Class LocalSolvablePolynomialRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.poly.GenPolynomialRing<SolvableLocal<C>>

edu.jas.poly.GenSolvablePolynomialRing<SolvableLocal<C>>

edu.jas.application.LocalSolvablePolynomialRing<C>

Type Parameters:

C - coefficient type.

All Implemented Interfaces:

AbelianGroupFactory<GenPolynomial<SolvableLocal<C>>>, ElemFactory<GenPolynomial<SolvableLocal<C>>>, MonoidFactory<GenPolynomial<SolvableLocal<C>>>, RingFactory<GenPolynomial<SolvableLocal<C>>>, Serializable, Iterable<GenPolynomial<SolvableLocal<C>>>

public class LocalSolvablePolynomialRing<C extends GcdRingElem<C>>
extends GenSolvablePolynomialRing<SolvableLocal<C>>

LocalSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory. Factory for n-variate ordered solvable polynomials over solvable polynomial 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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final org.apache.logging.log4j.Logger	logger
final LocalSolvablePolynomial<C>	ONE	The constant polynomial 1 for this ring.
final RecSolvablePolynomialRing<C>	polCoeff	Recursive solvable polynomial ring with polynomial coefficients.
final LocalSolvablePolynomial<C>	ZERO	The constant polynomial 0 for this ring.

Fields inherited from class GenSolvablePolynomialRing

table

Fields inherited from class GenPolynomialRing

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

Constructor Summary

Constructors

Constructor	Description
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n)	The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n, RelationTable<SolvableLocal<C>> rt)	The constructor creates a solvable polynomial factory object with the default term order.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n, TermOrder t)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n, TermOrder t, RelationTable<SolvableLocal<C>> rt)	The constructor creates a solvable polynomial factory object with the given term order.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n, TermOrder t, String[] v)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, int n, TermOrder t, String[] v, RelationTable<SolvableLocal<C>> rt)	The constructor creates a solvable polynomial factory object with the given term order.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, LocalSolvablePolynomialRing 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.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<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.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, TermOrder t, String[] v)	The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf, String[] v)	The constructor creates a solvable polynomial factory object with the default term order.

Method Summary

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

Methods inherited from class GenSolvablePolynomialRing

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

Methods inherited from class GenPolynomialRing

characteristic, charPolynomial, copy, copy, copy, determinant, determinantFromCharPol, extendLower, extendLower, extendLower, fromVector, generators, generators, getComparator, getComparator, getCreations, getGenerators, getONECoefficient, getVars, getZEROCoefficient, isField, isFinite, iterator, newVars, newVars, newVars, newVars, permuteVars, setVars, toScript, traceFromCharPol, univariate, univariate, valueOf, valueOf, varsToString

Methods inherited from class Object

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

Methods inherited from interface ElemFactory

valueOf

Methods inherited from interface Iterable

forEach, spliterator

Field Details

polCoeff

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

Recursive solvable polynomial ring with polynomial coefficients.

ZERO

public final LocalSolvablePolynomial<C extends GcdRingElem<C>> ZERO

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

ONE

public final LocalSolvablePolynomial<C extends GcdRingElem<C>> ONE

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

logger

private static final org.apache.logging.log4j.Logger logger

Constructor Details

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<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.

LocalSolvablePolynomialRing

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

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<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.

LocalSolvablePolynomialRing

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

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf,
 int n,
 TermOrder t,
 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.

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf,
 TermOrder t,
 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.

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf,
 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.

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf,
 int n,
 TermOrder t,
 String[] v,
 RelationTable<SolvableLocal<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.

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<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.

LocalSolvablePolynomialRing

public LocalSolvablePolynomialRing(RingFactory<SolvableLocal<C>> cf,
 LocalSolvablePolynomialRing 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 Details

toString

public String toString()

Get the String representation.

Overrides:

toString in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

See Also:

• Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<C extends GcdRingElem<C>>

Overrides:

toScript in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this Element.

See Also:

• Element.toScript()

equals

public boolean equals(Object other)

Comparison with any other object.

Overrides:

equals in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

See Also:

• Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

hashCode in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

See Also:

• Object.hashCode()

getZERO

public LocalSolvablePolynomial<C> getZERO()

Get the zero element.

Specified by:

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

Overrides:

getZERO in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

0 as LocalSolvablePolynomial.

getONE

public LocalSolvablePolynomial<C> getONE()

Get the one element.

Specified by:

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

Overrides:

getONE in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

1 as LocalSolvablePolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

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

Overrides:

isCommutative in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

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<C extends GcdRingElem<C>>

Overrides:

isAssociative in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

true, if this ring is associative, else false.

fromInteger

public LocalSolvablePolynomial<C> fromInteger(long a)

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

Specified by:

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

Overrides:

fromInteger in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

a - long.

Returns:

a LocalSolvablePolynomial<C>.

fromInteger

public LocalSolvablePolynomial<C> fromInteger(BigInteger a)

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

Specified by:

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

Overrides:

fromInteger in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

a - BigInteger.

Returns:

a LocalSolvablePolynomial<C>.

random

public LocalSolvablePolynomial<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 GcdRingElem<C>>

Overrides:

random in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

n - number of terms.

Returns:

a random solvable polynomial.

random

public LocalSolvablePolynomial<C> random(int n,
 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 GcdRingElem<C>>

Overrides:

random in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

n - number of terms.

rnd - is a source for random bits.

Returns:

a random solvable polynomial.

random

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

Generate a random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 LocalSolvablePolynomial<C> random(int k,
 int l,
 int d,
 float q,
 Random rnd)

Random solvable polynomial.

Overrides:

random in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 LocalSolvablePolynomial<C> copy(LocalSolvablePolynomial<C> c)

Copy polynomial c.

Parameters:

c -

Returns:

a copy of c.

parse

public LocalSolvablePolynomial<C> parse(String s)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

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

Overrides:

parse in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

s - String.

Returns:

LocalSolvablePolynomial from s.

parse

public LocalSolvablePolynomial<C> parse(Reader r)

Parse a solvable polynomial with the use of GenPolynomialTokenizer

Specified by:

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

Overrides:

parse in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

r - Reader.

Returns:

next LocalSolvablePolynomial from r.

univariate

public LocalSolvablePolynomial<C> univariate(int i)

Generate univariate solvable polynomial in a given variable.

Overrides:

univariate in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

i - the index of the variable.

Returns:

X_i as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as solvable univariate polynomial.

univariate

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

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

Overrides:

univariate in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 List<LocalSolvablePolynomial<C>> univariateList()

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

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

univariateList

public List<LocalSolvablePolynomial<C>> univariateList(int modv)

Generate list of univariate polynomials in all variables.

Overrides:

univariateList in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

Returns:

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

univariateList

public List<LocalSolvablePolynomial<C>> univariateList(int modv,
 long e)

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

Overrides:

univariateList in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 LocalSolvablePolynomialRing<C> extend(int i)

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

Overrides:

extend in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

i - number of variables to extend.

Returns:

extended solvable polynomial ring factory.

extend

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

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

Overrides:

extend in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 LocalSolvablePolynomialRing<C> extend(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 GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

vn - names for extended variables.

Returns:

extended polynomial ring factory.

extend

public LocalSolvablePolynomialRing<C> extend(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 GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<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 LocalSolvablePolynomialRing<C> contract(int i)

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

Overrides:

contract in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

i - number of variables to remove.

Returns:

contracted solvable polynomial ring factory.

reverse

public LocalSolvablePolynomialRing<C> reverse()

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

Overrides:

reverse in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

solvable polynomial ring factory with reversed variables.

reverse

public LocalSolvablePolynomialRing<C> reverse(boolean partial)

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

Overrides:

reverse in class GenSolvablePolynomialRing<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

partial - true for partially reversed term orders.

Returns:

solvable polynomial ring factory with reversed variables.

fromPolyCoefficients

public LocalSolvablePolynomial<C> fromPolyCoefficients(GenSolvablePolynomial<GenPolynomial<C>> A)

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

Parameters:

A - polynomial with integral polynomial coefficients to be converted.

Returns:

polynomial with type SolvableLocal coefficients.

toPolyCoefficients

public RecSolvablePolynomial<C> toPolyCoefficients(LocalSolvablePolynomial<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.

toPolyCoefficients

public RecSolvablePolynomial<C> toPolyCoefficients(GenPolynomial<SolvableLocal<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.