edu.jas.gbufd

Class GroebnerBasePartial<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gbufd.GroebnerBasePartial<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, java.io.Serializable

public class GroebnerBasePartial<C extends GcdRingElem<C>>
extends GroebnerBaseAbstract<C>

Partial Groebner Bases for subsets of variables. Let pvars be a subset of variables vars of the polynomial ring K[vars]. Methods compute Groebner bases with coefficients from K[vars \ pvars] in the polynomial ring K[vars \ pvars][pvars].

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected GroebnerBaseAbstract<C>	bb Backing Groebner base engine.
protected GroebnerBaseAbstract<GenPolynomial<C>>	rbb Backing recursive Groebner base engine.

Fields inherited from class edu.jas.gb.GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor and Description
GroebnerBasePartial() Constructor.
GroebnerBasePartial(GroebnerBaseAbstract<C> bb, GroebnerBaseAbstract<GenPolynomial<C>> rbb) Constructor.
GroebnerBasePartial(RingFactory<GenPolynomial<C>> rf) Constructor.

Method Summary

Modifier and Type	Method and Description
OptimizedPolynomialList<C>	elimPartialGB(java.util.List<GenPolynomial<C>> F, java.lang.String[] evars, java.lang.String[] pvars) Partial Groebner base for specific variables.
java.util.List<GenPolynomial<C>>	GB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base using pairlist class.
static java.util.List<java.lang.Integer>	getPermutation(java.lang.String[] aname, java.lang.String[] ename) Permutation of variables for elimination.
static int	indexOf(java.lang.String s, java.lang.String[] A) Index of s in A.
boolean	isGBrec(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Groebner base test.
boolean	isGBrec(java.util.List<GenPolynomial<GenPolynomial<C>>> F) Groebner base test.
OptimizedPolynomialList<C>	partialGB(java.util.List<GenPolynomial<C>> F, java.lang.String[] pvars) Partial Groebner base for specific variables.
OptimizedPolynomialList<GenPolynomial<C>>	partialGBrec(java.util.List<GenPolynomial<C>> F, java.lang.String[] pvars) Partial recursive Groebner base for specific variables.
static java.util.List<java.lang.Integer>	partialPermutation(java.lang.String[] vars, java.lang.String[] pvars) Partial permuation for specific variables.
static java.util.List<java.lang.Integer>	partialPermutation(java.lang.String[] vars, java.lang.String[] pvars, java.lang.String[] rvars) Partial permuation for specific variables.
static java.util.List<java.lang.Integer>	partialPermutation(java.lang.String[] vars, java.lang.String[] evars, java.lang.String[] pvars, java.lang.String[] rvars) Partial permuation for specific variables.
static java.lang.String[]	remainingVars(java.lang.String[] vars, java.lang.String[] pvars) Remaining variables vars \ pvars.

Methods inherited from class edu.jas.gb.GroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, extGB, extGB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isReductionMatrix, isReductionMatrix, minimalExtendedGB, minimalGB, normalizeMatrix, normalizeZerosOnes, terminate, toString, univariateDegrees

Methods inherited from class java.lang.Object

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

Field Detail

bb

protected GroebnerBaseAbstract<C extends GcdRingElem<C>> bb

Backing Groebner base engine.

rbb

protected GroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>> rbb

Backing recursive Groebner base engine.

Constructor Detail

GroebnerBasePartial

public GroebnerBasePartial()

Constructor.

GroebnerBasePartial

public GroebnerBasePartial(RingFactory<GenPolynomial<C>> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

GroebnerBasePartial

public GroebnerBasePartial(GroebnerBaseAbstract<C> bb,
                           GroebnerBaseAbstract<GenPolynomial<C>> rbb)

Constructor.

Parameters:

bb - Groebner base engine

rbb - recursive Groebner base engine

Method Detail

GB

public java.util.List<GenPolynomial<C>> GB(int modv,
                                           java.util.List<GenPolynomial<C>> F)

Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

isGBrec

public boolean isGBrec(java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Groebner base test.

Parameters:

F - polynomial list.

Returns:

true, if F is a partial Groebner base, else false.

isGBrec

public boolean isGBrec(int modv,
                       java.util.List<GenPolynomial<GenPolynomial<C>>> F)

Groebner base test.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

true, if F is a partial Groebner base, else false.

partialPermutation

public static java.util.List<java.lang.Integer> partialPermutation(java.lang.String[] vars,
                                                                   java.lang.String[] pvars)

Partial permuation for specific variables. Computes a permutation perm for the variables vars, such that perm(vars) == pvars ... (vars \ pvars). Uses internal (reversed) variable sorting.

Parameters:

vars - names for all variables.

pvars - names for main variables, pvars subseteq vars.

Returns:

permutation for vars, such that perm(vars) == pvars ... (vars \ pvars).

getPermutation

public static java.util.List<java.lang.Integer> getPermutation(java.lang.String[] aname,
                                                               java.lang.String[] ename)

Permutation of variables for elimination.

Parameters:

aname - variables for the full polynomial ring.

ename - variables for the elimination ring, subseteq aname.

Returns:

perm({vars \ ename},ename)

indexOf

public static int indexOf(java.lang.String s,
                          java.lang.String[] A)

Index of s in A.

Parameters:

s - search string

A - string array

Returns:

i if s == A[i] for some i, else -1.

partialPermutation

public static java.util.List<java.lang.Integer> partialPermutation(java.lang.String[] vars,
                                                                   java.lang.String[] pvars,
                                                                   java.lang.String[] rvars)

Partial permuation for specific variables. Computes a permutation perm for the variables vars, such that perm(vars) == pvars ... (vars \ pvars). Uses internal (reversed) variable sorting.

Parameters:

vars - names for all variables.

pvars - names for main variables, pvars subseteq vars.

rvars - names for remaining variables, rvars eq { vars \ pvars }.

Returns:

permutation for vars, such that perm(vars) == (pvars, {vars \ pvars}).

partialPermutation

public static java.util.List<java.lang.Integer> partialPermutation(java.lang.String[] vars,
                                                                   java.lang.String[] evars,
                                                                   java.lang.String[] pvars,
                                                                   java.lang.String[] rvars)

Partial permuation for specific variables. Computes a permutation perm for the variables vars, such that perm(vars) == (evars, pvars, (vars \ { evars, pvars }). Uses internal (reversed) variable sorting.

Parameters:

vars - names for all variables.

evars - names for elimination variables, evars subseteq vars.

pvars - names for main variables, pvars subseteq vars.

rvars - names for remaining variables, rvars eq {vars \ { evars, pvars } }.

Returns:

permutation for vars, such that perm(vars) == (evars,pvars, {vars \ {evars,pvars}}.

remainingVars

public static java.lang.String[] remainingVars(java.lang.String[] vars,
                                               java.lang.String[] pvars)

Remaining variables vars \ pvars. Uses internal (reversed) variable sorting, original order is preserved.

Parameters:

vars - names for all variables.

pvars - names for main variables, pvars subseteq vars.

Returns:

remaining vars = (vars \ pvars).

partialGBrec

public OptimizedPolynomialList<GenPolynomial<C>> partialGBrec(java.util.List<GenPolynomial<C>> F,
                                                              java.lang.String[] pvars)

Partial recursive Groebner base for specific variables. Computes Groebner base in K[vars \ pvars][pvars] with coefficients from K[vars \ pvars].

Parameters:

F - polynomial list.

pvars - names for main variables of partial Groebner base computation.

Returns:

a container for a partial Groebner base of F wrt pvars.

partialGB

public OptimizedPolynomialList<C> partialGB(java.util.List<GenPolynomial<C>> F,
                                            java.lang.String[] pvars)

Partial Groebner base for specific variables. Computes Groebner base in K[vars \ pvars][pvars] with coefficients from K[vars \ pvars] but returns polynomials in K[vars \ pvars, pvars].

Parameters:

F - polynomial list.

pvars - names for main variables of partial Groebner base computation.

Returns:

a container for a partial Groebner base of F wrt pvars.

elimPartialGB

public OptimizedPolynomialList<C> elimPartialGB(java.util.List<GenPolynomial<C>> F,
                                                java.lang.String[] evars,
                                                java.lang.String[] pvars)

Partial Groebner base for specific variables. Computes Groebner base with coefficients from K[pvars] but returns polynomials in K[pvars, evars].

Parameters:

F - polynomial list.

evars - names for upper main variables of partial Groebner base computation.

pvars - names for lower main variables of partial Groebner base computation.

Returns:

a container for a partial Groebner base of F wrt (pvars,evars).