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

Example 31 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));
            }
        }
    }
}

Example 32 with IInteger

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

the class NumberTheory method factorial.

public static IInteger factorial(final IInteger x) {
    try {
        int ni = x.toInt();
        BigInteger result;
        if (ni < 0) {
            result = BigIntegerMath.factorial(-1 * ni);
            if ((ni & 0x0001) == 0x0001) {
                // odd integer number
                result = result.multiply(BigInteger.valueOf(-1L));
            }
        } else {
            if (ni <= 20) {
                return AbstractIntegerSym.valueOf(LongMath.factorial(ni));
            }
            result = BigIntegerMath.factorial(ni);
        }
        return AbstractIntegerSym.valueOf(result);
    } catch (ArithmeticException ae) {
    //
    }
    IInteger result = F.C1;
    if (x.compareTo(F.C0) == -1) {
        result = F.CN1;
        for (IInteger i = F.CN2; i.compareTo(x) >= 0; i = i.add(F.CN1)) {
            result = result.multiply(i);
        }
    } else {
        for (IInteger i = F.C2; i.compareTo(x) <= 0; i = i.add(F.C1)) {
            result = result.multiply(i);
        }
    }
    return result;
}

Example 33 with IInteger

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

the class NumberTheory method fibonacci.

/**
	 * <p>
	 * Fibonacci sequence. Algorithm in <code>O(log(n))</code> time.
	 * </p>
	 * See: <a href= "https://www.rosettacode.org/wiki/Fibonacci_sequence#Iterative_28"> Roseatta code: Fibonacci
	 * sequence.</a>
	 * 
	 * @param iArg
	 * @return
	 */
public static IInteger fibonacci(final IInteger iArg) {
    IInteger a = F.C1;
    IInteger b = F.C0;
    IInteger c = F.C1;
    IInteger d = F.C0;
    IInteger result = F.C0;
    IInteger temp = iArg;
    if (iArg.isNegative()) {
        temp = temp.negate();
    }
    while (!temp.isZero()) {
        if (temp.isOdd()) {
            d = result.multiply(c);
            result = a.multiply(c).add(result.multiply(b).add(d));
            a = a.multiply(b).add(d);
        }
        d = c.multiply(c);
        c = b.multiply(c).shiftLeft(1).add(d);
        b = b.multiply(b).add(d);
        temp = temp.shiftRight(1);
    }
    if (iArg.isNegative() && iArg.isEven()) {
        return result.negate();
    }
    return result;
}

Example 34 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 symbol
	 *            the variable symbol
	 * @param engine
	 *            the evaluation engine
	 * @return the iterator
	 */
public static IIterator<IExpr> create(final IAST list, final ISymbol symbol, final EvalEngine engine) {
    EvalEngine evalEngine = engine;
    IExpr lowerLimit;
    IExpr upperLimit;
    IExpr step;
    ISymbol variable;
    boolean fNumericMode;
    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 = symbol;
                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(symbol, 1, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (upperLimit.isRational()) {
                    try {
                        return new RationalIterator(symbol, 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 = evalEngine.evalWithoutNumericReset(list.arg1());
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                step = F.C1;
                variable = symbol;
                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(symbol, iLowerLimit, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isRational() && upperLimit.isRational()) {
                    try {
                        return new RationalIterator(symbol, (IRational) lowerLimit, (IRational) upperLimit, F.C1);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isSignedNumber() && upperLimit.isSignedNumber()) {
                    return new ISignedNumberIterator(variable, (ISignedNumber) lowerLimit, (ISignedNumber) upperLimit, F.C1);
                }
                break;
            case 4:
                lowerLimit = evalEngine.evalWithoutNumericReset(list.arg1());
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                step = evalEngine.evalWithoutNumericReset(list.arg3());
                variable = symbol;
                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(symbol, iLowerLimit, iUpperLimit, iStep);
                    } catch (ArithmeticException ae) {
                    //
                    }
                } else if (lowerLimit.isRational() && upperLimit.isRational() && step.isRational()) {
                    try {
                        return new RationalIterator(symbol, (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 35 with IInteger

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

the class AbstractFractionSym method factorInteger.

@Override
public /** {@inheritDoc} */
IAST factorInteger() {
    IInteger num = getNumerator();
    IInteger den = getDenominator();
    IAST result = den.factorInteger();
    // negate the exponents of the denominator part
    for (int i = 1; i < result.size(); i++) {
        IAST list = (IAST) result.get(i);
        list.set(2, ((ISignedNumber) list.arg2()).negate());
    }
    // add the factors from the numerator part
    result.appendArgs(num.factorInteger());
    EvalAttributes.sort(result);
    return result;
}