edu.jas.poly

Class QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>

java.lang.Object

edu.jas.poly.GenPolynomialRing<C>

edu.jas.poly.GenSolvablePolynomialRing<C>

edu.jas.poly.QLRSolvablePolynomialRing<C,D>

Type Parameters:

C - polynomial coefficient type

D - quotient 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>>

public class QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>
extends GenSolvablePolynomialRing<C>

QLRSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory. Factory for n-variate ordered solvable polynomials over solvable quotient, local and local-residue 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 and Description
QLRSolvablePolynomial<C,D>	ONE The constant polynomial 1 for this ring.
RecSolvablePolynomialRing<D>	polCoeff Recursive solvable polynomial ring with polynomial coefficients.
QuotPairFactory<GenPolynomial<D>,C>	qpfac Factory to create coefficients.
QLRSolvablePolynomial<C,D>	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 and Description
QLRSolvablePolynomialRing(RingFactory<C> cf, GenSolvablePolynomialRing 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.
QLRSolvablePolynomialRing(RingFactory<C> cf, int n) The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
QLRSolvablePolynomialRing(RingFactory<C> cf, int n, RelationTable<C> rt) The constructor creates a solvable polynomial factory object with the default term order.
QLRSolvablePolynomialRing(RingFactory<C> cf, int n, TermOrder t) The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
QLRSolvablePolynomialRing(RingFactory<C> cf, int n, TermOrder t, RelationTable<C> rt) The constructor creates a solvable polynomial factory object with the given term order.
QLRSolvablePolynomialRing(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.
QLRSolvablePolynomialRing(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.
QLRSolvablePolynomialRing(RingFactory<C> cf, QLRSolvablePolynomialRing 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.
QLRSolvablePolynomialRing(RingFactory<C> cf, java.lang.String[] v) The constructor creates a solvable polynomial factory object with the default term order.
QLRSolvablePolynomialRing(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.

Method Summary

Modifier and Type	Method and Description
QLRSolvablePolynomialRing<C,D>	contract(int i) Contract variables.
QLRSolvablePolynomial<C,D>	copy(QLRSolvablePolynomial<C,D> c) Copy polynomial c.
boolean	equals(java.lang.Object other) Comparison with any other object.
QLRSolvablePolynomialRing<C,D>	extend(int i) Extend variables.
QLRSolvablePolynomial<C,D>	fromInteger(java.math.BigInteger a) Get a (constant) QLRSolvablePolynomial<C> element from a BigInteger value.
QLRSolvablePolynomial<C,D>	fromInteger(long a) Get a (constant) QLRSolvablePolynomial<C> element from a long value.
QLRSolvablePolynomial<C,D>	fromPolyCoefficients(GenSolvablePolynomial<GenPolynomial<D>> A) Rational function from integral polynomial coefficients.
QLRSolvablePolynomial<C,D>	getONE() Get the one element.
QLRSolvablePolynomial<C,D>	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.
QLRSolvablePolynomial<C,D>	parse(java.io.Reader r) Parse a solvable polynomial with the use of GenPolynomialTokenizer
QLRSolvablePolynomial<C,D>	parse(java.lang.String s) Parse a solvable polynomial with the use of GenPolynomialTokenizer
QLRSolvablePolynomial<C,D>	random(int n) Random solvable polynomial.
QLRSolvablePolynomial<C,D>	random(int k, int l, int d, float q) Generate a random solvable polynomial.
QLRSolvablePolynomial<C,D>	random(int k, int l, int d, float q, java.util.Random rnd) Random solvable polynomial.
QLRSolvablePolynomial<C,D>	random(int n, java.util.Random rnd) Random solvable polynomial.
java.util.List<QLRSolvablePolynomial<C,D>>	recUnivariateList() Generate list of univariate polynomials in all variables.
java.util.List<QLRSolvablePolynomial<C,D>>	recUnivariateList(int modv) Generate list of univariate polynomials in all variables.
java.util.List<QLRSolvablePolynomial<C,D>>	recUnivariateList(int modv, long e) Generate list of univariate polynomials in all variables with given exponent.
QLRSolvablePolynomialRing<C,D>	reverse() Reverse variables.
QLRSolvablePolynomialRing<C,D>	reverse(boolean partial) Reverse variables.
RecSolvablePolynomial<D>	toPolyCoefficients(GenPolynomial<C> A) Integral function from rational polynomial coefficients.
RecSolvablePolynomial<D>	toPolyCoefficients(QLRSolvablePolynomial<C,D> A) Integral function from rational polynomial coefficients.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() Get the String representation.
QLRSolvablePolynomial<C,D>	univariate(int i) Generate univariate solvable polynomial in a given variable.
QLRSolvablePolynomial<C,D>	univariate(int modv, int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.
QLRSolvablePolynomial<C,D>	univariate(int i, long e) Generate univariate solvable polynomial in a given variable with given exponent.

Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing

addRelations, addRelations, addSolvRelations, copy, distribute, extend, permutation, recursive, univariateList, univariateList, univariateList, valueOf, valueOf, valueOf

Methods inherited from class edu.jas.poly.GenPolynomialRing

addVars, characteristic, copy, copy, copy, extendLower, extendLower, generators, generators, getComparator, getComparator, getCreations, getGenerators, getONECoefficient, getVars, getZEROCoefficient, isField, isFinite, iterator, newVars, newVars, newVars, newVars, permuteVars, setVars, toScript, univariate, univariate, varsToString

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

polCoeff

public final RecSolvablePolynomialRing<D extends GcdRingElem<D>> polCoeff

Recursive solvable polynomial ring with polynomial coefficients.

ZERO

public final QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>> ZERO

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

ONE

public final QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>> ONE

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

qpfac

public final QuotPairFactory<GenPolynomial<D extends GcdRingElem<D>>,C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>> qpfac

Factory to create coefficients.

Constructor Detail

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(RingFactory<C> cf,
                                 GenSolvablePolynomialRing 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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(RingFactory<C> cf,
                                 QLRSolvablePolynomialRing 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.

QLRSolvablePolynomialRing

public QLRSolvablePolynomialRing(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.

Method Detail

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

toScript in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

hashCode in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

See Also:

Object.hashCode()

getZERO

public QLRSolvablePolynomial<C,D> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

getZERO in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

0 as QLRSolvablePolynomial.

getONE

public QLRSolvablePolynomial<C,D> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

getONE in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

1 as QLRSolvablePolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

isCommutative in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

isAssociative in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

true, if this ring is associative, else false.

fromInteger

public QLRSolvablePolynomial<C,D> fromInteger(long a)

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

Specified by:

fromInteger in interface ElemFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

a - long.

Returns:

a QLRSolvablePolynomial<C>.

fromInteger

public QLRSolvablePolynomial<C,D> fromInteger(java.math.BigInteger a)

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

Specified by:

fromInteger in interface ElemFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

fromInteger in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

a - BigInteger.

Returns:

a QLRSolvablePolynomial<C>.

random

public QLRSolvablePolynomial<C,D> 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<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

random in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

n - number of terms.

Returns:

a random solvable polynomial.

random

public QLRSolvablePolynomial<C,D> 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<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

random in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

random

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

Generate a random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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 QLRSolvablePolynomial<C,D> random(int k,
                                         int l,
                                         int d,
                                         float q,
                                         java.util.Random rnd)

Random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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 QLRSolvablePolynomial<C,D> copy(QLRSolvablePolynomial<C,D> c)

Copy polynomial c.

Parameters:

c -

Returns:

a copy of c.

parse

public QLRSolvablePolynomial<C,D> parse(java.lang.String s)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

parse in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

s - String.

Returns:

QLRSolvablePolynomial from s.

parse

public QLRSolvablePolynomial<C,D> parse(java.io.Reader r)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

parse in interface ElemFactory<GenPolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>>

Overrides:

parse in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

r - Reader.

Returns:

next QLRSolvablePolynomial from r.

univariate

public QLRSolvablePolynomial<C,D> univariate(int i)

Generate univariate solvable polynomial in a given variable.

Overrides:

univariate in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

i - the index of the variable.

Returns:

X_i as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

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.

recUnivariateList

public java.util.List<QLRSolvablePolynomial<C,D>> recUnivariateList()

Generate list of univariate polynomials in all variables.

Returns:

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

recUnivariateList

public java.util.List<QLRSolvablePolynomial<C,D>> recUnivariateList(int modv)

Generate list of univariate polynomials in all variables.

Parameters:

modv - number of module variables.

Returns:

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

recUnivariateList

public java.util.List<QLRSolvablePolynomial<C,D>> recUnivariateList(int modv,
                                                                    long e)

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

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 QLRSolvablePolynomialRing<C,D> extend(int i)

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

Overrides:

extend in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

i - number of variables to extend.

Returns:

extended solvable polynomial ring factory.

contract

public QLRSolvablePolynomialRing<C,D> contract(int i)

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

Overrides:

contract in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

i - number of variables to remove.

Returns:

contracted solvable polynomial ring factory.

reverse

public QLRSolvablePolynomialRing<C,D> reverse()

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

Overrides:

reverse in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Returns:

solvable polynomial ring factory with reversed variables.

reverse

public QLRSolvablePolynomialRing<C,D> reverse(boolean partial)

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

Overrides:

reverse in class GenSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>>

Parameters:

partial - true for partialy reversed term orders.

Returns:

solvable polynomial ring factory with reversed variables.

fromPolyCoefficients

public QLRSolvablePolynomial<C,D> fromPolyCoefficients(GenSolvablePolynomial<GenPolynomial<D>> A)

Rational function from integral polynomial coefficients. Represent as polynomial with type C coefficients.

Parameters:

A - polynomial with integral polynomial coefficients to be converted.

Returns:

polynomial with type C coefficients.

toPolyCoefficients

public RecSolvablePolynomial<D> toPolyCoefficients(QLRSolvablePolynomial<C,D> A)

Integral function from rational polynomial coefficients. Represent as polynomial with type GenSolvablePolynomial coefficients.

Parameters:

A - polynomial with rational polynomial coefficients to be converted.

Returns:

polynomial with type GenSolvablePolynomial coefficients.

toPolyCoefficients

public RecSolvablePolynomial<D> toPolyCoefficients(GenPolynomial<C> A)

Integral function from rational polynomial coefficients. Represent as polynomial with type GenSolvablePolynomial coefficients.

Parameters:

A - polynomial with rational polynomial coefficients to be converted.

Returns:

polynomial with type GenSolvablePolynomial coefficients.