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}.

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 long[]	longArrayPermutation(java.util.List<java.lang.Integer> P, long[] a) Permutation of a long array.
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>> OptimizedPolynomialList<C>	optimizeTermOrder(PolynomialList<C> P) Optimize variable order.
static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>>	optimizeTermOrderOnCoefficients(PolynomialList<GenPolynomial<C>> P) Optimize variable order on coefficients.
static ExpVector	permutation(java.util.List<java.lang.Integer> P, ExpVector e) Permutation of an exponent vector.
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>> 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.
static java.lang.String[]	stringArrayPermutation(java.util.List<java.lang.Integer> P, java.lang.String[] a) Permutation of an array.

Methods inherited from class java.lang.Object

equals, 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).

stringArrayPermutation

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

Permutation of an array.

Parameters:

a - array.

P - permutation.

Returns:

P(a).

longArrayPermutation

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

Permutation of a long array.

Parameters:

a - array of long.

P - permutation.

Returns:

P(a).

permutation

public static ExpVector permutation(java.util.List<java.lang.Integer> P,
                                    ExpVector e)

Permutation of an exponent vector.

Parameters:

e - exponent vector.

P - permutation.

Returns:

P(e).

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).

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.