edu.jas.poly

Class RelationTable<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.RelationTable<C>

All Implemented Interfaces:

java.io.Serializable

public class RelationTable<C extends RingElem<C>>
extends java.lang.Object
implements java.io.Serializable

RelationTable for solvable polynomials. This class maintains the non-commutative multiplication relations of solvable polynomial rings. The table entries are initialized with relations of the form x_j * x_i = p_ij. During multiplication the relations are updated by relations of the form x_j^k * x_i^l = p_ijkl. If no relation for x_j * x_i is found in the table, this multiplication is assumed to be commutative x_i x_j. Can also be used for relations between coefficients and main variables.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
boolean	coeffTable Usage indicator: table or coeffTable.
GenSolvablePolynomialRing<C>	ring The factory for the solvable polynomial ring.
java.util.Map<java.util.List<java.lang.Integer>,java.util.List>	table The data structure for the relations.

Constructor Summary

Constructors

Constructor and Description
RelationTable(GenSolvablePolynomialRing<C> r) Constructor for RelationTable requires ring factory.
RelationTable(GenSolvablePolynomialRing<C> r, boolean coeffTable) Constructor for RelationTable requires ring factory.

Method Summary

Modifier and Type	Method and Description
void	addRelations(java.util.List<GenPolynomial<C>> rel) Add list of polynomial triples as relations.
void	addSolvRelations(java.util.List<GenSolvablePolynomial<C>> rel) Add list of polynomial triples as relations.
void	contract(RelationTable<C> tab) Contract variables.
boolean	equals(java.lang.Object p) RelationTable equals.
void	extend(RelationTable<C> tab) Extend variables.
int	hashCode() Hash code for this relation table.
boolean	isEmpty() Test if the table is empty.
TableRelation<C>	lookup(ExpVector e, ExpVector f) Lookup RelationTable for existing relation.
protected java.util.List<java.lang.Integer>	makeKey(ExpVector e, ExpVector f) Construct a key for (e,f).
void	recursive(RelationTable tab) Recursive representation.
java.util.List<GenSolvablePolynomial<C>>	relationList() Convert relation table to list of polynomial triples.
void	reverse(RelationTable<C> tab) Reverse variables and relations.
int	size() Size of the table.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() Get the String representation.
java.lang.String	toString(java.lang.String[] vars) Get the String representation.
void	update(ExpVector e, ExpVector f, GenPolynomial<C> p) Update or initialize RelationTable with new relation. relation is e * f = p.
void	update(ExpVector e, ExpVector f, GenSolvablePolynomial<C> p) Update or initialize RelationTable with new relation. relation is e * f = p.
void	update(GenPolynomial<C> E, GenPolynomial<C> F, GenPolynomial<C> p) Update or initialize RelationTable with new relation. relation is e * f = p.
void	update(GenPolynomial<C> E, GenPolynomial<C> F, GenSolvablePolynomial<C> p) Update or initialize RelationTable with new relation. relation is e * f = p.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

table

public final java.util.Map<java.util.List<java.lang.Integer>,java.util.List> table

The data structure for the relations.

ring

public final GenSolvablePolynomialRing<C extends RingElem<C>> ring

The factory for the solvable polynomial ring.

coeffTable

public final boolean coeffTable

Usage indicator: table or coeffTable.

Constructor Detail

RelationTable

public RelationTable(GenSolvablePolynomialRing<C> r)

Constructor for RelationTable requires ring factory. Note: This constructor is called within the constructor of the ring factory, so methods of this class can only be used after the other constructor has terminated.

Parameters:

r - solvable polynomial ring factory.

RelationTable

public RelationTable(GenSolvablePolynomialRing<C> r,
                     boolean coeffTable)

Constructor for RelationTable requires ring factory. Note: This constructor is called within the constructor of the ring factory, so methods of this class can only be used after the other constructor has terminated.

Parameters:

r - solvable polynomial ring factory.

coeffTable - indicator for coeffTable.

Method Detail

equals

public boolean equals(java.lang.Object p)

RelationTable equals. Tests same keySets and base relations.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this relation table.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

isEmpty

public boolean isEmpty()

Test if the table is empty.

Returns:

true if the table is empty, else false.

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toString

public java.lang.String toString(java.lang.String[] vars)

Get the String representation.

Parameters:

vars - names for the variables.

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Returns:

script compatible representation for this relation table.

update

public void update(ExpVector e,
                   ExpVector f,
                   GenSolvablePolynomial<C> p)

Update or initialize RelationTable with new relation. relation is e * f = p.

Parameters:

e - first term.

f - second term.

p - solvable product polynomial.

update

public void update(GenPolynomial<C> E,
                   GenPolynomial<C> F,
                   GenSolvablePolynomial<C> p)

Update or initialize RelationTable with new relation. relation is e * f = p.

Parameters:

E - first term polynomial.

F - second term polynomial.

p - solvable product polynomial.

update

public void update(GenPolynomial<C> E,
                   GenPolynomial<C> F,
                   GenPolynomial<C> p)

Update or initialize RelationTable with new relation. relation is e * f = p.

Parameters:

E - first term polynomial.

F - second term polynomial.

p - product polynomial.

update

public void update(ExpVector e,
                   ExpVector f,
                   GenPolynomial<C> p)

Update or initialize RelationTable with new relation. relation is e * f = p.

Parameters:

e - first term.

f - second term.

p - solvable product polynomial.

lookup

public TableRelation<C> lookup(ExpVector e,
                               ExpVector f)

Lookup RelationTable for existing relation. Find p with e * f = p. If no relation for e * f is contained in the table then return the symmetric product p = 1 e f.

Parameters:

e - first term.

f - second term.

Returns:

t table relation container, contains e' and f' with e f = e' lt(p) f'.

makeKey

protected java.util.List<java.lang.Integer> makeKey(ExpVector e,
                                                    ExpVector f)

Construct a key for (e,f).

Parameters:

e - first term.

f - second term.

Returns:

k key for (e,f).

size

public int size()

Size of the table.

Returns:

n number of non-commutative relations.

extend

public void extend(RelationTable<C> tab)

Extend variables. Used e.g. in module embedding. Extend all ExpVectors and polynomials of the given relation table by i elements and put the relations into this table, i.e. this should be empty.

Parameters:

tab - a relation table to be extended and inserted into this.

contract

public void contract(RelationTable<C> tab)

Contract variables. Used e.g. in module embedding. Contract all ExpVectors and polynomials of the given relation table by i elements and put the relations into this table, i.e. this should be empty.

Parameters:

tab - a relation table to be contracted and inserted into this.

recursive

public void recursive(RelationTable tab)

Recursive representation. Split all ExpVectors and polynomials of the given relation table to lower elements and upper elements and put the relations into this table or this as coefficient table, i.e. this should be empty.

Parameters:

tab - a relation table to be contracted and inserted into this.

reverse

public void reverse(RelationTable<C> tab)

Reverse variables and relations. Used e.g. in opposite rings. Reverse all ExpVectors and polynomials of the given relation table and put the modified relations into this table, i.e. this should be empty.

Parameters:

tab - a relation table to be reverted and inserted into this.

relationList

public java.util.List<GenSolvablePolynomial<C>> relationList()

Convert relation table to list of polynomial triples.

Returns:

rel = (e1,f1,p1, ...) where ei * fi = pi are solvable relations.

addSolvRelations

public void addSolvRelations(java.util.List<GenSolvablePolynomial<C>> rel)

Add list of polynomial triples as relations.

Parameters:

rel - = (e1,f1,p1, ...) where ei * fi = pi are solvable relations. Note: Only because of type erasure, aequivalent to addRelations().

addRelations

public void addRelations(java.util.List<GenPolynomial<C>> rel)

Add list of polynomial triples as relations.

Parameters:

rel - = (e1,f1,p1, ...) where ei * fi = pi are solvable relations.