Package edu.jas.poly

Class GenExteriorPolynomialRing<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.GenExteriorPolynomialRing<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public final class GenExteriorPolynomialRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<GenExteriorPolynomial<C>>

GenExteriorPolynomialRing generic antisymmetric polynomial factory implementing RingFactory; Factory for antisymmetric polynomials (in fact vectors) over C. Objects of this class are intended to be immutable. Only the coefficients are modeled with generic types, the "exponents" are fixed to IndexList. C can also be a non integral domain, e.g. a ModInteger, i.e. it may contain zero divisors, since multiply() does check for zero coefficients and index lists.

Author:

Heinz Kredel

See Also:

"masnc.DIPE.mi from SAC2/MAS", Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
RingFactory<C>	coFac	The factory for the coefficients.
IndexFactory	ixfac	The factory for the IndexList.
GenExteriorPolynomial<C>	ONE	The constant polynomial 1 for this ring.
IndexList	wone	The constant empty index lists exponent for this ring.
GenExteriorPolynomial<C>	ZERO	The constant polynomial 0 for this ring.

Constructor Summary

Constructors

Constructor	Description
GenExteriorPolynomialRing(GenPolynomialRing<C> fac)	The constructor creates a polynomial factory object.
GenExteriorPolynomialRing(RingFactory<C> cf, GenExteriorPolynomialRing o)	The constructor creates a polynomial factory object.
GenExteriorPolynomialRing(RingFactory<C> cf, IndexFactory wf)	The constructor creates a polynomial factory object with the default term order.
GenExteriorPolynomialRing(RingFactory<C> cf, java.lang.String s)	The constructor creates a polynomial factory object.
GenExteriorPolynomialRing(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.
GenExteriorPolynomialRing<C>	copy()	Copy this factory.
GenExteriorPolynomial<C>	copy(GenExteriorPolynomial<C> c)	Copy polynomial c.
C	determinant(java.util.List<GenExteriorPolynomial<C>> A)	Determinant form exterior polynomial / matrix.
boolean	equals(java.lang.Object other)	Comparison with any other object.
GenExteriorPolynomial<C>	fromInteger(long a)	Get a (constant) GenExteriorPolynomial from a long value.
GenExteriorPolynomial<C>	fromInteger(java.math.BigInteger a)	Get a (constant) GenExteriorPolynomial from a BigInteger value.
java.util.List<GenExteriorPolynomial<C>>	fromMatrix(GenMatrix<C> A)	Get a list of GenExteriorPolynomials from a GenMatrix.
GenExteriorPolynomial<C>	fromPolynomial(GenPolynomial<C> a)	Get a GenExteriorPolynomial from a univariate GenPolynomial.
GenExteriorPolynomial<C>	fromVector(GenVector<C> a)	Get a GenExteriorPolynomial from a GenVector.
java.util.List<GenExteriorPolynomial<C>>	generators()	Get a list of all generating elements.
java.util.List<GenExteriorPolynomial<C>>	getGenerators()	Get the generating elements excluding the generators for the coefficient ring.
GenExteriorPolynomial<C>	getIMAX()	Get a GenExteriorPolynomial maximal index list element.
GenExteriorPolynomial<C>	getONE()	Get the one element.
C	getONECoefficient()	Get the one element from the coefficients.
GenExteriorPolynomial<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.
GenExteriorPolynomial<C>	parse(java.io.Reader r)	Parse a polynomial with the use of GenPolynomialTokenizer.
GenExteriorPolynomial<C>	parse(java.lang.String s)	Parse a polynomial with the use of GenExteriorPolynomialTokenizer.
GenExteriorPolynomial<C>	random(int n)	Random polynomial.
GenExteriorPolynomial<C>	random(int k, int l, int d)	Generate a random polynomial.
GenExteriorPolynomial<C>	random(int k, int l, int d, java.util.Random rnd)	Generate a random polynomial.
GenExteriorPolynomial<C>	random(int n, java.util.Random rnd)	Random polynomial.
GenExteriorPolynomial<C>	randomForm(int kl, int l, int k)	Generate a random k-form polynomial.
GenExteriorPolynomial<C>	randomForm(int kl, int l, int k, java.util.Random rnd)	Generate a random k-form polynomial.
C	resultant(GenPolynomial<C> A, GenPolynomial<C> B)	Resultant of two commutative polynaomials.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation.
GenExteriorPolynomial<C>	univariate(int i)	Generate univariate polynomial in a given variable.
java.util.List<GenExteriorPolynomial<C>>	univariateList()	Generate list of univariate polynomials in all variables.
GenExteriorPolynomial<C>	valueOf(C a)	Get a (constant) GenExteriorPolynomial element from a coefficient value.
GenExteriorPolynomial<C>	valueOf(C a, ExpVector e)	Get a GenExteriorPolynomial from a coefficient and an ExpVector.
GenExteriorPolynomial<C>	valueOf(C a, IndexList e)	Get a GenExteriorPolynomial from a coefficient and a IndexList.
GenExteriorPolynomial<C>	valueOf(ExpVector e)	Get a GenExteriorPolynomial from an ExpVector.
GenExteriorPolynomial<C>	valueOf(GenExteriorPolynomial<C> a)	Get a GenExteriorPolynomial from a GenExteriorPolynomial with conformant index lists.
GenExteriorPolynomial<C>	valueOf(GenPolynomial<C> a)	Get a GenExteriorPolynomial from a multivariate GenPolynomial, terms with exponents > 1 are set to zero.
GenExteriorPolynomial<C>	valueOf(IndexList e)	Get a GenExteriorPolynomial element from a index list.
java.util.List<GenExteriorPolynomial<C>>	valueOf(java.util.List<GenPolynomial<C>> A)	Get a list of GenExteriorPolynomials from a list of GenPolynomials.

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.

ixfac

public final IndexFactory ixfac

The factory for the IndexList.

ZERO

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

The constant polynomial 0 for this ring.

ONE

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

The constant polynomial 1 for this ring.

wone

public final IndexList wone

The constant empty index lists exponent for this ring.

Constructor Detail

GenExteriorPolynomialRing

public GenExteriorPolynomialRing(RingFactory<C> cf,
                                 IndexFactory wf)

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

Parameters:

cf - factory for coefficients of type C.

wf - factory for index list.

GenExteriorPolynomialRing

public GenExteriorPolynomialRing(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.

GenExteriorPolynomialRing

public GenExteriorPolynomialRing(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.

GenExteriorPolynomialRing

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

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

o - other polynomial ring.

GenExteriorPolynomialRing

public GenExteriorPolynomialRing(GenPolynomialRing<C> fac)

The constructor creates a polynomial factory object.

Parameters:

fac - polynomial ring.

Method Detail

copy

public GenExteriorPolynomialRing<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()

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()

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 GenExteriorPolynomial<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as GenExteriorPolynomial.

getONE

public GenExteriorPolynomial<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as GenExteriorPolynomial.

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 GenExteriorPolynomial<C> valueOf(C a)

Get a (constant) GenExteriorPolynomial element from a coefficient value.

Parameters:

a - coefficient.

Returns:

a constant GenExteriorPolynomial.

valueOf

public GenExteriorPolynomial<C> valueOf(IndexList e)

Get a GenExteriorPolynomial element from a index list.

Parameters:

e - index list.

Returns:

a GenExteriorPolynomial.

valueOf

public GenExteriorPolynomial<C> valueOf(ExpVector e)

Get a GenExteriorPolynomial from an ExpVector.

Parameters:

e - exponent vector.

Returns:

a GenExteriorPolynomial, if exponents are > 1 return ZERO.

valueOf

public GenExteriorPolynomial<C> valueOf(C a,
                                        IndexList e)

Get a GenExteriorPolynomial from a coefficient and a IndexList.

Parameters:

a - coefficient.

e - word.

Returns:

a GenExteriorPolynomial.

valueOf

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

Get a GenExteriorPolynomial from a coefficient and an ExpVector.

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a GenExteriorPolynomial, if exponents are > 1 return ZERO.

valueOf

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

Get a GenExteriorPolynomial from a multivariate GenPolynomial, terms with exponents > 1 are set to zero.

Parameters:

a - multivariate GenPolynomial.

Returns:

multivariate a GenExteriorPolynomial.

valueOf

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

Get a GenExteriorPolynomial from a GenExteriorPolynomial with conformant index lists.

Parameters:

a - GenExteriorPolynomial.

Returns:

a GenExteriorPolynomial with conformant index lists.

valueOf

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

Get a list of GenExteriorPolynomials from a list of GenPolynomials.

Parameters:

A - GenPolynomial list.

Returns:

a GenExteriorPolynomial list.

getIMAX

public GenExteriorPolynomial<C> getIMAX()

Get a GenExteriorPolynomial maximal index list element.

Returns:

a GenExteriorPolynomial with maximal index list.

fromInteger

public GenExteriorPolynomial<C> fromInteger(long a)

Get a (constant) GenExteriorPolynomial from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a GenExteriorPolynomial.

fromInteger

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

Get a (constant) GenExteriorPolynomial from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a GenExteriorPolynomial<C>.

fromVector

public GenExteriorPolynomial<C> fromVector(GenVector<C> a)

Get a GenExteriorPolynomial from a GenVector.

Parameters:

a - GenVector.

Returns:

a GenExteriorPolynomial.

fromMatrix

public java.util.List<GenExteriorPolynomial<C>> fromMatrix(GenMatrix<C> A)

Get a list of GenExteriorPolynomials from a GenMatrix.

Parameters:

A - GenMatrix

Returns:

a list of GenExteriorPolynomials.

determinant

public C determinant(java.util.List<GenExteriorPolynomial<C>> A)

Determinant form exterior polynomial / matrix.

Parameters:

A - list of GenExteriorPolynomials

Returns:

determinant of 'matrix' A.

fromPolynomial

public GenExteriorPolynomial<C> fromPolynomial(GenPolynomial<C> a)

Get a GenExteriorPolynomial from a univariate GenPolynomial. Different exponents are converted to different indexes.

Parameters:

a - univariate GenPolynomial.

Returns:

a multivariate GenExteriorPolynomial.

resultant

public C resultant(GenPolynomial<C> A,
                   GenPolynomial<C> B)

Resultant of two commutative polynaomials.

Parameters:

A - GenPolynomial

B - GenPolynomial

Returns:

res(A,B).

random

public GenExteriorPolynomial<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 GenExteriorPolynomial<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 GenExteriorPolynomial<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 GenExteriorPolynomial<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.

randomForm

public GenExteriorPolynomial<C> randomForm(int kl,
                                           int l,
                                           int k)

Generate a random k-form polynomial.

Parameters:

kl - bitsize of random coefficients.

l - number of terms.

k - length of any random word.

Returns:

a random k-form polynomial.

randomForm

public GenExteriorPolynomial<C> randomForm(int kl,
                                           int l,
                                           int k,
                                           java.util.Random rnd)

Generate a random k-form polynomial.

Parameters:

kl - bitsize of random coefficients.

l - number of terms.

k - length of any random word.

rnd - is a source for random bits.

Returns:

a random k-form polynomial.

copy

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

Parse a polynomial with the use of GenExteriorPolynomialTokenizer.

Specified by:

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

Parameters:

s - String.

Returns:

GenExteriorPolynomial from s.

parse

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

Parse a polynomial with the use of GenPolynomialTokenizer.

Specified by:

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

Parameters:

r - Reader.

Returns:

next GenExteriorPolynomial from r.

univariate

public GenExteriorPolynomial<C> univariate(int i)

Generate univariate polynomial in a given variable.

Parameters:

i - the index of the variable.

Returns:

X_i as univariate polynomial.

univariateList

public java.util.List<GenExteriorPolynomial<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<GenExteriorPolynomial<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<GenExteriorPolynomial<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()