GenWordPolynomialRing

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 and 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 and 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, 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.
`GenWordPolynomialRing(RingFactory<C> cf, WordFactory wf)` The constructor creates a polynomial factory object with the default term order.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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(java.math.BigInteger a)` Get a (constant) GenWordPolynomial<C> element from a BigInteger value.
`GenWordPolynomial<C>`	`fromInteger(long a)` Get a (constant) GenWordPolynomial<C> element from a long 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 coeffcient and an ExpVector.
`GenWordPolynomial<C>`	`valueOf(C a, Word e)` Get a GenWordPolynomial<C> element from a coeffcient 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>.
`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>.
`GenWordPolynomial<C>`	`valueOf(Word e)` Get a GenWordPolynomial<C> element from a word.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- 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<GenWordPolynomial<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<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    0 as GenWordPolynomial.
  - getONE
```
public GenWordPolynomial<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    1 as GenWordPolynomial.
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    false.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<GenWordPolynomial<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 coeffcient 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 coeffcient 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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    list of generators for the algebraic structure.
    
    See Also:
    
    ElemFactory.generators()

Class GenWordPolynomialRing<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

coFac

alphabet

ZERO

ONE

wone

Constructor Detail

GenWordPolynomialRing

GenWordPolynomialRing

GenWordPolynomialRing

GenWordPolynomialRing

GenWordPolynomialRing

Method Detail

copy

toString

toScript

extend

extend

equals

hashCode

getVars

getZEROCoefficient

getONECoefficient

getZERO

getONE

isCommutative

isAssociative

isFinite

isField

characteristic

valueOf

valueOf

valueOf

valueOf

valueOf

valueOf

valueOf

valueOf

fromInteger

fromInteger

random

random

random

random

copy

parse

parse

univariate

commute

commute

commute

univariateList

getGenerators

generators