RecSolvablePolynomialRing

java.lang.Object
- edu.jas.poly.GenPolynomialRing<C>
- - edu.jas.poly.GenSolvablePolynomialRing<GenPolynomial<C>>
  - - edu.jas.poly.RecSolvablePolynomialRing<C>

Type Parameters:

C - coefficient type.

All Implemented Interfaces:

AbelianGroupFactory<GenPolynomial<GenPolynomial<C>>>, ElemFactory<GenPolynomial<GenPolynomial<C>>>, MonoidFactory<GenPolynomial<GenPolynomial<C>>>, RingFactory<GenPolynomial<GenPolynomial<C>>>, java.io.Serializable, java.lang.Iterable<GenPolynomial<GenPolynomial<C>>>
```
public class RecSolvablePolynomialRing<C extends RingElem<C>>
extends GenSolvablePolynomialRing<GenPolynomial<C>>
```
RecSolvablePolynomialRing 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.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`RelationTable<GenPolynomial<C>>`	`coeffTable` The solvable multiplication relations between variables and coefficients.
`RecSolvablePolynomial<C>`	`ONE` The constant polynomial 1 for this ring.
`RecSolvablePolynomial<C>`	`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
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n)` The constructor creates a solvable polynomial factory object with the default term order and commutative relations.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, RelationTable<GenPolynomial<C>> rt)` The constructor creates a solvable polynomial factory object with the default term order.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t)` The constructor creates a solvable polynomial factory object with the given term order and commutative relations.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, RelationTable<GenPolynomial<C>> rt)` The constructor creates a solvable polynomial factory object with the given term order.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, int n, TermOrder t, java.lang.String[] v, RelationTable<GenPolynomial<C>> rt)` The constructor creates a solvable polynomial factory object with the given term order.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, RecSolvablePolynomialRing 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.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf, java.lang.String[] v)` The constructor creates a solvable polynomial factory object with the default term order.
`RecSolvablePolynomialRing(RingFactory<GenPolynomial<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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`RecSolvablePolynomialRing<C>`	`contract(int i)` Contract variables.
`RecSolvablePolynomial<C>`	`copy(RecSolvablePolynomial<C> c)` Copy polynomial c.
`static <C extends RingElem<C>> GenSolvablePolynomialRing<C>`	`distribute(RecSolvablePolynomialRing<C> rf)` Distributive representation as polynomial with all main variables.
`boolean`	`equals(java.lang.Object other)` Comparison with any other object.
`RecSolvablePolynomialRing<C>`	`extend(int i)` Extend variables.
`RecSolvablePolynomialRing<C>`	`extend(java.lang.String[] vs)` Extend variables.
`RecSolvablePolynomial<C>`	`fromInteger(java.math.BigInteger a)` Get a (constant) RecSolvablePolynomial<C> element from a BigInteger value.
`RecSolvablePolynomial<C>`	`fromInteger(long a)` Get a (constant) RecSolvablePolynomial<C> element from a long value
`RecSolvablePolynomial<C>`	`getONE()` Get the one element.
`RecSolvablePolynomial<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.
`RecSolvablePolynomial<C>`	`parse(java.io.Reader r)` Parse a solvable polynomial with the use of GenPolynomialTokenizer
`RecSolvablePolynomial<C>`	`parse(java.lang.String s)` Parse a solvable polynomial with the use of GenPolynomialTokenizer
`GenSolvablePolynomialRing<GenPolynomial<C>>`	`permutation(java.util.List<java.lang.Integer> P)` Permutation of polynomial ring variables.
`RecSolvablePolynomial<C>`	`random(int n)` Random solvable polynomial.
`RecSolvablePolynomial<C>`	`random(int k, int l, int d, float q)` Generate a random solvable polynomial.
`RecSolvablePolynomial<C>`	`random(int k, int l, int d, float q, java.util.Random rnd)` Random solvable polynomial.
`RecSolvablePolynomial<C>`	`random(int n, java.util.Random rnd)` Random solvable polynomial.
`java.util.List<RecSolvablePolynomial<C>>`	`recUnivariateList()` Generate list of univariate polynomials in all variables.
`java.util.List<RecSolvablePolynomial<C>>`	`recUnivariateList(int modv)` Generate list of univariate polynomials in all variables.
`java.util.List<RecSolvablePolynomial<C>>`	`recUnivariateList(int modv, long e)` Generate list of univariate polynomials in all variables with given exponent.
`RecSolvablePolynomialRing<C>`	`reverse()` Reverse variables.
`RecSolvablePolynomialRing<C>`	`reverse(boolean partial)` Reverse variables.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toString()` Get the String representation.
`RecSolvablePolynomial<C>`	`univariate(int i)` Generate univariate solvable polynomial in a given variable.
`RecSolvablePolynomial<C>`	`univariate(int modv, int i, long e)` Generate univariate solvable polynomial in a given variable with given exponent.
`RecSolvablePolynomial<C>`	`univariate(int i, long e)` Generate univariate solvable polynomial in a given variable with given exponent.
`RecSolvablePolynomial<C>`	`valueOf(ExpVector e)` Get a RecSolvablePolynomial<C> element from an exponent vector.
`RecSolvablePolynomial<C>`	`valueOf(GenPolynomial<C> a)` Get a (constant) RecSolvablePolynomial<C> element from a coefficient value.
`RecSolvablePolynomial<C>`	`valueOf(GenPolynomial<C> a, ExpVector e)` Get a RecSolvablePolynomial<C> element from a coeffcient and an exponent vector.

Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing
addRelations, addRelations, addSolvRelations, copy, distribute, recursive, univariateList, univariateList, univariateList

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
  - coeffTable
```
public final RelationTable<GenPolynomial<C extends RingElem<C>>> coeffTable
```
    The solvable multiplication relations between variables and coefficients.
  - ZERO
```
public final RecSolvablePolynomial<C extends RingElem<C>> ZERO
```
    The constant polynomial 0 for this ring. Hides super ZERO.
  - ONE
```
public final RecSolvablePolynomial<C extends RingElem<C>> ONE
```
    The constant polynomial 1 for this ring. Hides super ONE.
- Constructor Detail
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf,
                                 int n,
                                 RelationTable<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf,
                                 int n,
                                 TermOrder t,
                                 RelationTable<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf,
                                 int n,
                                 TermOrder t,
                                 java.lang.String[] v,
                                 RelationTable<GenPolynomial<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.
  - RecSolvablePolynomialRing
```
public RecSolvablePolynomialRing(RingFactory<GenPolynomial<C>> cf,
                                 RecSolvablePolynomialRing 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 Detail
  - toString
```
public java.lang.String toString()
```
    Get the String representation.
    
    Overrides:
    
    toString in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface ElemFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    toScript in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    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<GenPolynomial<C extends RingElem<C>>>
    
    See Also:
    
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this polynomial ring.
    
    Overrides:
    
    hashCode in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    See Also:
    
    Object.hashCode()
  - getZERO
```
public RecSolvablePolynomial<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    getZERO in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    0 as RecSolvablePolynomial.
  - getONE
```
public RecSolvablePolynomial<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    getONE in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    1 as RecSolvablePolynomial.
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    isCommutative in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<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<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    isAssociative in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    true, if this ring is associative, else false.
  - valueOf
```
public RecSolvablePolynomial<C> valueOf(GenPolynomial<C> a)
```
    Get a (constant) RecSolvablePolynomial<C> element from a coefficient value.
    
    Overrides:
    
    valueOf in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    a - coefficient.
    
    Returns:
    
    a RecSolvablePolynomial<C>.
  - valueOf
```
public RecSolvablePolynomial<C> valueOf(ExpVector e)
```
    Get a RecSolvablePolynomial<C> element from an exponent vector.
    
    Overrides:
    
    valueOf in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    e - exponent vector.
    
    Returns:
    
    a RecSolvablePolynomial<C>.
  - valueOf
```
public RecSolvablePolynomial<C> valueOf(GenPolynomial<C> a,
                                        ExpVector e)
```
    Get a RecSolvablePolynomial<C> element from a coeffcient and an exponent vector.
    
    Overrides:
    
    valueOf in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    a - coefficient.
    
    e - exponent vector.
    
    Returns:
    
    a RecSolvablePolynomial<C>.
  - fromInteger
```
public RecSolvablePolynomial<C> fromInteger(long a)
```
    Get a (constant) RecSolvablePolynomial<C> element from a long value
    
    Specified by:
    
    fromInteger in interface ElemFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    fromInteger in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a RecSolvablePolynomial<C>.
  - fromInteger
```
public RecSolvablePolynomial<C> fromInteger(java.math.BigInteger a)
```
    Get a (constant) RecSolvablePolynomial<C> element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    fromInteger in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a RecSolvablePolynomial<C>.
  - random
```
public RecSolvablePolynomial<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<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    random in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    n - number of terms.
    
    Returns:
    
    a random solvable polynomial.
  - random
```
public RecSolvablePolynomial<C> 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<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    random in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    n - number of terms.
    
    rnd - is a source for random bits.
    
    Returns:
    
    a random solvable polynomial.
  - random
```
public RecSolvablePolynomial<C> random(int k,
                                       int l,
                                       int d,
                                       float q)
```
    Generate a random solvable polynomial.
    
    Overrides:
    
    random in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<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 RecSolvablePolynomial<C> random(int k,
                                       int l,
                                       int d,
                                       float q,
                                       java.util.Random rnd)
```
    Random solvable polynomial.
    
    Overrides:
    
    random in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<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 RecSolvablePolynomial<C> copy(RecSolvablePolynomial<C> c)
```
    Copy polynomial c.
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - parse
```
public RecSolvablePolynomial<C> parse(java.lang.String s)
```
    Parse a solvable polynomial with the use of GenPolynomialTokenizer
    
    Specified by:
    
    parse in interface ElemFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    parse in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    s - String.
    
    Returns:
    
    RecSolvablePolynomial from s.
  - parse
```
public RecSolvablePolynomial<C> parse(java.io.Reader r)
```
    Parse a solvable polynomial with the use of GenPolynomialTokenizer
    
    Specified by:
    
    parse in interface ElemFactory<GenPolynomial<GenPolynomial<C extends RingElem<C>>>>
    
    Overrides:
    
    parse in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    r - Reader.
    
    Returns:
    
    next RecSolvablePolynomial from r.
  - univariate
```
public RecSolvablePolynomial<C> univariate(int i)
```
    Generate univariate solvable polynomial in a given variable.
    
    Overrides:
    
    univariate in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    i - the index of the variable.
    
    Returns:
    
    X_i as solvable univariate polynomial.
  - univariate
```
public RecSolvablePolynomial<C> univariate(int i,
                                           long e)
```
    Generate univariate solvable polynomial in a given variable with given exponent.
    
    Overrides:
    
    univariate in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    i - the index of the variable.
    
    e - the exponent of the variable.
    
    Returns:
    
    X_i^e as solvable univariate polynomial.
  - univariate
```
public RecSolvablePolynomial<C> univariate(int modv,
                                           int i,
                                           long e)
```
    Generate univariate solvable polynomial in a given variable with given exponent.
    
    Overrides:
    
    univariate in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<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.
  - recUnivariateList
```
public java.util.List<RecSolvablePolynomial<C>> 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<RecSolvablePolynomial<C>> 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<RecSolvablePolynomial<C>> 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 RecSolvablePolynomialRing<C> extend(int i)
```
    Extend variables. Used e.g. in module embedding. Extend number of variables by i.
    
    Overrides:
    
    extend in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    i - number of variables to extend.
    
    Returns:
    
    extended solvable polynomial ring factory.
  - extend
```
public RecSolvablePolynomialRing<C> extend(java.lang.String[] vs)
```
    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<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    vs - names for extended variables.
    
    Returns:
    
    extended polynomial ring factory.
  - contract
```
public RecSolvablePolynomialRing<C> contract(int i)
```
    Contract variables. Used e.g. in module embedding. Contract number of variables by i.
    
    Overrides:
    
    contract in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    i - number of variables to remove.
    
    Returns:
    
    contracted solvable polynomial ring factory.
  - reverse
```
public RecSolvablePolynomialRing<C> reverse()
```
    Reverse variables. Used e.g. in opposite rings.
    
    Overrides:
    
    reverse in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Returns:
    
    solvable polynomial ring factory with reversed variables.
  - reverse
```
public RecSolvablePolynomialRing<C> reverse(boolean partial)
```
    Reverse variables. Used e.g. in opposite rings.
    
    Overrides:
    
    reverse in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    partial - true for partialy reversed term orders.
    
    Returns:
    
    solvable polynomial ring factory with reversed variables.
  - distribute
```
public static <C extends RingElem<C>> GenSolvablePolynomialRing<C> distribute(RecSolvablePolynomialRing<C> rf)
```
    Distributive representation as polynomial with all main variables.
    
    Returns:
    
    distributive polynomial ring factory.
  - permutation
```
public GenSolvablePolynomialRing<GenPolynomial<C>> permutation(java.util.List<java.lang.Integer> P)
```
    Permutation of polynomial ring variables.
    
    Overrides:
    
    permutation in class GenSolvablePolynomialRing<GenPolynomial<C extends RingElem<C>>>
    
    Parameters:
    
    P - permutation.
    
    Returns:
    
    P(this).

Class RecSolvablePolynomialRing<C extends RingElem<C>>

Field Summary

Fields inherited from class edu.jas.poly.GenSolvablePolynomialRing

Fields inherited from class edu.jas.poly.GenPolynomialRing

Constructor Summary

Method Summary

Methods inherited from class edu.jas.poly.GenSolvablePolynomialRing

Methods inherited from class edu.jas.poly.GenPolynomialRing

Methods inherited from class java.lang.Object

Methods inherited from interface java.lang.Iterable

Field Detail

coeffTable

ZERO

ONE

Constructor Detail

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

RecSolvablePolynomialRing

Method Detail

toString

toScript

equals

hashCode

getZERO

getONE

isCommutative

isAssociative

valueOf

valueOf

valueOf

fromInteger

fromInteger

random

random

random

random

copy

parse

parse

univariate

univariate

univariate

recUnivariateList

recUnivariateList

recUnivariateList

extend

extend

contract

reverse

reverse

distribute

permutation