ExprPolynomialRing

java.lang.Object
- org.matheclipse.core.polynomials.ExprPolynomialRing

Type Parameters:

C - coefficient type
```
public class ExprPolynomialRing
extends java.lang.Object
```
GenPolynomialRing generic polynomial factory implementing ExprRingFactory; Factory for n-variate ordered polynomials over C. Almost immutable object, except variable names.

Author:

Heinz Kredel

Field Summary

Fields
Modifier and Type	Field and Description
`ExprRingFactory`	`coFac` The factory for the coefficients.
`static int`	`creations` Count for number of polynomial creations.
`ExpVectorLong`	`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.
`ExprPolynomial`	`ONE` The constant polynomial 1 for this ring.
`protected boolean`	`partial` True for partially reversed variables.
`protected static java.util.Random`	`random` A default random sequence generator.
`ExprTermOrder`	`tord` The term order.
`protected IAST`	`vars` The names of the variables.
`ExprPolynomial`	`ZERO` The constant polynomial 0 for this ring.

Constructor Summary

Constructors
Constructor and Description
`ExprPolynomialRing(ExprPolynomialRing o, ExprTermOrder 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.
`ExprPolynomialRing(ExprRingFactory cf, ExprPolynomialRing 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.
`ExprPolynomialRing(ExprRingFactory cf, IAST v)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(ExprRingFactory cf, IAST listOfVariables, ExprTermOrder t)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(ExprRingFactory cf, IAST listOfVariables, int n)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(ExprRingFactory cf, IAST listOfVariables, int n, ExprTermOrder t)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(ExprRingFactory cf, IAST listOfVariables, int n, ExprTermOrder t, boolean numericFunction)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(IAST listOfVariables)` The constructor creates a polynomial factory object.
`ExprPolynomialRing(IAST listOfVariables, ExprTermOrder t)` The constructor creates a polynomial factory object.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static void`	`addVars(IAST vars)` Add variable names.
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`ExprPolynomialRing`	`copy()` Copy this factory.
`ExprPolynomial`	`copy(ExprPolynomial c)` Copy polynomial c.
`ExprPolynomial`	`create(IExpr exprPoly)` Create a `Polynomial` from the given `exprPoly`.
`ExprPolynomial`	`create(IExpr exprPoly, boolean coefficient)` Create a `Polynomial` from the given `exprPoly`.
`ExprPolynomialRing`	`distribute()` Distributive representation as polynomial with all main variables.
`boolean`	`equals(java.lang.Object other)` Comparison with any other object.
`ExprPolynomialRing`	`extend(IAST vn)` Extend variables.
`ExprPolynomialRing`	`extendLower(IAST vn)` Extend lower variables.
`ExprPolynomial`	`fromInteger(java.math.BigInteger a)` Get a (constant) GenPolynomial<C> element from a BigInteger value.
`ExprPolynomial`	`fromInteger(long a)` Get a (constant) GenPolynomial<C> element from a long value.
`java.util.List<ExprPolynomial>`	`generators()` Get a list of the generating elements.
`java.util.List<ExprPolynomial>`	`generators(int modv)` Get a list of the generating elements excluding the module variables.
`ExprPolynomialComparator`	`getComparator()` Get PolynomialComparator.
`ExprPolynomialComparator`	`getComparator(boolean rev)` Get PolynomialComparator.
`int`	`getCreations()` Get the number of polynomial creations.
`java.util.List<ExprPolynomial>`	`getGenerators()` Get the generating elements excluding the generators for the coefficient ring.
`ExprPolynomial`	`getOne()` Get the one element.
`IExpr`	`getONECoefficient()` Get the one element from the coefficients.
`IAST`	`getVars()` Get the variable names.
`ExprPolynomial`	`getZero()` Get the zero element.
`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`.
`java.util.Iterator<ExprPolynomial>`	`iterator()` Get a GenPolynomial iterator.
`static java.lang.String[]`	`permuteVars(java.util.List<java.lang.Integer> P, java.lang.String[] vars)` Permute variable names.
`IAST`	`setVars(IAST v)` Set the variable names.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toScript(ExpVectorLong e)` Get a scripting compatible string representation of an ExpVectorLong of this ring.
`java.lang.String`	`toString()` Get the String representation.
`ExprPolynomial`	`univariate(int i)` Generate univariate polynomial in a given variable.
`ExprPolynomial`	`univariate(int modv, int i, long e)` Generate univariate polynomial in a given variable with given exponent.
`ExprPolynomial`	`univariate(int i, long e)` Generate univariate polynomial in a given variable with given exponent.
`java.util.List<? extends ExprPolynomial>`	`univariateList()` Generate list of univariate polynomials in all variables.
`java.util.List<? extends ExprPolynomial>`	`univariateList(int modv)` Generate list of univariate polynomials in all variables.
`java.util.List<? extends ExprPolynomial>`	`univariateList(int modv, long e)` Generate list of univariate polynomials in all variables with given exponent.
`ExprPolynomial`	`valueOf(ExpVectorLong e)` Get a GenPolynomial<C> element from an exponent vector.
`ExprPolynomial`	`valueOf(IExpr a)` Get a (constant) GenPolynomial<C> element from a coefficient value.
`ExprPolynomial`	`valueOf(IExpr a, ExpVectorLong e)` Get a GenPolynomial<C> element from a coeffcient and an exponent vector.
`java.lang.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

- Field Detail
  - coFac
```
public final ExprRingFactory coFac
```
    The factory for the coefficients.
  - nvar
```
public final int nvar
```
    The number of variables.
  - tord
```
public final ExprTermOrder 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 ExprPolynomial ZERO
```
    The constant polynomial 0 for this ring.
  - ONE
```
public final ExprPolynomial ONE
```
    The constant polynomial 1 for this ring.
  - evzero
```
public final ExpVectorLong evzero
```
    The constant exponent vector 0 for this ring.
  - random
```
protected static final java.util.Random random
```
    A default random sequence generator.
  - isField
```
protected int isField
```
    Indicator if this ring is a field.
  - creations
```
public static int creations
```
    Count for number of polynomial creations.
- Constructor Detail
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          IAST v)
```
    The constructor creates a polynomial factory object.
    
    Parameters:
    
    cf - factory for coefficients of type C.
    
    v - names for the variables.
  - ExprPolynomialRing
```
public ExprPolynomialRing(IAST listOfVariables)
```
    The constructor creates a polynomial factory object.
    
    Parameters:
    
    listOfVariables - names for the variables.
  - ExprPolynomialRing
```
public ExprPolynomialRing(IAST listOfVariables,
                          ExprTermOrder t)
```
    The constructor creates a polynomial factory object.
    
    Parameters:
    
    listOfVariables - names for the variables.
    
    t - a term order.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          IAST listOfVariables,
                          int n)
```
    The constructor creates a polynomial factory object.
    
    Parameters:
    
    cf - factory for coefficients of type C.
    
    listOfVariables - names for the variables.
    
    n - number of variables.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          IAST listOfVariables,
                          ExprTermOrder 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.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          IAST listOfVariables,
                          int n,
                          ExprTermOrder t)
```
    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.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          IAST listOfVariables,
                          int n,
                          ExprTermOrder t,
                          boolean numericFunction)
```
    The constructor creates a polynomial factory object.
    
    Parameters:
    
    cf - factory for coefficients of type C.
    
    v - names for the variables.
    
    n - number of variables.
    
    t - a term order.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprRingFactory cf,
                          ExprPolynomialRing 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.
  - ExprPolynomialRing
```
public ExprPolynomialRing(ExprPolynomialRing o,
                          ExprTermOrder 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 ExprPolynomialRing copy()
```
    Copy this factory.
    
    Returns:
    
    a clone of this.
  - create
```
public ExprPolynomial create(IExpr exprPoly)
                      throws java.lang.ArithmeticException,
                             java.lang.ClassCastException
```
    Create a Polynomial from the given exprPoly.
    
    Parameters:
    
    exprPoly - the polynomial expression
    
    Returns:
    
    Throws:
    
    java.lang.ArithmeticException
    
    java.lang.ClassCastException
  - create
```
public ExprPolynomial create(IExpr exprPoly,
                             boolean coefficient)
                      throws java.lang.ArithmeticException,
                             java.lang.ClassCastException
```
    Create a Polynomial from the given exprPoly.
    
    Parameters:
    
    exprPoly - the polynomial expression
    
    coefficient - set to true if called by the Coefficient() function
    
    Returns:
    
    Throws:
    
    java.lang.ArithmeticException
    
    java.lang.ClassCastException
  - isPolynomial
```
public boolean isPolynomial(IExpr expression)
                     throws java.lang.ArithmeticException,
                            java.lang.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:
    
    java.lang.ArithmeticException
    
    java.lang.ClassCastException
  - isPolynomial
```
public boolean isPolynomial(IExpr expression,
                            boolean coefficient)
                     throws java.lang.ArithmeticException,
                            java.lang.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:
    
    java.lang.ArithmeticException
    
    java.lang.ClassCastException
  - 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.
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()
  - toScript
```
public java.lang.String toScript(ExpVectorLong 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(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()
  - getCreations
```
public int getCreations()
```
    Get the number of polynomial creations.
    
    Returns:
    
    creations.
  - 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 java.lang.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 ExprPolynomial getZero()
```
    Get the zero element.
    
    Returns:
    
    0 as GenPolynomial.
  - getOne
```
public ExprPolynomial getOne()
```
    Get the one element.
    
    Returns:
    
    1 as GenPolynomial.
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Returns:
    
    true if this ring is commutative, else false.
  - isAssociative
```
public boolean isAssociative()
```
    Query if this ring is associative.
    
    Returns:
    
    true if this ring is associative, else false.
  - isField
```
public boolean isField()
```
    Query if this ring is a field.
    
    Returns:
    
    false.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Returns:
    
    characteristic of this ring.
  - valueOf
```
public ExprPolynomial valueOf(IExpr a)
```
    Get a (constant) GenPolynomial<C> element from a coefficient value.
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    a GenPolynomial<C>.
  - valueOf
```
public ExprPolynomial valueOf(ExpVectorLong e)
```
    Get a GenPolynomial<C> element from an exponent vector.
    
    Parameters:
    
    e - exponent vector.
    
    Returns:
    
    a GenPolynomial<C>.
  - valueOf
```
public ExprPolynomial valueOf(IExpr a,
                              ExpVectorLong 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 ExprPolynomial fromInteger(long a)
```
    Get a (constant) GenPolynomial<C> element from a long value.
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a GenPolynomial<C>.
  - fromInteger
```
public ExprPolynomial fromInteger(java.math.BigInteger a)
```
    Get a (constant) GenPolynomial<C> element from a BigInteger value.
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a GenPolynomial<C>.
  - copy
```
public ExprPolynomial copy(ExprPolynomial c)
```
    Copy polynomial c.
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - univariate
```
public ExprPolynomial 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 ExprPolynomial univariate(int i,
                                 long 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 ExprPolynomial univariate(int modv,
                                 int i,
                                 long 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 java.util.List<ExprPolynomial> 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<ExprPolynomial> generators()
```
    Get a list of the generating elements.
    
    Returns:
    
    list of generators for the algebraic structure.
    
    See Also:
    
    ElemFactory.generators()
  - generators
```
public java.util.List<ExprPolynomial> 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.
    
    Returns:
    
    true if this structure is finite, else false.
    
    See Also:
    
    ElemFactory.isFinite()
  - univariateList
```
public java.util.List<? extends ExprPolynomial> univariateList()
```
    Generate list of univariate polynomials in all variables.
    
    Returns:
    
    List(X_1,...,X_n) a list of univariate polynomials.
  - univariateList
```
public java.util.List<? extends ExprPolynomial> 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 java.util.List<? extends ExprPolynomial> univariateList(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 ExprPolynomialRing 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.
  - extendLower
```
public ExprPolynomialRing extendLower(IAST vn)
```
    Extend lower variables. Extend number of variables by length(vn).
    
    Parameters:
    
    vn - names for extended lower variables.
    
    Returns:
    
    extended polynomial ring factory.
  - distribute
```
public ExprPolynomialRing distribute()
```
    Distributive representation as polynomial with all main variables.
    
    Returns:
    
    distributive polynomial ring factory.
  - getComparator
```
public ExprPolynomialComparator getComparator()
```
    Get PolynomialComparator.
    
    Returns:
    
    polynomial comparator.
  - getComparator
```
public ExprPolynomialComparator getComparator(boolean rev)
```
    Get PolynomialComparator.
    
    Parameters:
    
    rev - for reverse comparator.
    
    Returns:
    
    polynomial comparator.
  - addVars
```
public static void addVars(IAST vars)
```
    Add variable names.
    
    Parameters:
    
    vars - variable names to be recorded.
  - permuteVars
```
public static java.lang.String[] permuteVars(java.util.List<java.lang.Integer> P,
                                             java.lang.String[] vars)
```
    Permute variable names.
    
    Parameters:
    
    vars - variable names.
    
    P - permutation.
    
    Returns:
    
    P(vars).
  - iterator
```
public java.util.Iterator<ExprPolynomial> iterator()
```
    Get a GenPolynomial iterator.
    
    Returns:
    
    an iterator over all polynomials.

Class ExprPolynomialRing

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

coFac

nvar

tord

partial

vars

ZERO

ONE

evzero

random

isField

creations

Constructor Detail

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

ExprPolynomialRing

Method Detail

copy

create

create

isPolynomial

isPolynomial

toString

toScript

toScript

equals

hashCode

getCreations

getVars

setVars

varsToString

getZEROCoefficient

getONECoefficient

getZero

getOne

isCommutative

isAssociative

isField

characteristic

valueOf

valueOf

valueOf

fromInteger

fromInteger

copy

univariate

univariate

univariate

getGenerators

generators

generators

isFinite

univariateList

univariateList

univariateList

extend

extendLower

distribute

getComparator

getComparator

addVars

permuteVars

iterator