edu.jas.poly

Class TermOrderOptimization

java.lang.Object

edu.jas.poly.TermOrderOptimization

public class TermOrderOptimization
extends java.lang.Object

Term order optimization. See mas10/maspoly/DIPTOO.m{di}.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor and Description
TermOrderOptimization()

Method Summary

Modifier and Type	Method and Description
static <T> T[]	arrayPermutation(java.util.List<java.lang.Integer> P, T[] a) Permutation of an array.
static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>>	degreeMatrix(java.util.Collection<GenPolynomial<C>> L) Degree matrix.
static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>>	degreeMatrix(GenPolynomial<C> A) Degree matrix.
static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>>	degreeMatrixOfCoefficients(java.util.Collection<GenPolynomial<GenPolynomial<C>>> L) Degree matrix of coefficient polynomials.
static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>>	degreeMatrixOfCoefficients(GenPolynomial<GenPolynomial<C>> A) Degree matrix of coefficient polynomials.
static java.util.List<GenPolynomial<BigInteger>>	expVectorAdd(java.util.List<GenPolynomial<BigInteger>> dm, ExpVector e) Degree matrix exponent vector add.
static java.util.List<java.lang.Integer>	inversePermutation(java.util.List<java.lang.Integer> P) Inverse of a permutation.
static boolean	isIdentityPermutation(java.util.List<java.lang.Integer> P) Test for identity permutation.
static <T> java.util.List<T>	listPermutation(java.util.List<java.lang.Integer> P, java.util.List<T> L) Permutation of a list.
static java.util.List<java.lang.Integer>	multiplyPermutation(java.util.List<java.lang.Integer> P, java.util.List<java.lang.Integer> S) Multiplication permutations.
static java.util.List<java.lang.Integer>	optimalPermutation(java.util.List<GenPolynomial<BigInteger>> D) Optimal permutation for the Degree matrix.
static <C extends RingElem<C>> OptimizedPolynomialList<C>	optimizeTermOrder(GenPolynomialRing<C> R, java.util.List<GenPolynomial<C>> L) Optimize variable order.
static <C extends RingElem<C>> OptimizedModuleList<C>	optimizeTermOrder(ModuleList<C> P) Optimize variable order.
static <C extends RingElem<C>> OptimizedPolynomialList<C>	optimizeTermOrder(PolynomialList<C> P) Optimize variable order.
static <C extends RingElem<C>> OptimizedModuleList<C>	optimizeTermOrderModule(GenPolynomialRing<C> R, java.util.List<java.util.List<GenPolynomial<C>>> L) Optimize variable order.
static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>>	optimizeTermOrderOnCoefficients(GenPolynomialRing<GenPolynomial<C>> ring, java.util.List<GenPolynomial<GenPolynomial<C>>> L) Optimize variable order on coefficients.
static <C extends RingElem<C>> OptimizedModuleList<GenPolynomial<C>>	optimizeTermOrderOnCoefficients(ModuleList<GenPolynomial<C>> P) Optimize variable order on coefficients.
static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>>	optimizeTermOrderOnCoefficients(PolynomialList<GenPolynomial<C>> P) Optimize variable order on coefficients.
static <C extends RingElem<C>> GenPolynomialRing<C>	permutation(java.util.List<java.lang.Integer> P, GenPolynomialRing<C> R) Permutation of polynomial ring variables.
static <C extends RingElem<C>> GenPolynomial<C>	permutation(java.util.List<java.lang.Integer> P, GenPolynomialRing<C> R, GenPolynomial<C> A) Permutation of polynomial exponent vectors.
static <C extends RingElem<C>> java.util.List<GenPolynomial<C>>	permutation(java.util.List<java.lang.Integer> P, GenPolynomialRing<C> R, java.util.List<GenPolynomial<C>> L) Permutation of polynomial exponent vectors.
static <C extends RingElem<C>> java.util.List<GenSolvablePolynomial<C>>	permutation(java.util.List<java.lang.Integer> P, GenSolvablePolynomialRing<C> R, java.util.List<GenSolvablePolynomial<C>> L) Permutation of solvable polynomial exponent vectors.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	permutationOnCoefficients(java.util.List<java.lang.Integer> P, GenPolynomialRing<GenPolynomial<C>> R, GenPolynomial<GenPolynomial<C>> A) Permutation of polynomial exponent vectors of coefficient polynomials.
static <C extends RingElem<C>> java.util.List<GenPolynomial<GenPolynomial<C>>>	permutationOnCoefficients(java.util.List<java.lang.Integer> P, GenPolynomialRing<GenPolynomial<C>> R, java.util.List<GenPolynomial<GenPolynomial<C>>> L) Permutation of polynomial exponent vectors of coefficients.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

TermOrderOptimization

public TermOrderOptimization()

Method Detail

degreeMatrix

public static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>> degreeMatrix(GenPolynomial<C> A)

Degree matrix.

Parameters:

A - polynomial to be considered.

Returns:

degree matrix.

expVectorAdd

public static java.util.List<GenPolynomial<BigInteger>> expVectorAdd(java.util.List<GenPolynomial<BigInteger>> dm,
                                                                     ExpVector e)

Degree matrix exponent vector add.

Parameters:

dm - degree matrix.

e - exponent vector.

Returns:

degree matrix + e.

degreeMatrixOfCoefficients

public static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>> degreeMatrixOfCoefficients(GenPolynomial<GenPolynomial<C>> A)

Degree matrix of coefficient polynomials.

Parameters:

A - polynomial to be considered.

Returns:

degree matrix for the coeficients.

degreeMatrix

public static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>> degreeMatrix(java.util.Collection<GenPolynomial<C>> L)

Degree matrix.

Parameters:

L - list of polynomial to be considered.

Returns:

degree matrix.

degreeMatrixOfCoefficients

public static <C extends RingElem<C>> java.util.List<GenPolynomial<BigInteger>> degreeMatrixOfCoefficients(java.util.Collection<GenPolynomial<GenPolynomial<C>>> L)

Degree matrix of coefficient polynomials.

Parameters:

L - list of polynomial to be considered.

Returns:

degree matrix for the coeficients.

optimalPermutation

public static java.util.List<java.lang.Integer> optimalPermutation(java.util.List<GenPolynomial<BigInteger>> D)

Optimal permutation for the Degree matrix.

Parameters:

D - degree matrix.

Returns:

optimal permutation for D.

inversePermutation

public static java.util.List<java.lang.Integer> inversePermutation(java.util.List<java.lang.Integer> P)

Inverse of a permutation.

Parameters:

P - permutation.

Returns:

S with S*P = id.

isIdentityPermutation

public static boolean isIdentityPermutation(java.util.List<java.lang.Integer> P)

Test for identity permutation.

Parameters:

P - permutation.

Returns:

true , if P = id, else false.

multiplyPermutation

public static java.util.List<java.lang.Integer> multiplyPermutation(java.util.List<java.lang.Integer> P,
                                                                    java.util.List<java.lang.Integer> S)

Multiplication permutations.

Parameters:

P - permutation.

S - permutation.

Returns:

P*S.

listPermutation

public static <T> java.util.List<T> listPermutation(java.util.List<java.lang.Integer> P,
                                                    java.util.List<T> L)

Permutation of a list.

Parameters:

L - list.

P - permutation.

Returns:

P(L).

arrayPermutation

public static <T> T[] arrayPermutation(java.util.List<java.lang.Integer> P,
                                       T[] a)

Permutation of an array. Compiles, but does not work, requires JDK 1.6 to work.

Parameters:

a - array.

P - permutation.

Returns:

P(a).

permutation

public static <C extends RingElem<C>> GenPolynomial<C> permutation(java.util.List<java.lang.Integer> P,
                                                                   GenPolynomialRing<C> R,
                                                                   GenPolynomial<C> A)

Permutation of polynomial exponent vectors.

Parameters:

A - polynomial.

R - polynomial ring.

P - permutation.

Returns:

P(A).

permutation

public static <C extends RingElem<C>> java.util.List<GenPolynomial<C>> permutation(java.util.List<java.lang.Integer> P,
                                                                                   GenPolynomialRing<C> R,
                                                                                   java.util.List<GenPolynomial<C>> L)

Permutation of polynomial exponent vectors.

Parameters:

L - list of polynomials.

R - polynomial ring.

P - permutation.

Returns:

P(L).

permutation

public static <C extends RingElem<C>> java.util.List<GenSolvablePolynomial<C>> permutation(java.util.List<java.lang.Integer> P,
                                                                                           GenSolvablePolynomialRing<C> R,
                                                                                           java.util.List<GenSolvablePolynomial<C>> L)

Permutation of solvable polynomial exponent vectors.

Parameters:

L - list of solvable polynomials.

R - solvable polynomial ring.

P - permutation, must be compatible with the commutator relations.

Returns:

P(L).

permutationOnCoefficients

public static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>> permutationOnCoefficients(java.util.List<java.lang.Integer> P,
                                                                                                GenPolynomialRing<GenPolynomial<C>> R,
                                                                                                GenPolynomial<GenPolynomial<C>> A)

Permutation of polynomial exponent vectors of coefficient polynomials.

Parameters:

A - polynomial.

R - polynomial ring.

P - permutation.

Returns:

P(A).

permutationOnCoefficients

public static <C extends RingElem<C>> java.util.List<GenPolynomial<GenPolynomial<C>>> permutationOnCoefficients(java.util.List<java.lang.Integer> P,
                                                                                                                GenPolynomialRing<GenPolynomial<C>> R,
                                                                                                                java.util.List<GenPolynomial<GenPolynomial<C>>> L)

Permutation of polynomial exponent vectors of coefficients.

Parameters:

L - list of polynomials.

R - polynomial ring.

P - permutation.

Returns:

P(L).

permutation

public static <C extends RingElem<C>> GenPolynomialRing<C> permutation(java.util.List<java.lang.Integer> P,
                                                                       GenPolynomialRing<C> R)

Permutation of polynomial ring variables.

Parameters:

R - polynomial ring.

P - permutation.

Returns:

P(R).

optimizeTermOrder

public static <C extends RingElem<C>> OptimizedPolynomialList<C> optimizeTermOrder(GenPolynomialRing<C> R,
                                                                                   java.util.List<GenPolynomial<C>> L)

Optimize variable order.

Parameters:

R - polynomial ring.

L - list of polynomials.

Returns:

optimized polynomial list.

optimizeTermOrder

public static <C extends RingElem<C>> OptimizedPolynomialList<C> optimizeTermOrder(PolynomialList<C> P)

Optimize variable order.

Parameters:

P - polynomial list.

Returns:

optimized polynomial list.

optimizeTermOrderOnCoefficients

public static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>> optimizeTermOrderOnCoefficients(PolynomialList<GenPolynomial<C>> P)

Optimize variable order on coefficients.

Parameters:

P - polynomial list.

Returns:

optimized polynomial list.

optimizeTermOrderOnCoefficients

public static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>> optimizeTermOrderOnCoefficients(GenPolynomialRing<GenPolynomial<C>> ring,
                                                                                                                java.util.List<GenPolynomial<GenPolynomial<C>>> L)

Optimize variable order on coefficients.

Parameters:

ring - polynomial ring.

L - list of polynomials.

Returns:

optimized polynomial list.

optimizeTermOrder

public static <C extends RingElem<C>> OptimizedModuleList<C> optimizeTermOrder(ModuleList<C> P)

Optimize variable order.

Parameters:

P - module list.

Returns:

optimized module list.

optimizeTermOrderModule

public static <C extends RingElem<C>> OptimizedModuleList<C> optimizeTermOrderModule(GenPolynomialRing<C> R,
                                                                                     java.util.List<java.util.List<GenPolynomial<C>>> L)

Optimize variable order.

Parameters:

R - polynomial ring.

L - list of lists of polynomials.

Returns:

optimized module list.

optimizeTermOrderOnCoefficients

public static <C extends RingElem<C>> OptimizedModuleList<GenPolynomial<C>> optimizeTermOrderOnCoefficients(ModuleList<GenPolynomial<C>> P)

Optimize variable order on coefficients.

Parameters:

P - module list.

Returns:

optimized module list.