Examples with ASTRange org.matheclipse.core.expression.ASTRange used on opensource projects

Example 1 with ASTRange

use of org.matheclipse.core.expression.ASTRange in project symja_android_library by axkr.

the class Algebra method partialFractionDecompositionRational.

/**
	 * Returns an AST with head <code>Plus</code>, which contains the partial fraction decomposition of the numerator
	 * and denominator parts.
	 * 
	 * @param pf
	 *            partial fraction generator
	 * @param parts
	 * @param variable
	 *            a variable
	 * @return <code>F.NIL</code> if the partial fraction decomposition wasn't constructed
	 */
public static IExpr partialFractionDecompositionRational(IPartialFractionGenerator pf, IExpr[] parts, ISymbol variable) {
    try {
        IAST variableList = F.List(variable);
        IExpr exprNumerator = F.evalExpandAll(parts[0]);
        IExpr exprDenominator = F.evalExpandAll(parts[1]);
        ASTRange r = new ASTRange(variableList, 1);
        List<IExpr> varList = r;
        String[] varListStr = new String[1];
        varListStr[0] = variableList.arg1().toString();
        JASConvert<BigRational> jas = new JASConvert<BigRational>(varList, BigRational.ZERO);
        GenPolynomial<BigRational> numerator = jas.expr2JAS(exprNumerator, false);
        GenPolynomial<BigRational> denominator = jas.expr2JAS(exprDenominator, false);
        // get factors
        FactorAbstract<BigRational> factorAbstract = FactorFactory.getImplementation(BigRational.ZERO);
        SortedMap<GenPolynomial<BigRational>, Long> sfactors = factorAbstract.baseFactors(denominator);
        List<GenPolynomial<BigRational>> D = new ArrayList<GenPolynomial<BigRational>>(sfactors.keySet());
        SquarefreeAbstract<BigRational> sqf = SquarefreeFactory.getImplementation(BigRational.ZERO);
        List<List<GenPolynomial<BigRational>>> Ai = sqf.basePartialFraction(numerator, sfactors);
        if (Ai.size() > 0) {
            // IAST result = F.Plus();
            pf.allocPlus(Ai.size() * 2);
            pf.setJAS(jas);
            if (!Ai.get(0).get(0).isZERO()) {
                pf.addNonFractionalPart(Ai.get(0).get(0));
            }
            for (int i = 1; i < Ai.size(); i++) {
                List<GenPolynomial<BigRational>> list = Ai.get(i);
                int j = 0;
                for (GenPolynomial<BigRational> genPolynomial : list) {
                    if (!genPolynomial.isZERO()) {
                        GenPolynomial<BigRational> Di_1 = D.get(i - 1);
                        pf.addSinglePartialFraction(genPolynomial, Di_1, j);
                    }
                    j++;
                }
            }
            return pf.getResult();
        }
    } catch (JASConversionException e) {
        if (Config.DEBUG) {
            e.printStackTrace();
        }
    }
    return F.NIL;
}

Example 2 with ASTRange

use of org.matheclipse.core.expression.ASTRange in project symja_android_library by axkr.

the class Roots method rootsOfVariable.

/**
	 * 
	 * @param expr
	 * @param denominator
	 * @param variables
	 * @param numericSolutions
	 * @param engine
	 * @return <code>F.NIL</code> if no evaluation was possible.
	 */
protected static IAST rootsOfVariable(final IExpr expr, final IExpr denominator, final IAST variables, boolean numericSolutions, EvalEngine engine) {
    IAST result = F.NIL;
    ASTRange r = new ASTRange(variables, 1);
    List<IExpr> varList = r;
    try {
        IExpr temp;
        IAST list = rootsOfQuadraticExprPolynomial(expr, variables);
        if (list.isPresent()) {
            return list;
        }
        JASConvert<BigRational> jas = new JASConvert<BigRational>(varList, BigRational.ZERO);
        GenPolynomial<BigRational> polyRat = jas.expr2JAS(expr, numericSolutions);
        // if (polyRat.degree(0) <= 2) {
        result = rootsOfExprPolynomial(expr, variables, false);
        if (result.isPresent()) {
            return result;
        }
        // }
        result = F.List();
        IAST factorRational = Algebra.factorRational(polyRat, jas, varList, F.List);
        for (int i = 1; i < factorRational.size(); i++) {
            temp = F.evalExpand(factorRational.get(i));
            IAST quarticResultList = QuarticSolver.solve(temp, variables.arg1());
            if (quarticResultList.isPresent()) {
                for (int j = 1; j < quarticResultList.size(); j++) {
                    if (numericSolutions) {
                        result.append(F.chopExpr(engine.evalN(quarticResultList.get(j)), Config.DEFAULT_ROOTS_CHOP_DELTA));
                    } else {
                        result.append(quarticResultList.get(j));
                    }
                }
            } else {
                polyRat = jas.expr2JAS(temp, numericSolutions);
                IAST factorComplex = Algebra.factorComplex(polyRat, jas, varList, F.List, true);
                for (int k = 1; k < factorComplex.size(); k++) {
                    temp = F.evalExpand(factorComplex.get(k));
                    quarticResultList = QuarticSolver.solve(temp, variables.arg1());
                    if (quarticResultList.isPresent()) {
                        for (int j = 1; j < quarticResultList.size(); j++) {
                            if (numericSolutions) {
                                result.append(F.chopExpr(engine.evalN(quarticResultList.get(j)), Config.DEFAULT_ROOTS_CHOP_DELTA));
                            } else {
                                result.append(quarticResultList.get(j));
                            }
                        }
                    } else {
                        double[] coefficients = CoefficientList.coefficientList(temp, (ISymbol) variables.arg1());
                        if (coefficients == null) {
                            return F.NIL;
                        }
                        IAST resultList = findRoots(coefficients);
                        // true);
                        if (resultList.size() > 0) {
                            result.appendArgs(resultList);
                        }
                    }
                }
            }
        }
        result = QuarticSolver.createSet(result);
        return result;
    } catch (JASConversionException e) {
        result = rootsOfExprPolynomial(expr, variables, true);
    }
    if (result.isPresent()) {
        if (!denominator.isNumber()) {
            // eliminate roots from the result list, which occur in the
            // denominator
            int i = 1;
            while (i < result.size()) {
                IExpr temp = denominator.replaceAll(F.Rule(variables.arg1(), result.get(i)));
                if (temp.isPresent() && engine.evaluate(temp).isZero()) {
                    result.remove(i);
                    continue;
                }
                i++;
            }
        }
        return result;
    }
    return F.NIL;
}

Example 3 with ASTRange

use of org.matheclipse.core.expression.ASTRange in project symja_android_library by axkr.

the class Algebra method cancelGCD.

/**
	 * Calculate the 3 elements result array
	 * 
	 * <pre>
	 * [ 
	 *   commonFactor, 
	 *   numeratorPolynomial.divide(gcd(numeratorPolynomial, denominatorPolynomial)), 
	 *   denominatorPolynomial.divide(gcd(numeratorPolynomial, denominatorPolynomial)) 
	 * ]
	 * </pre>
	 * 
	 * for the given expressions <code>numeratorPolynomial</code> and <code>denominatorPolynomial</code>.
	 * 
	 * 
	 * @param numeratorPolynomial
	 *            a <code>BigRational</code> polynomial which could be converted to JAS polynomial
	 * @param denominatorPolynomial
	 *            a <code>BigRational</code> polynomial which could be converted to JAS polynomial
	 * @return <code>null</code> if the expressions couldn't be converted to JAS polynomials or gcd equals 1
	 * @throws JASConversionException
	 */
public static IExpr[] cancelGCD(IExpr numeratorPolynomial, IExpr denominatorPolynomial) throws JASConversionException {
    try {
        if (denominatorPolynomial.isInteger() && numeratorPolynomial.isPlus()) {
            IExpr[] result = Cancel.cancelPlusIntegerGCD((IAST) numeratorPolynomial, (IInteger) denominatorPolynomial);
            if (result != null) {
                return result;
            }
        }
        VariablesSet eVar = new VariablesSet(numeratorPolynomial);
        eVar.addVarList(denominatorPolynomial);
        if (eVar.size() == 0) {
            return null;
        }
        IAST vars = eVar.getVarList();
        ExprPolynomialRing ring = new ExprPolynomialRing(vars);
        ExprPolynomial pol1 = ring.create(numeratorPolynomial);
        ExprPolynomial pol2 = ring.create(denominatorPolynomial);
        ASTRange r = new ASTRange(eVar.getVarList(), 1);
        JASIExpr jas = new JASIExpr(r, true);
        GenPolynomial<IExpr> p1 = jas.expr2IExprJAS(pol1);
        GenPolynomial<IExpr> p2 = jas.expr2IExprJAS(pol2);
        GreatestCommonDivisor<IExpr> engine;
        engine = GCDFactory.getImplementation(ExprRingFactory.CONST);
        GenPolynomial<IExpr> gcd = engine.gcd(p1, p2);
        IExpr[] result = new IExpr[3];
        if (gcd.isONE()) {
            result[0] = jas.exprPoly2Expr(gcd);
            result[1] = jas.exprPoly2Expr(p1);
            result[2] = jas.exprPoly2Expr(p2);
        } else {
            result[0] = F.C1;
            result[1] = F.eval(jas.exprPoly2Expr(p1.divide(gcd)));
            result[2] = F.eval(jas.exprPoly2Expr(p2.divide(gcd)));
        }
        return result;
    } catch (RuntimeException e) {
        if (Config.DEBUG) {
            e.printStackTrace();
        }
    }
    return null;
}

Example 4 with ASTRange

use of org.matheclipse.core.expression.ASTRange in project symja_android_library by axkr.

the class RootIntervals method croots.

/**
	 * Complex numeric roots intervals.
	 * 
	 * @param ast
	 * @return
	 */
public static IAST croots(final IExpr arg, boolean numeric) {
    try {
        VariablesSet eVar = new VariablesSet(arg);
        if (!eVar.isSize(1)) {
            // only possible for univariate polynomials
            return F.NIL;
        }
        IExpr expr = F.evalExpandAll(arg);
        ASTRange r = new ASTRange(eVar.getVarList(), 1);
        List<IExpr> varList = r;
        ComplexRing<BigRational> cfac = new ComplexRing<BigRational>(new BigRational(1));
        ComplexRootsAbstract<BigRational> cr = new ComplexRootsSturm<BigRational>(cfac);
        JASConvert<Complex<BigRational>> jas = new JASConvert<Complex<BigRational>>(varList, cfac);
        GenPolynomial<Complex<BigRational>> poly = jas.numericExpr2JAS(expr);
        Squarefree<Complex<BigRational>> engine = SquarefreeFactory.<Complex<BigRational>>getImplementation(cfac);
        poly = engine.squarefreePart(poly);
        List<Rectangle<BigRational>> roots = cr.complexRoots(poly);
        BigRational len = new BigRational(1, 100000L);
        IAST resultList = F.List();
        if (numeric) {
            for (Rectangle<BigRational> root : roots) {
                Rectangle<BigRational> refine = cr.complexRootRefinement(root, poly, len);
                resultList.append(JASConvert.jas2Numeric(refine.getCenter(), Config.DEFAULT_ROOTS_CHOP_DELTA));
            }
        } else {
            IAST rectangleList;
            for (Rectangle<BigRational> root : roots) {
                rectangleList = F.List();
                Rectangle<BigRational> refine = cr.complexRootRefinement(root, poly, len);
                rectangleList.append(JASConvert.jas2Complex(refine.getNW()));
                rectangleList.append(JASConvert.jas2Complex(refine.getSW()));
                rectangleList.append(JASConvert.jas2Complex(refine.getSE()));
                rectangleList.append(JASConvert.jas2Complex(refine.getNE()));
                resultList.append(rectangleList);
            // System.out.println("refine = " + refine);
            }
        }
        return resultList;
    } catch (InvalidBoundaryException e) {
        if (Config.SHOW_STACKTRACE) {
            e.printStackTrace();
        }
    } catch (JASConversionException e) {
        if (Config.SHOW_STACKTRACE) {
            e.printStackTrace();
        }
    }
    return F.NIL;
}