Class TermOrderOptimization

java.lang.Object

edu.jas.poly.TermOrderOptimization

public class TermOrderOptimization
extends Object

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

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
private static final org.apache.logging.log4j.Logger	logger

Constructor Summary

Constructors

Constructor	Description
TermOrderOptimization()

Method Summary

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

Methods inherited from class Object

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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

Constructor Details

TermOrderOptimization

public TermOrderOptimization()

Method Details

degreeMatrix

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

Degree matrix.

Parameters:

A - polynomial to be considered.

Returns:

degree matrix.

expVectorAdd

public static List<GenPolynomial<BigInteger>> expVectorAdd(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>>
List<GenPolynomial<BigInteger>> degreeMatrixOfCoefficients(GenPolynomial<GenPolynomial<C>> A)

Degree matrix of coefficient polynomials.

Parameters:

A - polynomial to be considered.

Returns:

degree matrix for the coefficients.

degreeMatrix

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

Degree matrix.

Parameters:

L - list of polynomial to be considered.

Returns:

degree matrix.

degreeMatrixOfCoefficients

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

Degree matrix of coefficient polynomials.

Parameters:

L - list of polynomial to be considered.

Returns:

degree matrix for the coefficients.

optimalPermutation

public static List<Integer> optimalPermutation(List<GenPolynomial<BigInteger>> D)

Optimal permutation for the Degree matrix.

Parameters:

D - degree matrix.

Returns:

optimal permutation for D.

inversePermutation

public static List<Integer> inversePermutation(List<Integer> P)

Inverse of a permutation.

Parameters:

P - permutation.

Returns:

S with S*P = id.

isIdentityPermutation

public static boolean isIdentityPermutation(List<Integer> P)

Test for identity permutation.

Parameters:

P - permutation.

Returns:

true , if P = id, else false.

multiplyPermutation

public static List<Integer> multiplyPermutation(List<Integer> P,
 List<Integer> S)

Multiplication permutations.

Parameters:

P - permutation.

S - permutation.

Returns:

P*S.

listPermutation

public static <T> List<T> listPermutation(List<Integer> P,
 List<T> L)

Permutation of a list.

Parameters:

P - permutation.

L - list.

Returns:

P(L).

arrayPermutation

public static <T> T[] arrayPermutation(List<Integer> P,
 T[] a)

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

Parameters:

P - permutation.

a - array.

Returns:

P(a).

permutation

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

Permutation of polynomial exponent vectors.

Parameters:

P - permutation.

R - polynomial ring.

A - polynomial.

Returns:

P(A).

permutation

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

Permutation of polynomial exponent vectors.

Parameters:

P - permutation.

R - polynomial ring.

L - list of polynomials.

Returns:

P(L).

permutation

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

Permutation of solvable polynomial exponent vectors.

Parameters:

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

R - solvable polynomial ring.

L - list of solvable polynomials.

Returns:

P(L).

permutationOnCoefficients

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

Permutation of polynomial exponent vectors of coefficient polynomials.

Parameters:

P - permutation.

R - polynomial ring.

A - polynomial.

Returns:

P(A).

permutationOnCoefficients

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

Permutation of polynomial exponent vectors of coefficients.

Parameters:

P - permutation.

R - polynomial ring.

L - list of polynomials.

Returns:

P(L).

permutation

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

Permutation of polynomial ring variables.

Parameters:

P - permutation.

R - polynomial ring.

Returns:

P(R).

optimizeTermOrder

public static <C extends RingElem<C>>
OptimizedPolynomialList<C> optimizeTermOrder(GenPolynomialRing<C> R,
 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,
 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,
 List<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.