/*
* Redberry: symbolic tensor computations.
*
* Copyright (c) 2010-2013:
* Stanislav Poslavsky <stvlpos@mail.ru>
* Bolotin Dmitriy <bolotin.dmitriy@gmail.com>
*
* This file is part of Redberry.
*
* Redberry is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Redberry is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Redberry. If not, see <http://www.gnu.org/licenses/>.
*/
package cc.redberry.core.groups.permutations;
import cc.redberry.core.utils.IntArrayList;
import java.util.ArrayList;
import java.util.Arrays;
/**
* @author Dmitry Bolotin
* @author Stanislav Poslavsky
*/
final class SchreierSimsAlgorithm {
private SchreierSimsAlgorithm() {
}
static StripResult strip(Permutation permutation,
ArrayList<SGSIntermediateElement> intermediateGeneratingSet) {
Permutation temp = permutation;
int i;
for (i = 0; i < intermediateGeneratingSet.size(); ++i) {
int beta = temp.newIndexOf(intermediateGeneratingSet.get(i).basePoint);
if (!intermediateGeneratingSet.get(i).belongsToOrbit(beta))
return new StripResult(temp, i);
temp = temp.composition(intermediateGeneratingSet.get(i).getInverseTransversalOf(beta));
}
return new StripResult(temp, i);
}
static class StripResult {
final int stopPoint;
final Permutation remainderPermutation;
public StripResult(Permutation remainderPermutation, int stopPoint) {
this.stopPoint = stopPoint;
this.remainderPermutation = remainderPermutation;
}
@Override
public String toString() {
return remainderPermutation + ", (" + stopPoint + ")";
}
}
static SGSElement[] createSGS(Permutation[] generators) {
if (generators.length == 0)
return new SGSElement[0];
final int length = generators[0].length();
int firstBase = -1;
for (int i = generators.length - 1; i >= 0; --i) {
for (int j = length - 1; j >= 0; --j)
if (generators[i].newIndexOf(j) != j) {
firstBase = j;
break;
}
}
if (firstBase == -1)
return new SGSElement[0];
IntArrayList base = new IntArrayList();
base.add(firstBase);
ArrayList<SGSIntermediateElement> intermediateSGSElements = new ArrayList<>();
intermediateSGSElements.add(
new SGSIntermediateElement(firstBase,
new ArrayList<>(Arrays.asList(generators)),
length));
schreierSimsAlgorithm(intermediateSGSElements);
SGSElement[] sgs = new SGSElement[intermediateSGSElements.size()];
for (int i = sgs.length - 1; i >= 0; --i) {
intermediateSGSElements.get(i).trimToSize();
sgs[i] = new SGSElement(intermediateSGSElements.get(i));
}
return sgs;
}
static void schreierSimsAlgorithm(ArrayList<SGSIntermediateElement> intermediateSGSElements) {
boolean y;
int dimension = intermediateSGSElements.get(0).schreierVector.length;
for (Permutation generator : intermediateSGSElements.get(0).stabilizerGenerators) {
y = false;
for (SGSIntermediateElement sgsElement : intermediateSGSElements) {
if (generator.newIndexOf(sgsElement.basePoint) != sgsElement.basePoint) {
y = true;
break;
}
}
if (!y)
for (int i = 0; i < dimension; ++i)
if (generator.newIndexOf(i) != i)
intermediateSGSElements.add(
new SGSIntermediateElement(i,
intermediateSGSElements.get(intermediateSGSElements.size() - 1).getBasePointStabilizerGenerators(),
dimension));
}
int i = intermediateSGSElements.size() - 1;
SGSIntermediateElement currentElement;
int orbitIndex, beta;
out:
while (i >= 0) {
currentElement = intermediateSGSElements.get(i);
//enumerating orbit elements
for (orbitIndex = 0; orbitIndex < currentElement.orbit.size(); ++orbitIndex) {
beta = currentElement.orbit.get(orbitIndex);
//enumerating stabilizers from current sgsElement
for (Permutation stabilizerGenerator : currentElement.stabilizerGenerators) {
if (!currentElement.getTransversalOf(beta).composition(stabilizerGenerator)
.equals(currentElement.getTransversalOf(stabilizerGenerator.newIndexOf(beta)))) {
y = true;
StripResult str = strip(
currentElement.getTransversalOf(beta).composition(
stabilizerGenerator).composition(
currentElement.getInverseTransversalOf(stabilizerGenerator.newIndexOf(beta))),
intermediateSGSElements);
if (str.stopPoint < intermediateSGSElements.size()) {
y = false;
} else if (!str.remainderPermutation.isIdentity()) {
y = false;
for (int a = 0; a < dimension; ++a)
if (str.remainderPermutation.newIndexOf(a) != a) {
intermediateSGSElements.add(new SGSIntermediateElement(a, new ArrayList<Permutation>(), dimension));
break;
}
}
if (!y) {
for (int l = i + 1; l <= str.stopPoint; ++l) {
intermediateSGSElements.get(l).stabilizerGenerators.add(str.remainderPermutation);
intermediateSGSElements.get(l).reCalculateSchreierVector();
}
i = str.stopPoint;
continue out;
}
}
}
}
--i;
}
}
}