Examples with IRational org.matheclipse.core.interfaces.IRational used on opensource projects

Example 11 with IRational

use of org.matheclipse.core.interfaces.IRational in project symja_android_library by axkr.

the class PolynomialHomogenization method determineLCM.

private void determineLCM(final IExpr expression) {
    if (expression instanceof IAST) {
        final IAST ast = (IAST) expression;
        if (ast.isPlus() || ast.isTimes()) {
            for (int i = 1; i < ast.size(); i++) {
                determineLCM(ast.get(i));
            }
            return;
        } else if (ast.isPower()) {
            IExpr exp = ast.exponent();
            IExpr base = ast.base();
            if (exp.isReal()) {
                IInteger lcm = F.C1;
                IRational rat = ((ISignedNumber) exp).rationalFactor();
                if (rat == null) {
                    return;
                }
                if (!rat.isInteger()) {
                    IInteger denominator = rat.denominator();
                    if (denominator.isNegative()) {
                        denominator = denominator.negate();
                    }
                    lcm = denominator;
                }
                // if (base.isTimes()) {
                // 
                // }
                replaceExpressionLCM(base, lcm);
                return;
            }
            if (exp.isTimes()) {
                determineTimes(ast, base, (IAST) exp);
                // ((IAST) exp).forEach(x -> determineLCM(F.Power(base, x)));
                return;
            } else if (exp.isPlus()) {
                // && base.isExactNumber()) {
                // ex: 4^(2*x+3)
                IAST plusAST = (IAST) exp;
                if (plusAST.first().isInteger()) {
                    determineLCM(S.Power.of(base, plusAST.first()));
                    determineLCM(S.Power.of(base, plusAST.rest().oneIdentity0()));
                    return;
                }
            }
            replaceExpressionLCM(ast, F.C1);
            return;
        }
        replaceExpressionLCM(expression, F.C1);
        return;
    }
    if (expression instanceof ISymbol) {
        replaceExpressionLCM(expression, F.C1);
    }
}

Example 12 with IRational

use of org.matheclipse.core.interfaces.IRational in project symja_android_library by axkr.

the class D method binaryD.

/**
 * Evaluate <code>D(functionO>fX, x)</code> for some general cases.
 *
 * @param functionOfX the function of <code>x</code>
 * @param x derive w.r.t this variable
 * @param ast
 * @param engine
 * @return
 */
private static IExpr binaryD(final IExpr functionOfX, IExpr x, final IAST ast, EvalEngine engine) {
    int[] dim = functionOfX.isPiecewise();
    if (dim != null) {
        return dPiecewise(dim, (IAST) functionOfX, ast, engine);
    }
    if (functionOfX instanceof ASTSeriesData) {
        ASTSeriesData series = ((ASTSeriesData) functionOfX);
        if (series.getX().equals(x)) {
            final IExpr temp = ((ASTSeriesData) functionOfX).derive(x);
            if (temp != null) {
                return temp;
            }
            return F.NIL;
        }
        return F.C0;
    }
    if (functionOfX.isFree(x, true)) {
        return F.C0;
    }
    if (functionOfX.isNumber()) {
        // D[x_?NumberQ,y_] -> 0
        return F.C0;
    }
    if (functionOfX.equals(x)) {
        // D[x_,x_] -> 1
        return F.C1;
    }
    if (functionOfX.isAST()) {
        final IAST function = (IAST) functionOfX;
        final IExpr header = function.head();
        if (function.isPlus()) {
            // D(a_+b_+c_,x_) -> D(a,x)+D(b,x)+D(c,x)
            IExpr result = function.mapThread(F.D(F.Slot1, x), 1);
            return engine.evaluate(result);
        } else if (function.isTimes()) {
            return function.map(F.PlusAlloc(16), new BinaryBindIth1st(function, F.D(S.Null, x)));
        } else if (function.isPower()) {
            // f ^ g
            final IExpr f = function.base();
            final IExpr g = function.exponent();
            if (g.isFree(x)) {
                // g*D(f,y)*f^(g-1)
                return F.Times(g, F.D(f, x), F.Power(f, g.dec()));
            }
            if (f.isFree(x)) {
                if (f.isE()) {
                    return F.Times(F.D(g, x), F.Exp(g));
                }
                // D(g,y)*Log(f)*f^g
                return F.Times(F.D(g, x), F.Log(f), F.Power(f, g));
            }
            // D[f_^g_,y_]:= f^g*(((g*D[f,y])/f)+Log[f]*D[g,y])
            final IASTAppendable resultList = F.TimesAlloc(2);
            resultList.append(F.Power(f, g));
            resultList.append(F.Plus(F.Times(g, F.D(f, x), F.Power(f, F.CN1)), F.Times(F.Log(f), F.D(g, x))));
            return resultList;
        } else if (function.isAST(S.Surd, 3)) {
            // Surd[f,g]
            final IExpr f = function.base();
            if (function.exponent().isInteger()) {
                final IInteger g = (IInteger) function.exponent();
                if (g.isMinusOne()) {
                    return F.Times(F.CN1, F.D(f, x), F.Power(f, F.CN2));
                }
                final IRational gInverse = g.inverse();
                if (g.isNegative()) {
                    if (g.isEven()) {
                        return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g.negate()), g.dec()));
                    }
                    return F.Times(gInverse, F.D(f, x), F.Power(f, F.CN1), F.Power(F.Surd(f, g.negate()), F.CN1));
                }
                return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g), g.dec().negate()));
            }
        } else if ((header == S.Log) && (function.isAST2())) {
            if (function.isFreeAt(1, x)) {
                // D[Log[i_FreeQ(x), x_], z_]:= (x*Log[a])^(-1)*D[x,z];
                return F.Times(F.Power(F.Times(function.arg2(), F.Log(function.arg1())), F.CN1), F.D(function.arg2(), x));
            }
        // } else if (header == F.LaplaceTransform && (listArg1.size()
        // == 4)) {
        // if (listArg1.arg3().equals(x) && listArg1.arg1().isFree(x,
        // true)) {
        // // D(LaplaceTransform(c,t,s), s) -> -c / s^2
        // return F.Times(-1L, listArg1.arg2(), F.Power(x, -2L));
        // } else if (listArg1.arg1().equals(x)) {
        // // D(LaplaceTransform(c,t,s), c) -> 1/s
        // return F.Power(x, -1L);
        // } else if (listArg1.arg1().isFree(x, true) &&
        // listArg1.arg2().isFree(x, true) && listArg1.arg3().isFree(x,
        // true))
        // {
        // // D(LaplaceTransform(c,t,s), w) -> 0
        // return F.C0;
        // } else if (listArg1.arg2().equals(x)) {
        // // D(LaplaceTransform(c,t,s), t) -> 0
        // return F.C0;
        // }
        } else if (function.isAST1() && ast.isEvalFlagOff(IAST.IS_DERIVATIVE_EVALED)) {
            IAST[] derivStruct = function.isDerivativeAST1();
            if (derivStruct != null && derivStruct[2] != null) {
                IAST headAST = derivStruct[1];
                IAST a1Head = derivStruct[0];
                if (a1Head.isAST1() && a1Head.arg1().isInteger()) {
                    try {
                        int n = ((IInteger) a1Head.arg1()).toInt();
                        IExpr arg1 = function.arg1();
                        if (n > 0) {
                            IAST fDerivParam = Derivative.createDerivative(n + 1, headAST.arg1(), arg1);
                            if (x.equals(arg1)) {
                                return fDerivParam;
                            }
                            return F.Times(F.D(arg1, x), fDerivParam);
                        }
                    } catch (ArithmeticException ae) {
                    }
                }
                return F.NIL;
            }
            return getDerivativeArg1(x, function.arg1(), header, engine);
        } else if (function.isAST() && ast.isEvalFlagOff(IAST.IS_DERIVATIVE_EVALED)) {
            return getDerivativeArgN(x, function, header);
        }
    }
    return F.NIL;
}

Example 13 with IRational

use of org.matheclipse.core.interfaces.IRational in project symja_android_library by axkr.

the class TeXFormFactory method convertComplex.

public void convertComplex(final StringBuffer buf, final IComplex c, final int precedence) {
    if (c.isImaginaryUnit()) {
        buf.append("i ");
        return;
    }
    if (precedence > plusPrec) {
        buf.append("\\left( ");
    }
    IRational re = c.getRealPart();
    IRational im = c.getImaginaryPart();
    if (!re.isZero()) {
        convert(buf, c.getRealPart(), 0);
        if (im.compareInt(0) >= 0) {
            buf.append(" + ");
        } else {
            buf.append(" - ");
            im = im.negate();
        }
    }
    convert(buf, im, 0);
    // InvisibleTimes
    buf.append("\\,");
    buf.append("i ");
    if (precedence > plusPrec) {
        buf.append("\\right) ");
    }
}

Example 14 with IRational

use of org.matheclipse.core.interfaces.IRational in project symja_android_library by axkr.

the class ContinuedFraction method evaluate.

@Override
public IExpr evaluate(final IAST ast, EvalEngine engine) {
    Validate.checkRange(ast, 2, 3);
    IExpr arg1 = ast.arg1();
    int maxIterations = Integer.MAX_VALUE;
    if (ast.isAST2() && ast.arg2().isInteger()) {
        maxIterations = Validate.checkIntType(ast, 2);
    }
    if (arg1 instanceof INum) {
        arg1 = F.fraction(((INum) arg1).getRealPart());
    } else if (arg1.isAST() || arg1.isSymbol() && arg1.isNumericFunction()) {
        IExpr num = engine.evalN(arg1);
        if (num instanceof INum) {
            arg1 = F.fraction(((INum) num).getRealPart());
        }
    }
    if (arg1.isRational()) {
        IRational rat = (IRational) arg1;
        IAST continuedFractionList;
        if (rat.getDenominator().isOne()) {
            continuedFractionList = F.List(rat.getNumerator());
        } else if (rat.getNumerator().isOne()) {
            continuedFractionList = F.ListAlloc(2);
            continuedFractionList.append(F.C0);
            continuedFractionList.append(rat.getDenominator());
        } else {
            IFraction temp = F.fraction(rat.getNumerator(), rat.getDenominator());
            IInteger quotient;
            IInteger remainder;
            continuedFractionList = F.ListAlloc(10);
            while (temp.getDenominator().compareInt(1) > 0 && (0 < maxIterations--)) {
                quotient = temp.getNumerator().div(temp.getDenominator());
                remainder = temp.getNumerator().mod(temp.getDenominator());
                continuedFractionList.append(quotient);
                temp = F.fraction(temp.getDenominator(), remainder);
                if (temp.getDenominator().isOne()) {
                    continuedFractionList.append(temp.getNumerator());
                }
            }
        }
        return continuedFractionList;
    }
    return F.NIL;
}

Example 15 with IRational

use of org.matheclipse.core.interfaces.IRational in project symja_android_library by axkr.

the class JASConvert method rationalPoly2Expr.

/**
 * Converts a <a href="http://krum.rz.uni-mannheim.de/jas/">JAS</a> polynomial to a Symja AST with
 * head <code>Plus</code>
 *
 * @param poly a JAS polynomial
 * @param factorTerms
 * @return
 * @throws ArithmeticException
 * @throws JASConversionException
 */
public IAST rationalPoly2Expr(final GenPolynomial<BigRational> poly, boolean factorTerms) throws ArithmeticException, JASConversionException {
    if (poly.length() == 0) {
        return F.Plus(F.C0);
    }
    if (factorTerms) {
        // pull out overall numerical factor in poly.
        Object[] objects = factorTerms(poly);
        GenPolynomial<edu.jas.arith.BigInteger> p2 = (GenPolynomial<edu.jas.arith.BigInteger>) objects[2];
        java.math.BigInteger gcd = (java.math.BigInteger) objects[0];
        java.math.BigInteger lcm = (java.math.BigInteger) objects[1];
        IRational factor = F.fraction(gcd, lcm).normalize();
        IASTAppendable result = F.PlusAlloc(p2.length());
        for (Monomial<edu.jas.arith.BigInteger> monomial : p2) {
            edu.jas.arith.BigInteger coeff = monomial.coefficient();
            ExpVector exp = monomial.exponent();
            IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
            monomialToExpr(coeff, exp, monomTimes);
            result.append(monomTimes.oneIdentity1());
        }
        if (factor.isOne()) {
            return result;
        }
        return F.Times(F.fraction(gcd, lcm), result);
    }
    IASTAppendable result = F.PlusAlloc(poly.length());
    for (Monomial<BigRational> monomial : poly) {
        BigRational coeff = monomial.coefficient();
        ExpVector exp = monomial.exponent();
        IASTAppendable monomTimes = F.TimesAlloc(exp.length() + 1);
        monomialToExpr(coeff, exp, monomTimes);
        result.append(monomTimes.oneIdentity1());
    }
    return result;
}