org.uacalc.alg
Class AlgebraFromMinimalSets

java.lang.Object
  org.uacalc.alg.GeneralAlgebra
      org.uacalc.alg.BasicAlgebra
          org.uacalc.alg.AlgebraFromMinimalSets

All Implemented Interfaces:

Algebra, SmallAlgebra

public class AlgebraFromMinimalSets
extends BasicAlgebra
implements SmallAlgebra

Starting with an algebra B which is permutational (nonconstant unary polynomials are permutations) and a geometry for the minimal sets, this constructs an algebra A with tame minimal sets, having B as a minimal set. Initially we will assume the geometry has 3 minimal sets, B, C, D, with C And D disjoint and the intersection of B and C just 0 and B and D the last element of B.

If n is the size of A and k is the size of each minimal set, we can specify the geometry of a list of maps 0 to k-1 into A.

Author:

ralph

Nested Class Summary

Nested classes/interfaces inherited from interface org.uacalc.alg.SmallAlgebra

SmallAlgebra.AlgebraType

Field Summary

Fields inherited from class org.uacalc.alg.BasicAlgebra

universeList, universeOrder

Fields inherited from class org.uacalc.alg.GeneralAlgebra

con, description, monitor, name, operations, operationsMap, similarityType, size, sub, universe

Fields inherited from interface org.uacalc.alg.Algebra

CARDINALITY_COUNTABLE, CARDINALITY_COUNTABLY_INFINITE, CARDINALITY_FINITE, CARDINALITY_INFINITE, CARDINALITY_UNKNOWN

Constructor Summary

AlgebraFromMinimalSets(SmallAlgebra minAlg)

AlgebraFromMinimalSets(SmallAlgebra minAlg, int algSize, java.util.List<int[]> maps)

AlgebraFromMinimalSets(java.lang.String name, SmallAlgebra minAlg)

AlgebraFromMinimalSets(java.lang.String name, SmallAlgebra minAlg, int algSize, java.util.List<int[]> maps, java.util.List<java.lang.Integer> connectPts)
If k is the cardinality of minAlg, each map maps k = {0,..., k-1} one-to-one into n = {0,...,n-1}.

AlgebraFromMinimalSets(java.lang.String name, SmallAlgebra minAlg, java.util.List<java.lang.Integer> connectPts)

Method Summary

static void

main(java.lang.String[] args)

Methods inherited from class org.uacalc.alg.BasicAlgebra

algebraType, con, convertToDefaultValueOps, elementIndex, getElement, getUniverseList, getUniverseOrder, intUniverse, resetConAndSub, setUniverseList, setUniverseOrder, sub

Methods inherited from class org.uacalc.alg.GeneralAlgebra

cardinality, constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, makeOperationTables, monitoring, operations, parent, parents, setDescription, setMonitor, setName, setOperations, setUniverse, similarityType, universe

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.uacalc.alg.SmallAlgebra

algebraType, con, convertToDefaultValueOps, elementIndex, getElement, getUniverseList, getUniverseOrder, parent, parents, resetConAndSub, sub

Methods inherited from interface org.uacalc.alg.Algebra

cardinality, constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, makeOperationTables, monitoring, operations, setDescription, setMonitor, setName, similarityType, universe

Constructor Detail

AlgebraFromMinimalSets

public AlgebraFromMinimalSets(SmallAlgebra minAlg)

AlgebraFromMinimalSets

public AlgebraFromMinimalSets(SmallAlgebra minAlg,
                              int algSize,
                              java.util.List<int[]> maps)

AlgebraFromMinimalSets

public AlgebraFromMinimalSets(java.lang.String name,
                              SmallAlgebra minAlg)

AlgebraFromMinimalSets

public AlgebraFromMinimalSets(java.lang.String name,
                              SmallAlgebra minAlg,
                              java.util.List<java.lang.Integer> connectPts)

AlgebraFromMinimalSets

public AlgebraFromMinimalSets(java.lang.String name,
                              SmallAlgebra minAlg,
                              int algSize,
                              java.util.List<int[]> maps,
                              java.util.List<java.lang.Integer> connectPts)

If k is the cardinality of minAlg, each map maps k = {0,..., k-1} one-to-one into n = {0,...,n-1}. The first map must be the identity. Each element of n must be in the range of at least one map. Given any two elements of n, there are overlapping ranges of the maps going from on to the other.

Parameters:

name -

minAlg - a permutational algebra

maps -

Method Detail

main

public static void main(java.lang.String[] args)

Parameters:

args -