent vector.

Returns:

a GenWordPolynomial<C>.

valueOf

public GenWordPolynomial<C> valueOf(C a,
                                    Word e)

Get a GenWordPolynomial<C> element from a coefficient and a word.

Parameters:

a - coefficient.

e - word.

Returns:

a GenWordPolynomial<C>.

valueOf

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

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

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a GenWordPolynomial<C>.

valueOf

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

Get a GenWordPolynomial<C> element from a GenPolynomial<C>.

Parameters:

a - GenPolynomial.

Returns:

a GenWordPolynomial<C>.

valueOf

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

Get a GenWordPolynomial<C> element from a GenWordPolynomial<C>.

Parameters:

a - GenWordPolynomial.

Returns:

a GenWordPolynomial<C>.

valueOf

public java.util.List<GenWordPolynomial<C>> valueOf(java.util.List<GenPolynomial<C>> A)

Get a list of GenWordPolynomial<C> element from a list of GenPolynomial<C>.

Parameters:

A - GenPolynomial list.

Returns:

a GenWordPolynomial<C> list.

fromInteger

public GenWordPolynomial<C> fromInteger(long a)

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

Specified by:

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

Parameters:

a - long.

Returns:

a GenWordPolynomial<C>.

fromInteger

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

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

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a GenWordPolynomial<C>.

random

public GenWordPolynomial<C> random(int n)

Random polynomial. Generates a random polynomial.

Specified by:

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

Parameters:

n - number of terms.

Returns:

a random polynomial.

random

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

Random polynomial. Generates a random polynomial with k = 5, l = n, d = 3.

Specified by:

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

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random polynomial.

random

public GenWordPolynomial<C> random(int k,
                                   int l,
                                   int d)

Generate a random polynomial.

Parameters:

k - bitsize of random coefficients.

l - number of terms.

d - maximal length of a random word.

Returns:

a random polynomial.

random

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

Generate a random polynomial.

Parameters:

k - bitsize of random coefficients.

l - number of terms.

d - maximal length of a random word.

rnd - is a source for random bits.

Returns:

a random polynomial.

copy

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

Copy polynomial c.

Specified by:

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

Parameters:

c - polynomial to copy.

Returns:

a copy of c.

parse

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

Parse a polynomial with the use of GenWordPolynomialTokenizer.

Specified by:

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

Parameters:

s - String.

Returns:

GenWordPolynomial from s.

parse

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

Parse a polynomial with the use of GenWordPolynomialTokenizer.

Specified by:

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

Parameters:

r - Reader.

Returns:

next GenWordPolynomial from r.

univariate

public GenWordPolynomial<C> univariate(int i)

Generate univariate polynomial in a given variable.

Parameters:

i - the index of the variable.

Returns:

X_i as univariate polynomial.

commute

public GenWordPolynomial<C> commute(int i,
                                    int j)

Generate commute polynomial in two variables.

Parameters:

i - the index of the first variable.

j - the index of the second variable.

Returns:

X_i * x_j - X_j * X_i as polynomial.

commute

public java.util.List<GenWordPolynomial<C>> commute(int i)

Generate commute polynomials for given variable.

Parameters:

i - the index of the variable.

Returns:

[X_i * x_j - X_j * X_i, i != j] as list of polynomials.

commute

public java.util.List<GenWordPolynomial<C>> commute()

Generate commute polynomials for all variables.

Returns:

[X_i * x_j - X_j * X_i, i != j] as list of polynomials.

univariateList

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

Generate list of univariate polynomials in all variables.

Returns:

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

getGenerators

public java.util.List<GenWordPolynomial<C>> getGenerators()

Get the generating elements excluding the generators for the coefficient ring.

Returns:

a list of generating elements for this ring.

generators

public java.util.List<GenWordPolynomial<C>> generators()

Get a list of all generating elements.

Specified by:

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

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()