Package org.matheclipse.core.polynomials.symbolicexponent

Class SymbolicPolynomialRing

java.lang.Object

org.matheclipse.core.polynomials.symbolicexponent.SymbolicPolynomialRing

All Implemented Interfaces:

edu.jas.structure.AbelianGroupFactory<SymbolicPolynomial>, edu.jas.structure.ElemFactory<SymbolicPolynomial>, edu.jas.structure.MonoidFactory<SymbolicPolynomial>, edu.jas.structure.RingFactory<SymbolicPolynomial>, Serializable

public class SymbolicPolynomialRing
extends Object
implements edu.jas.structure.RingFactory<SymbolicPolynomial>

GenPolynomialRing generic polynomial factory implementing ExprRingFactory; Factory for n-variate ordered polynomials over C with Java IExpr exponents. Almost immutable object, except variable names.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
ExprRingFactory	coFac	The factory for the coefficients.
ExpVectorSymbolic	evzero	The constant exponent vector 0 for this ring.
protected int	isField	Indicator if this ring is a field.
int	nvar	The number of variables.
SymbolicPolynomial	ONE	The constant polynomial 1 for this ring.
protected boolean	partial	True for partially reversed variables.
protected static ThreadLocalRandom	random	A default random sequence generator.
SymbolicTermOrder	tord	The term order.
protected IAST	vars	The names of the variables.
SymbolicPolynomial	ZERO	The constant polyl 0 for this ring.

Constructor Summary

Constructors

Constructor	Description
SymbolicPolynomialRing(IAST listOfVariables)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(IAST listOfVariables, SymbolicTermOrder t)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ISymbol symbol)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ISymbol symbol, SymbolicTermOrder t)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ExprRingFactory cf, IAST listOfVariables)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ExprRingFactory cf, IAST listOfVariables, int n, SymbolicTermOrder t, boolean numericFunction)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ExprRingFactory cf, IAST listOfVariables, SymbolicTermOrder t)	The constructor creates a polynomial factory object.
SymbolicPolynomialRing(ExprRingFactory cf, SymbolicPolynomialRing o)	The constructor creates a 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.
SymbolicPolynomialRing(SymbolicPolynomialRing o, SymbolicTermOrder to)	The constructor creates a polynomial factory object with the the same coefficient factory, number of variables and variable names as the given polynomial factory, only the term order differs.

Method Summary

Modifier and Type	Method	Description
BigInteger	characteristic()	Characteristic of this ring.
SymbolicPolynomialRing	copy()	Copy this factory.
SymbolicPolynomial	copy(SymbolicPolynomial c)	Copy polynomial c.
SymbolicPolynomial	create(IExpr exprPoly)	Create a Polynomial from the given exprPoly.
SymbolicPolynomial	create(IExpr exprPoly, boolean coefficient, boolean checkNegativeExponents, boolean coefficientListMode)	Create a Polynomial from the given exprPoly.
static Map<IExpr,IExpr>	create(IExpr exprPoly, IExpr x, Map<IExpr,IExpr> coefficientMap, IASTAppendable restList)	Create the coefficients of the (univariate) polynomial in coefficientMap and append non-polynomial terms to restList
static Map<IExpr,IExpr>	createTimes(IAST ast, IExpr x, Map<IExpr,IExpr> coefficientMap, IASTAppendable restList)
boolean	equals(Object other)	Comparison with any other object.
SymbolicPolynomialRing	extend(IAST vn)	Extend variables.
SymbolicPolynomial	fromInteger(long a)	Get a (constant) GenPolynomial<C> element from a long value.
SymbolicPolynomial	fromInteger(BigInteger a)	Get a (constant) GenPolynomial<C> element from a BigInteger value.
List<SymbolicPolynomial>	generators()	Get a list of the generating elements.
List<SymbolicPolynomial>	generators(int modv)	Get a list of the generating elements excluding the module variables.
org.matheclipse.core.polynomials.symbolicexponent.SymbolicPolynomialRing.SymbolicPolynomialComparator	getComparator()	Get PolynomialComparator.
org.matheclipse.core.polynomials.symbolicexponent.SymbolicPolynomialRing.SymbolicPolynomialComparator	getComparator(boolean rev)	Get PolynomialComparator.
List<SymbolicPolynomial>	getGenerators()	Get the generating elements excluding the generators for the coefficient ring.
SymbolicPolynomial	getOne()	Get the one element.
SymbolicPolynomial	getONE()
IExpr	getONECoefficient()	Get the one element from the coefficients.
IAST	getVars()	Get the variable names.
SymbolicPolynomial	getZero()	Get the zero element.
SymbolicPolynomial	getZERO()
IExpr	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.
boolean	isPolynomial(IExpr expression)	Create a Polynomial from the given exprPoly.
boolean	isPolynomial(IExpr expression, boolean coefficient)	Create a Polynomial from the given exprPoly.
Iterator<SymbolicPolynomial>	iterator()	Get a GenPolynomial iterator.
SymbolicPolynomial	parse(Reader r)
SymbolicPolynomial	parse(String s)
static String[]	permuteVars(List<Integer> P, String[] vars)	Permute variable names.
SymbolicPolynomial	random(int n)
SymbolicPolynomial	random(int n, Random random)
IAST	setVars(IAST v)	Set the variable names.
String	toScript()	Get a scripting compatible string representation.
String	toScript(ExpVectorSymbolic e)	Get a scripting compatible string representation of an ExpVectorLong of this ring.
String	toString()	Get the String representation.
SymbolicPolynomial	univariate(int i)	Generate univariate polynomial in a given variable.
SymbolicPolynomial	univariate(int modv, int i, IExpr e)	Generate univariate polynomial in a given variable with given exponent.
SymbolicPolynomial	univariate(int i, IExpr e)	Generate univariate polynomial in a given variable with given exponent.
List<? extends SymbolicPolynomial>	univariateList()	Generate list of univariate polynomials in all variables.
List<? extends SymbolicPolynomial>	univariateList(int modv)	Generate list of univariate polynomials in all variables.
List<? extends SymbolicPolynomial>	univariateList(int modv, IExpr e)	Generate list of univariate polynomials in all variables with given exponent.
SymbolicPolynomial	valueOf(IExpr a)	Get a (constant) GenPolynomial<C> element from a coefficient value.
SymbolicPolynomial	valueOf(IExpr a, ExpVectorSymbolic e)	Get a GenPolynomial<C> element from a coeffcient and an exponent vector.
SymbolicPolynomial	valueOf(ExpVectorSymbolic e)	Get a GenPolynomial<C> element from an exponent vector.
String	varsToString()	Get a String representation of the variable names.

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 ExprRingFactory coFac

The factory for the coefficients.

nvar

public final int nvar

The number of variables.

tord

public final SymbolicTermOrder tord

The term order.

partial

protected boolean partial

True for partially reversed variables.

vars

protected IAST vars

The names of the variables. This value can be modified.

ZERO

public final SymbolicPolynomial ZERO

The constant polyl 0 for this ring.

ONE

public final SymbolicPolynomial ONE

The constant polynomial 1 for this ring.

evzero

public final ExpVectorSymbolic evzero

The constant exponent vector 0 for this ring.

random

protected static final ThreadLocalRandom random

A default random sequence generator.

isField

protected int isField

Indicator if this ring is a field.

Constructor Detail

SymbolicPolynomialRing

public SymbolicPolynomialRing(IAST listOfVariables)

The constructor creates a polynomial factory object.

Parameters:

listOfVariables - names for the variables.

SymbolicPolynomialRing

public SymbolicPolynomialRing(IAST listOfVariables,
                              SymbolicTermOrder t)

The constructor creates a polynomial factory object.

Parameters:

listOfVariables - names for the variables.

t - a term order.

SymbolicPolynomialRing

public SymbolicPolynomialRing(ISymbol symbol)

The constructor creates a polynomial factory object.

Parameters:

symbol - name of a variable.

SymbolicPolynomialRing

public SymbolicPolynomialRing(ISymbol symbol,
                              SymbolicTermOrder t)

The constructor creates a polynomial factory object.

Parameters:

symbol - name of a variable.

t - a term order.

SymbolicPolynomialRing

public SymbolicPolynomialRing(ExprRingFactory cf,
                              IAST listOfVariables)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

listOfVariables - names for the variables.

SymbolicPolynomialRing

public SymbolicPolynomialRing(ExprRingFactory cf,
                              IAST listOfVariables,
                              SymbolicTermOrder t)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

listOfVariables - names for the variables.

t - a term order.

SymbolicPolynomialRing

public SymbolicPolynomialRing(ExprRingFactory cf,
                              IAST listOfVariables,
                              int n,
                              SymbolicTermOrder t,
                              boolean numericFunction)

The constructor creates a polynomial factory object.

Parameters:

cf - factory for coefficients of type C.

listOfVariables - names for the variables.

n - number of variables.

t - a term order.

numericFunction -

SymbolicPolynomialRing

public SymbolicPolynomialRing(ExprRingFactory cf,
                              SymbolicPolynomialRing o)

The constructor creates a 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.

Parameters:

cf - factory for coefficients of type C.

o - other polynomial ring.

SymbolicPolynomialRing

public SymbolicPolynomialRing(SymbolicPolynomialRing o,
                              SymbolicTermOrder to)

The constructor creates a polynomial factory object with the the same coefficient factory, number of variables and variable names as the given polynomial factory, only the term order differs.

Parameters:

to - term order.

o - other polynomial ring.

Method Detail

copy

public SymbolicPolynomialRing copy()

Copy this factory.

Returns:

a clone of this.

create

public SymbolicPolynomial create(IExpr exprPoly)
                          throws ArithmeticException,
                                 ClassCastException

Create a Polynomial from the given exprPoly.

Parameters:

exprPoly - the polynomial expression

Returns:

Throws:

ArithmeticException

ClassCastException

create

public SymbolicPolynomial create(IExpr exprPoly,
                                 boolean coefficient,
                                 boolean checkNegativeExponents,
                                 boolean coefficientListMode)
                          throws ArithmeticException,
                                 ClassCastException

Create a Polynomial from the given exprPoly.

Parameters:

exprPoly - the polynomial expression

coefficient - set to true if called by the Coefficient() function

checkNegativeExponents - if true don't allow negative exponents and throw an ArithmeticException

coefficientListMode - if in coefficient list mode don't collect negative Power() exponents

Returns:

Throws:

ArithmeticException

ClassCastException

create

public static Map<IExpr,IExpr> create(IExpr exprPoly,
                                            IExpr x,
                                            Map<IExpr,IExpr> coefficientMap,
                                            IASTAppendable restList)
                                     throws ArithmeticException

Create the coefficients of the (univariate) polynomial in coefficientMap and append non-polynomial terms to restList

Parameters:

exprPoly - the polynomial expression

x - the variable x

coefficientMap - the map of exponents to the associated coefficients

restList - the terms which are non-polynomial

Returns:

Throws:

ArithmeticException

createTimes

public static Map<IExpr,IExpr> createTimes(IAST ast,
                                                 IExpr x,
                                                 Map<IExpr,IExpr> coefficientMap,
                                                 IASTAppendable restList)

isPolynomial

public boolean isPolynomial(IExpr expression)
                     throws ArithmeticException,
                            ClassCastException

Create a Polynomial from the given exprPoly.

Parameters:

expression - the expression which should be checked if it's a polynomial

Returns:

true if the given expression is a polynomial

Throws:

ArithmeticException

ClassCastException

isPolynomial

public boolean isPolynomial(IExpr expression,
                            boolean coefficient)
                     throws ArithmeticException,
                            ClassCastException

Create a Polynomial from the given exprPoly.

Parameters:

expression - the expression which should be checked if it's a polynomial

coefficient - set to true if called by the Coefficient() function

Returns:

true if the given expression is a polynomial

Throws:

ArithmeticException

ClassCastException

toString

public String toString()

Get the String representation.

Overrides:

toString in class Object

See Also:

Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

toScript

public String toScript(ExpVectorSymbolic e)

Get a scripting compatible string representation of an ExpVectorLong of this ring.

Parameters:

e - exponent vector

Returns:

script compatible representation for the ExpVectorLong.

equals

public boolean equals(Object other)

Comparison with any other object.

Overrides:

equals in class Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this polynomial ring.

Overrides:

hashCode in class Object

See Also:

Object.hashCode()

getVars

public IAST getVars()

Get the variable names.

Returns:

vars.

setVars

public IAST setVars(IAST v)

Set the variable names.

Returns:

old vars.

varsToString

public String varsToString()

Get a String representation of the variable names.

Returns:

names seperated by commas.

getZEROCoefficient

public IExpr getZEROCoefficient()

Get the zero element from the coefficients.

Returns:

0 as C.

getONECoefficient

public IExpr getONECoefficient()

Get the one element from the coefficients.

Returns:

1 as C.

getZero

public SymbolicPolynomial getZero()

Get the zero element.

Returns:

0 as GenPolynomial.

getOne

public SymbolicPolynomial getOne()

Get the one element.

Returns:

1 as GenPolynomial.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface edu.jas.structure.MonoidFactory<SymbolicPolynomial>

Returns:

true if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface edu.jas.structure.MonoidFactory<SymbolicPolynomial>

Returns:

true if this ring is associative, else false.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface edu.jas.structure.RingFactory<SymbolicPolynomial>

Returns:

false.

characteristic

public BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface edu.jas.structure.RingFactory<SymbolicPolynomial>

Returns:

characteristic of this ring.

valueOf

public SymbolicPolynomial valueOf(IExpr a)

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

Parameters:

a - coefficient.

Returns:

a GenPolynomial<C>.

valueOf

public SymbolicPolynomial valueOf(ExpVectorSymbolic e)

Get a GenPolynomial<C> element from an exponent vector.

Parameters:

e - exponent vector.

Returns:

a GenPolynomial<C>.

valueOf

public SymbolicPolynomial valueOf(IExpr a,
                                  ExpVectorSymbolic e)

Get a GenPolynomial<C> element from a coeffcient and an exponent vector.

Parameters:

a - coefficient.

e - exponent vector.

Returns:

a GenPolynomial<C>.

fromInteger

public SymbolicPolynomial fromInteger(long a)

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

Specified by:

fromInteger in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Parameters:

a - long.

Returns:

a GenPolynomial<C>.

fromInteger

public SymbolicPolynomial fromInteger(BigInteger a)

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

Specified by:

fromInteger in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Parameters:

a - BigInteger.

Returns:

a GenPolynomial<C>.

copy

public SymbolicPolynomial copy(SymbolicPolynomial c)

Copy polynomial c.

Specified by:

copy in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Parameters:

c -

Returns:

a copy of c.

univariate

public SymbolicPolynomial univariate(int i)

Generate univariate polynomial in a given variable.

Parameters:

i - the index of the variable.

Returns:

X_i as univariate polynomial.

univariate

public SymbolicPolynomial univariate(int i,
                                     IExpr e)

Generate univariate polynomial in a given variable with given exponent.

Parameters:

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as univariate polynomial.

univariate

public SymbolicPolynomial univariate(int modv,
                                     int i,
                                     IExpr e)

Generate univariate polynomial in a given variable with given exponent.

Parameters:

modv - number of module variables.

i - the index of the variable.

e - the exponent of the variable.

Returns:

X_i^e as univariate polynomial.

getGenerators

public List<SymbolicPolynomial> getGenerators()

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

Returns:

a list of generating elements for this ring.

generators

public List<SymbolicPolynomial> generators()

Get a list of the generating elements.

Specified by:

generators in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

generators

public List<SymbolicPolynomial> generators(int modv)

Get a list of the generating elements excluding the module variables.

Parameters:

modv - number of module variables

Returns:

list of generators for the polynomial ring.

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

univariateList

public List<? extends SymbolicPolynomial> univariateList()

Generate list of univariate polynomials in all variables.

Returns:

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

univariateList

public List<? extends SymbolicPolynomial> univariateList(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.

univariateList

public List<? extends SymbolicPolynomial> univariateList(int modv,
                                                         IExpr 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 SymbolicPolynomialRing extend(IAST vn)

Extend variables. Used e.g. in module embedding. Extend number of variables by length(vn).

Parameters:

vn - names for extended variables.

Returns:

extended polynomial ring factory.

getComparator

public org.matheclipse.core.polynomials.symbolicexponent.SymbolicPolynomialRing.SymbolicPolynomialComparator getComparator()

Get PolynomialComparator.

Returns:

polynomial comparator.

getComparator

public org.matheclipse.core.polynomials.symbolicexponent.SymbolicPolynomialRing.SymbolicPolynomialComparator getComparator(boolean rev)

Get PolynomialComparator.

Parameters:

rev - for reverse comparator.

Returns:

polynomial comparator.

permuteVars

public static String[] permuteVars(List<Integer> P,
                                   String[] vars)

Permute variable names.

Parameters:

vars - variable names.

P - permutation.

Returns:

P(vars).

iterator

public Iterator<SymbolicPolynomial> iterator()

Get a GenPolynomial iterator.

Returns:

an iterator over all polynomials.

getZERO

public SymbolicPolynomial getZERO()

Specified by:

getZERO in interface edu.jas.structure.AbelianGroupFactory<SymbolicPolynomial>

random

public SymbolicPolynomial random(int n)

Specified by:

random in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

random

public SymbolicPolynomial random(int n,
                                 Random random)

Specified by:

random in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

parse

public SymbolicPolynomial parse(String s)

Specified by:

parse in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

parse

public SymbolicPolynomial parse(Reader r)

Specified by:

parse in interface edu.jas.structure.ElemFactory<SymbolicPolynomial>

getONE

public SymbolicPolynomial getONE()

Specified by:

getONE in interface edu.jas.structure.MonoidFactory<SymbolicPolynomial>