Examples with BinaryBindIth1st org.matheclipse.core.generic.BinaryBindIth1st used on opensource projects

Example 1 with BinaryBindIth1st

use of org.matheclipse.core.generic.BinaryBindIth1st 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;
}