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Redberry is an open source computer algebra system designed for tensor
manipulation. It implements basic computer algebra system routines as well as
complex tools for real computations in physics.
This is Redberry core, which contains the implementation of the basic
computer algebra routines and general-purpose transformations.
/*
* Redberry: symbolic tensor computations.
*
* Copyright (c) 2010-2014:
* Stanislav Poslavsky
* Bolotin Dmitriy
*
* 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 tensorSubstitutions = new THashMap<>();
//all symbols will have names scalar1,scalar2, etc.
//processing equations
int i;
for (i = 0; i < equations.length; ++i) {
Expression eq = equations[i];
//iterating over the whole equation
FromChildToParentIterator iterator = new FromChildToParentIterator(eq);
Tensor t;
while ((t = iterator.next()) != null) {
if (!(t instanceof Product) || t.getIndices().size() == 0)
continue;
//scalars content
Tensor[] scalars = ((Product) t).getContent().getScalars();
for (Tensor scalar : scalars) {
if (!tensorSubstitutions.containsKey(scalar)) {
//map does not contains rule for current scalar (e.g. k_{i}*k^{i})
//adding new rule for the scalar, e.g. k_{i}*k^{i} = scalar2
tensorSubstitutions.put(scalar, CC.generateNewSymbol());
}
}
}
}
final Expression[] scalarSubs = new Expression[tensorSubstitutions.size()];
i = -1;
for (Map.Entry entry : tensorSubstitutions.entrySet())
scalarSubs[++i] = Tensors.expression(entry.getKey(), entry.getValue());
SubstitutionTransformation fullSub = new SubstitutionTransformation(scalarSubs, true);
for (i = 0; i < equations.length; ++i)
equations[i] = (Expression) fullSub.transform(equations[i]);
/*if (scalarSubs.length != 0) {
StringBuilder scalarsString = new StringBuilder().append('[');
for (Expression sub : scalarSubs)
scalarsString.append(sub).append(", ");
scalarsString.deleteCharAt(scalarsString.length() - 1).deleteCharAt(scalarsString.length() - 1).append(']');
System.out.println(scalarsString.toString());
}*/
/*System.out.println("Reduced solution: " + Arrays.toString(reducedSystem.generalSolutions));
System.out.println();*/
scriptCreator.createScript(equations, reducedSystem, path, keepFreeParameters);
//cleaning previous output
new File(path + "/equations." + scriptCreator.getScriptExtension() + "Out").delete();
//running external program
try {
Process p = Runtime.getRuntime().exec(programBinDir + "/" + scriptCreator.getScriptExecutionCommand() + " " + path + "/equations." + scriptCreator.getScriptExtension());
BufferedReader bri = new BufferedReader(new InputStreamReader(p.getInputStream()));
BufferedReader bre = new BufferedReader(new InputStreamReader(p.getErrorStream()));
String line;
while ((line = bri.readLine()) != null)
System.out.println(line);
bri.close();
while ((line = bre.readLine()) != null)
System.out.println(line);
bre.close();
p.waitFor();
} catch (IOException | InterruptedException ex) {
throw new RuntimeException(ex);
}
//reading the produced output with the solution
//allocating resulting coefficients array
Expression[] coefficientsResults = new Expression[reducedSystem.unknownCoefficients.length];
//no solutions
if (!new File(path + "/equations." + scriptCreator.getScriptExtension() + "Out").exists()) {
return new Expression[0][];
}
FileInputStream fstream = new FileInputStream(path + "/equations." + scriptCreator.getScriptExtension() + "Out");
if (fstream.available() == 0)
return null;
DataInputStream in = new DataInputStream(fstream);
BufferedReader br = new BufferedReader(new InputStreamReader(in));
String strLine;
i = -1;
List solutions = new ArrayList<>();
//reading resulting solutions from file
while ((strLine = br.readLine()) != null) {
if (strLine.equals("//solution")) {
//solution parser
Expression[] solution = reducedSystem.generalSolutions.clone();
//substituting coefficients into general inverse form
List zeroSubs = new ArrayList<>();
for (Expression coef : coefficientsResults)
if (coef.isIdentity() && !keepFreeParameters)//if current coefficient is free parameter
{
zeroSubs.add(Tensors.expression(coef.get(0), Complex.ZERO));
} else {
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) coef.transform(solution[si]);
}
if (!keepFreeParameters)
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) new TransformationCollection(zeroSubs).transform(solution[si]);
//substituting the renamed tensors combinations
for (Expression sub : scalarSubs)
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) sub.transpose().transform(solution[si]);
solutions.add(solution);
coefficientsResults = new Expression[reducedSystem.unknownCoefficients.length];
i = -1;
} else
coefficientsResults[++i] = Tensors.parseExpression(strLine);
}
in.close();
return solutions.toArray(new Expression[solutions.size()][]);
}
public static interface ExternalScriptCreator {
void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException;
String getScriptExecutionCommand();
String getScriptExtension();
}
public static final class MathematicaScriptCreator implements ExternalScriptCreator {
public static final MathematicaScriptCreator INSTANCE = new MathematicaScriptCreator();
private MathematicaScriptCreator() {
}
@Override
public void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException {
//creating file with Mathematica code to solve the system of equations
FileOutputStream output = new FileOutputStream(path + "/equations.mathematica");
PrintStream file = new PrintStream(output);
file.append("$equations = {\n");
int i;
for (i = 0; ; i++) {
file.append(equations[i].toString(OutputFormat.WolframMathematica).replace("=", "=="));
if (i == equations.length - 1)
break;
file.append(",\n");
}
file.append("\n};\n");
file.append("$coefficients = {");
for (i = 0; ; i++) {
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.WolframMathematica));
if (i == reducedSystem.unknownCoefficients.length - 1)
break;
file.append(',');
}
file.append(" };\n");
file.append("$result = Solve[$equations,$coefficients];\n");
file.append("If[Length[$result] != 0, ");
file.append("$result = Simplify[$result];\n");
file.append("$stream = OpenWrite[\"" + path + "/equations.mathematicaOut\"];\n");
file.append("For[$solution = 1, $solution <= Length[$result], ++$solution, ");
file.append("$tempResult = $result[[$solution]];");
file.append("$found = $tempResult[[All, 1]];\n");
if (!keepFreeParams)
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i,If[!MemberQ[$found, $coefficients[[$i]]], $tempResult = $tempResult/.{$coefficients[[$i]] -> 0}; AppendTo[$tempResult, $coefficients[[$i]] -> 0];]];\n");
else
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i,If[!MemberQ[$found, $coefficients[[$i]]], AppendTo[$tempResult, $coefficients[[$i]] -> $coefficients[[$i]]];]];\n");
file.append("$tempResult = Simplify[$tempResult];\n");
// file.append("left = Array[Function[x,Coefficient[equations[[x, 1]], #] & /@ coefficients], Length[equations]];\n");
// file.append("right = equations[[All, 2]];\n");
// file.append("result = LinearSolve[left, right]\n");
// file.append("For[i = 1, i <= Length[coefficients], ++i, WriteString[stream, StringReplace[ToString[coefficients[[i]] == result[[i]] // InputForm], {\"==\" -> \"=\", \"^\" -> \"**\"}] <> If[i != Length[coefficients], \"\\n\", \"\"]]];\n");
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i, WriteString[$stream, StringReplace[ToString[$tempResult[[$i]] // InputForm], {\"->\" -> \"=\", \"^\" -> \"**\"}] <> If[$i != Length[$coefficients], \"\\n\", \"\"]]];\n");
file.append("WriteString[$stream, \"\n//solution\n\"];");
file.append("];");
file.append("Close[$stream];");
file.append("];");
output.close();
file.close();
}
@Override
public String getScriptExecutionCommand() {
return "MathematicaScript -script";
}
@Override
public String getScriptExtension() {
return "mathematica";
}
}
public static final class MapleScriptCreator implements ExternalScriptCreator {
public static final MapleScriptCreator INSTANCE = new MapleScriptCreator();
private MapleScriptCreator() {
}
@Override
public void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException {
//creating file with Maple code to solve the system of equations
FileOutputStream output = new FileOutputStream(path + "/equations.maple");
PrintStream file = new PrintStream(output);
file.append("with(StringTools):\n");
file.append("ans:=array([");
int i;
for (i = 0; i < reducedSystem.unknownCoefficients.length; ++i)
if (i == reducedSystem.unknownCoefficients.length - 1)
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple));
else
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple) + ",");
file.append("]):\n");
file.println("eq:=array(1.." + equations.length + "):");
for (i = 0; i < equations.length; i++)
file.println("eq[" + (i + 1) + "]:=" + equations[i].toString(OutputFormat.Maple) + ":");
file.print("Result := solve(simplify({seq(eq[i],i=1.." + equations.length + ")}),[");
for (i = 0; i < reducedSystem.unknownCoefficients.length; ++i)
if (i == reducedSystem.unknownCoefficients.length - 1)
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple));
else
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple) + ",");
file.append("],explicit=true):\n");
file.append("if nops(Result) <> 0 then\n");
file.append("Result:= factor(Result);\n");
file.println("file:=fopen(\"" + path + "/equations.mapleOut\",WRITE):");
file.append("for maple_positionInResult from 1 to nops(Result) do\n");
file.append("for maple_counter from 1 to " + reducedSystem.unknownCoefficients.length + " do\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \"^\", \"**\");\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \"(\", \"[\");\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \")\", \"]\");\n");
file.append("temp2 := SubstituteAll(convert(rhs(Result[maple_positionInResult][maple_counter]), string), \"^\", \"**\");\n");
file.append("fprintf(file,\"%s=%s\\n\",temp1,temp2);\n");
file.append("od:\n");
file.append("fprintf(file,\"//solution\\n\");\n");
file.append("od:\n");
file.append("end if;\n");
file.append("fclose(file):");
output.close();
file.close();
}
@Override
public String getScriptExecutionCommand() {
return "maple";
}
@Override
public String getScriptExtension() {
return "maple";
}
}
}
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