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

Example 16 with IInteger

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

the class ExtendedGCD method extendedGCD.

public static BigInteger extendedGCD(final IAST ast, BigInteger[] subBezouts) {
    BigInteger factor;
    BigInteger gcd = ((IInteger) ast.arg1()).toBigNumerator();
    Object[] stepResult = extendedGCD(((IInteger) ast.arg2()).toBigNumerator(), gcd);
    gcd = (BigInteger) stepResult[0];
    subBezouts[0] = ((BigInteger[]) stepResult[1])[0];
    subBezouts[1] = ((BigInteger[]) stepResult[1])[1];
    for (int i = 3; i < ast.size(); i++) {
        stepResult = extendedGCD(((IInteger) ast.get(i)).toBigNumerator(), gcd);
        gcd = (BigInteger) stepResult[0];
        factor = ((BigInteger[]) stepResult[1])[0];
        for (int j = 0; j < i - 1; j++) {
            subBezouts[j] = subBezouts[j].multiply(factor);
        }
        subBezouts[i - 1] = ((BigInteger[]) stepResult[1])[1];
    }
    return gcd;
}

Example 17 with IInteger

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

the class NumberTheory method multinomial.

/**
	 * 
	 * @param indices
	 *            the non-negative coefficients
	 * @param n
	 *            the sum of the non-negative coefficients
	 * @return
	 */
public static IInteger multinomial(final int[] indices, final int n) {
    IInteger bn = AbstractIntegerSym.valueOf(n);
    IInteger result = factorial(bn);
    for (int i = 0; i < indices.length; i++) {
        if (indices[i] != 0) {
            result = result.div(factorial(AbstractIntegerSym.valueOf(indices[i])));
        }
    }
    return result;
}

Example 18 with IInteger

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

the class Iterator method create.

/**
	 * Iterator specification for functions like <code>Table()</code> or
	 * <code>Sum()</code> or <code>Product()</code>
	 * 
	 * @param list
	 *            a list representing an iterator specification
	 * @param engine
	 *            the evaluation engine
	 * @return the iterator
	 */
public static IIterator<IExpr> create(final IAST list, final EvalEngine engine) {
    EvalEngine evalEngine = engine;
    IExpr lowerLimit;
    IExpr upperLimit;
    IExpr step;
    ISymbol variable;
    boolean fNumericMode;
    // fNumericMode = evalEngine.isNumericMode() ||
    // list.isMember(Predicates.isNumeric(), false);
    boolean localNumericMode = evalEngine.isNumericMode();
    try {
        if (list.hasNumericArgument()) {
            evalEngine.setNumericMode(true);
        }
        fNumericMode = evalEngine.isNumericMode();
        switch(list.size()) {
            case 2:
                lowerLimit = F.C1;
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg1());
                step = F.C1;
                variable = null;
                if (upperLimit instanceof Num) {
                    return new DoubleIterator(variable, 1.0, ((INum) upperLimit).doubleValue(), 1.0);
                }
                if (upperLimit.isInteger()) {
                    try {
                        int iUpperLimit = ((IInteger) upperLimit).toInt();
                        return new IntIterator(variable, 1, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (upperLimit.isRational()) {
                    try {
                        return new RationalIterator(variable, F.C1, (IRational) upperLimit, F.C1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (upperLimit.isSignedNumber()) {
                    return new ISignedNumberIterator(variable, F.C1, (ISignedNumber) upperLimit, F.C1);
                }
                break;
            case 3:
                lowerLimit = F.C1;
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                step = F.C1;
                if (list.arg1() instanceof ISymbol) {
                    variable = (ISymbol) list.arg1();
                } else {
                    variable = null;
                }
                if (upperLimit instanceof Num) {
                    return new DoubleIterator(variable, 1.0, ((INum) upperLimit).doubleValue(), 1.0);
                }
                if (upperLimit.isInteger()) {
                    try {
                        int iUpperLimit = ((IInteger) upperLimit).toInt();
                        return new IntIterator(variable, 1, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (upperLimit.isRational()) {
                    try {
                        return new RationalIterator(variable, F.C1, (IRational) upperLimit, F.C1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (upperLimit.isSignedNumber()) {
                    return new ISignedNumberIterator(variable, F.C1, (ISignedNumber) upperLimit, F.C1);
                }
                break;
            case 4:
                lowerLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg3());
                step = F.C1;
                if (list.arg1().isSymbol()) {
                    variable = (ISymbol) list.arg1();
                } else {
                    variable = null;
                }
                if (lowerLimit instanceof Num && upperLimit instanceof Num) {
                    return new DoubleIterator(variable, ((INum) lowerLimit).doubleValue(), ((INum) upperLimit).doubleValue(), 1.0);
                }
                if (lowerLimit.isInteger() && upperLimit.isInteger()) {
                    try {
                        int iLowerLimit = ((IInteger) lowerLimit).toInt();
                        int iUpperLimit = ((IInteger) upperLimit).toInt();
                        return new IntIterator(variable, iLowerLimit, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isRational() && upperLimit.isRational()) {
                    try {
                        return new RationalIterator(variable, (IRational) lowerLimit, (IRational) upperLimit, F.C1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isSignedNumber() && upperLimit.isSignedNumber()) {
                    ISignedNumber iLowerLimit = (ISignedNumber) lowerLimit;
                    ISignedNumber iUpperLimit = (ISignedNumber) upperLimit;
                    return new ISignedNumberIterator(variable, iLowerLimit, iUpperLimit, F.C1);
                }
                break;
            case 5:
                lowerLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg3());
                step = evalEngine.evalWithoutNumericReset(list.arg4());
                if (list.arg1() instanceof ISymbol) {
                    variable = (ISymbol) list.arg1();
                } else {
                    variable = null;
                }
                if (lowerLimit instanceof Num && upperLimit instanceof Num && step instanceof Num) {
                    return new DoubleIterator(variable, ((INum) lowerLimit).doubleValue(), ((INum) upperLimit).doubleValue(), ((INum) step).doubleValue());
                }
                if (lowerLimit.isInteger() && upperLimit.isInteger() && step.isInteger()) {
                    try {
                        int iLowerLimit = ((IInteger) lowerLimit).toInt();
                        int iUpperLimit = ((IInteger) upperLimit).toInt();
                        int iStep = ((IInteger) step).toInt();
                        return new IntIterator(variable, iLowerLimit, iUpperLimit, iStep);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isRational() && upperLimit.isRational() && step.isRational()) {
                    try {
                        return new RationalIterator(variable, (IRational) lowerLimit, (IRational) upperLimit, (IRational) step);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isSignedNumber() && upperLimit.isSignedNumber() && step.isSignedNumber()) {
                    return new ISignedNumberIterator(variable, (ISignedNumber) lowerLimit, (ISignedNumber) upperLimit, (ISignedNumber) step);
                }
                break;
            default:
                lowerLimit = null;
                upperLimit = null;
                step = null;
                variable = null;
        }
        return new ExprIterator(variable, evalEngine, lowerLimit, upperLimit, step, fNumericMode);
    } finally {
        evalEngine.setNumericMode(localNumericMode);
    }
}

Example 19 with IInteger

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

the class AbstractAST method internalJavaString.

/** {@inheritDoc} */
@Override
public final String internalJavaString(boolean symbolsAsFactoryMethod, int depth, boolean useOperators) {
    final String sep = ",";
    final IExpr temp = head();
    if (temp.equals(F.HoldForm) && size() == 2) {
        return arg1().internalFormString(symbolsAsFactoryMethod, depth);
    }
    if (temp.equals(F.Hold) && size() == 2) {
        return arg1().internalFormString(symbolsAsFactoryMethod, depth);
    }
    if (isInfinity()) {
        return "oo";
    }
    if (isNegativeInfinity()) {
        return "Noo";
    }
    if (isComplexInfinity()) {
        return "CComplexInfinity";
    }
    if (this.equals(F.Slot1)) {
        return "Slot1";
    }
    if (this.equals(F.Slot2)) {
        return "Slot2";
    }
    if (temp.equals(F.Rational) && size() == 3) {
        if (arg1().isInteger() && arg2().isInteger()) {
            return F.QQ((IInteger) arg1(), (IInteger) arg2()).internalJavaString(symbolsAsFactoryMethod, depth, useOperators);
        }
        return arg1().internalFormString(symbolsAsFactoryMethod, depth);
    }
    if (isPower()) {
        if (equalsAt(2, F.C1D2)) {
            if (arg1().isInteger()) {
                // square root of an integer number
                IInteger i = (IInteger) arg1();
                if (i.equals(F.C2)) {
                    return "CSqrt2";
                } else if (i.equals(F.C3)) {
                    return "CSqrt3";
                } else if (i.equals(F.C5)) {
                    return "CSqrt5";
                } else if (i.equals(F.C6)) {
                    return "CSqrt6";
                } else if (i.equals(F.C7)) {
                    return "CSqrt7";
                } else if (i.equals(F.C10)) {
                    return "CSqrt10";
                }
            }
            return "Sqrt(" + arg1().internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators) + ")";
        }
        if (equalsAt(2, F.C2)) {
            return "Sqr(" + arg1().internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators) + ")";
        }
        if (equalsAt(2, F.CN1D2) && arg1().isInteger()) {
            // negative square root of an integer number
            IInteger i = (IInteger) arg1();
            if (i.equals(F.C2)) {
                return "C1DSqrt2";
            } else if (i.equals(F.C3)) {
                return "C1DSqrt3";
            } else if (i.equals(F.C5)) {
                return "C1DSqrt5";
            } else if (i.equals(F.C6)) {
                return "C1DSqrt6";
            } else if (i.equals(F.C7)) {
                return "C1DSqrt7";
            } else if (i.equals(F.C10)) {
                return "C1DSqrt10";
            }
        }
        if (arg2().isInteger()) {
            try {
                long exp = ((IInteger) arg2()).toLong();
                // create Power(arg1, exp)
                return "Power(" + arg1().internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators) + "," + Long.toString(exp) + ")";
            } catch (RuntimeException ex) {
            }
        }
    }
    StringBuilder text = new StringBuilder(size() * 10);
    if (temp.isSymbol()) {
        ISymbol sym = (ISymbol) temp;
        String name = null;
        if (Config.PARSER_USE_LOWERCASE_SYMBOLS) {
            name = sym.toString();
            if (name.length() > 0) {
                name = name.toLowerCase(Locale.ENGLISH);
            }
            name = AST2Expr.PREDEFINED_SYMBOLS_MAP.get(name);
        }
        if (name == null && !Character.isUpperCase(sym.toString().charAt(0))) {
            text.append("$(");
            for (int i = 0; i < size(); i++) {
                text.append(get(i).internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators));
                if (i < size() - 1) {
                    text.append(sep);
                }
            }
            text.append(')');
            return text.toString();
        }
    } else if (temp.isPattern() || temp.isAST()) {
        text.append("$(");
        for (int i = 0; i < size(); i++) {
            text.append(get(i).internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators));
            if (i < size() - 1) {
                text.append(sep);
            }
        }
        text.append(')');
        return text.toString();
    }
    if (isTimes() && size() == 3 && arg1().isMinusOne() && !arg2().isTimes()) {
        return "Negate(" + arg2().internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators) + ")";
    }
    if (useOperators && size() == 3) {
        if (isTimes()) {
            IExpr arg1 = arg1();
            IExpr arg2 = arg2();
            boolean isLowerPrecedence = arg1.isPlus();
            internalOperatorForm(arg1, isLowerPrecedence, symbolsAsFactoryMethod, depth, useOperators, text);
            text.append('*');
            isLowerPrecedence = arg2.isPlus();
            internalOperatorForm(arg2, isLowerPrecedence, symbolsAsFactoryMethod, depth, useOperators, text);
            return text.toString();
        } else if (isPlus()) {
            IExpr arg1 = arg1();
            IExpr arg2 = arg2();
            internalOperatorForm(arg1, false, symbolsAsFactoryMethod, depth, useOperators, text);
            text.append('+');
            internalOperatorForm(arg2, false, symbolsAsFactoryMethod, depth, useOperators, text);
            return text.toString();
        } else if (isPower()) {
            IExpr arg1 = arg1();
            IExpr arg2 = arg2();
            boolean isLowerPrecedence = arg1.isTimes() || arg1.isPlus();
            internalOperatorForm(arg1, isLowerPrecedence, symbolsAsFactoryMethod, depth, useOperators, text);
            text.append('^');
            isLowerPrecedence = arg2.isTimes() || arg2.isPlus();
            internalOperatorForm(arg2, isLowerPrecedence, symbolsAsFactoryMethod, depth, useOperators, text);
            return text.toString();
        }
    }
    text.append(temp.internalJavaString(false, 0, useOperators));
    text.append('(');
    if (isTimes() || isPlus()) {
        if (depth == 0 && isList()) {
            text.append('\n');
        }
        internalFormOrderless(this, text, sep, symbolsAsFactoryMethod, depth, useOperators);
        if (depth == 0 && isList()) {
            text.append('\n');
        }
    } else {
        if (depth == 0 && isList()) {
            text.append('\n');
        }
        for (int i = 1; i < size(); i++) {
            text.append(get(i).internalJavaString(symbolsAsFactoryMethod, depth + 1, useOperators));
            if (i < size() - 1) {
                text.append(sep);
                if (depth == 0 && isList()) {
                    text.append('\n');
                }
            }
        }
        if (depth == 0 && isList()) {
            text.append('\n');
        }
    }
    text.append(')');
    return text.toString();
}

Example 20 with IInteger

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

the class PartialFractionIntegrateGenerator method addSinglePartialFraction.

@Override
public void addSinglePartialFraction(GenPolynomial<BigRational> genPolynomial, GenPolynomial<BigRational> Di_1, int j) {
    if (!genPolynomial.isZERO()) {
        BigRational[] numer = new BigRational[3];
        BigRational[] denom = new BigRational[3];
        IExpr temp;
        boolean isDegreeLE2 = Di_1.degree() <= 2;
        if (isDegreeLE2 && j == 1L) {
            Object[] objects = jas.factorTerms(genPolynomial);
            java.math.BigInteger gcd = (java.math.BigInteger) objects[0];
            java.math.BigInteger lcm = (java.math.BigInteger) objects[1];
            GenPolynomial<edu.jas.arith.BigInteger> genPolynomial2 = ((GenPolynomial<edu.jas.arith.BigInteger>) objects[2]).multiply(edu.jas.arith.BigInteger.valueOf(gcd));
            if (genPolynomial2.isONE()) {
                GenPolynomial<BigRational> newDi_1 = Di_1.multiply(BigRational.valueOf(lcm));
                isQuadratic(newDi_1, denom);
                IFraction a = F.fraction(denom[2].numerator(), denom[2].denominator());
                IFraction b = F.fraction(denom[1].numerator(), denom[1].denominator());
                IFraction c = F.fraction(denom[0].numerator(), denom[0].denominator());
                if (a.isZero()) {
                    // JavaForm[Log[b*x+c]/b]
                    result.append(Times(Log(Plus(c, Times(b, x))), Power(b, CN1)));
                } else {
                    // compute b^2-4*a*c from
                    // (a*x^2+b*x+c)
                    BigRational cmp = denom[1].multiply(denom[1]).subtract(BigRational.valueOf(4L).multiply(denom[2]).multiply(denom[0]));
                    int cmpTo = cmp.compareTo(BigRational.ZERO);
                    // (2*a*x+b)
                    IExpr ax2Plusb = F.Plus(F.Times(F.C2, a, x), b);
                    if (cmpTo == 0) {
                        // (-2) / (2*a*x+b)
                        result.append(F.Times(F.integer(-2L), F.Power(ax2Plusb, F.CN1)));
                    } else if (cmpTo > 0) {
                        // (b^2-4ac)^(1/2)
                        temp = F.eval(F.Power(F.Subtract(F.Sqr(b), F.Times(F.C4, a, c)), F.C1D2));
                        result.append(F.Times(F.Power(temp, F.CN1), F.Log(F.Times(F.Subtract(ax2Plusb, temp), Power(F.Plus(ax2Plusb, temp), F.CN1)))));
                    } else {
                        // (4ac-b^2)^(1/2)
                        temp = F.eval(F.Power(F.Subtract(F.Times(F.C4, a, c), F.Sqr(b)), F.CN1D2));
                        result.append(F.Times(F.C2, temp, F.ArcTan(Times(ax2Plusb, temp))));
                    }
                }
            } else {
                // (B*A*x) / (q*p*x)
                isQuadratic(genPolynomial, numer);
                IFraction A = F.fraction(numer[1].numerator(), numer[1].denominator());
                IFraction B = F.fraction(numer[0].numerator(), numer[0].denominator());
                isQuadratic(Di_1, denom);
                IFraction p = F.fraction(denom[1].numerator(), denom[1].denominator());
                IFraction q = F.fraction(denom[0].numerator(), denom[0].denominator());
                if (A.isZero() && !p.isZero()) {
                    // JavaForm[B*Log[p*x+q]/p]
                    if (q.isNegative()) {
                        temp = Times(B, Log(Plus(q.negate(), Times(p.negate(), x))), Power(p, CN1));
                    } else {
                        temp = Times(B, Log(Plus(q, Times(p, x))), Power(p, CN1));
                    }
                } else {
                    // JavaForm[A/2*Log[x^2+p*x+q]+(2*B-A*p)/(4*q-p^2)^(1/2)*ArcTan[(2*x+p)/(4*q-p^2)^(1/2)]]
                    temp = Plus(Times(C1D2, A, Log(Plus(q, Times(p, x), Power(x, C2)))), Times(ArcTan(Times(Plus(p, Times(C2, x)), Power(Plus(Times(CN1, Power(p, C2)), Times(C4, q)), CN1D2))), Plus(Times(C2, B), Times(CN1, A, p)), Power(Plus(Times(CN1, Power(p, C2)), Times(C4, q)), CN1D2)));
                }
                result.append(F.eval(temp));
            }
        } else if (isDegreeLE2 && j > 1L) {
            isQuadratic(genPolynomial, numer);
            IFraction A = F.fraction(numer[1].numerator(), numer[1].denominator());
            IFraction B = F.fraction(numer[0].numerator(), numer[0].denominator());
            isQuadratic(Di_1, denom);
            IFraction a = F.fraction(denom[2].numerator(), denom[2].denominator());
            IFraction b = F.fraction(denom[1].numerator(), denom[1].denominator());
            IFraction c = F.fraction(denom[0].numerator(), denom[0].denominator());
            IInteger k = F.integer(j);
            if (A.isZero()) {
                // JavaForm[B*((2*a*x+b)/((k-1)*(4*a*c-b^2)*(a*x^2+b*x+c)^(k-1))+
                // (4*k*a-6*a)/((k-1)*(4*a*c-b^2))*Integrate[(a*x^2+b*x+c)^(-k+1),x])]
                temp = Times(B, Plus(Times(Integrate(Power(Plus(c, Times(b, x), Times(a, Power(x, C2))), Plus(C1, Times(CN1, k))), x), Plus(Times(F.integer(-6L), a), Times(C4, a, k)), Power(Plus(CN1, k), CN1), Power(Plus(Times(CN1, Power(b, C2)), Times(C4, a, c)), CN1)), Times(Plus(b, Times(C2, a, x)), Power(Plus(CN1, k), CN1), Power(Plus(Times(CN1, Power(b, C2)), Times(C4, a, c)), CN1), Power(Plus(c, Times(b, x), Times(a, Power(x, C2))), Times(CN1, Plus(CN1, k))))));
            } else {
                // JavaForm[(-A)/(2*a*(k-1)*(a*x^2+b*x+c)^(k-1))+(B-A*b/(2*a))*Integrate[(a*x^2+b*x+c)^(-k),x]]
                temp = Plus(Times(Integrate(Power(Plus(c, Times(b, x), Times(a, Power(x, C2))), Times(CN1, k)), x), Plus(B, Times(CN1D2, A, Power(a, CN1), b))), Times(CN1D2, A, Power(a, CN1), Power(Plus(CN1, k), CN1), Power(Plus(c, Times(b, x), Times(a, Power(x, C2))), Times(CN1, Plus(CN1, k)))));
            }
            result.append(F.eval(temp));
        } else {
            // ElementaryIntegration<BigRational> ei = new
            // ElementaryIntegration<BigRational>(BigRational.ZERO);
            // Integral<BigRational> integral= ei.integrate(genPolynomial,
            // Di_1);
            temp = F.eval(F.Times(jas.rationalPoly2Expr(genPolynomial), F.Power(jas.rationalPoly2Expr(Di_1), F.integer(j * (-1L)))));
            if (!temp.isZero()) {
                if (temp.isAST()) {
                    ((IAST) temp).addEvalFlags(IAST.IS_DECOMPOSED_PARTIAL_FRACTION);
                }
                result.append(F.Integrate(temp, x));
            }
        }
    }
}