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

Example 16 with IRational

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

the class F method complexNum.

public static IComplexNum complexNum(final IComplex value) {
    final IRational realFraction = value.getRealPart();
    final IRational imagFraction = value.getImaginaryPart();
    final EvalEngine engine = EvalEngine.get();
    if (engine.isArbitraryMode()) {
        return ApcomplexNum.valueOf(realFraction.toBigNumerator(), realFraction.toBigDenominator(), imagFraction.toBigNumerator(), imagFraction.toBigDenominator());
    }
    // double precision complex number
    double nr = realFraction.numerator().doubleValue();
    double dr = realFraction.denominator().doubleValue();
    double ni = imagFraction.numerator().doubleValue();
    double di = imagFraction.denominator().doubleValue();
    return complexNum(nr / dr, ni / di);
}

Example 17 with IRational

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

the class ComplexSym method complexArg.

@Override
public IExpr complexArg() {
    // ic == ( x + I * y )
    IRational x = getRealPart();
    IRational y = getImaginaryPart();
    int xi = x.compareTo(F.C0);
    int yi = y.compareTo(F.C0);
    if (xi < 0) {
        // x < 0
        if (yi < 0) {
            // -Pi + ArcTan(y/x)
            return Plus(Negate(Pi), ArcTan(Divide(y, x)));
        } else {
            // Pi + ArcTan(y/x)
            return Plus(Pi, ArcTan(Divide(y, x)));
        }
    }
    if (xi > 0) {
        // ArcTan(y/x)
        return ArcTan(Divide(y, x));
    }
    if (yi < 0) {
        // -Pi/2 + ArcTan(x/y)
        return Plus(Times(CN1D2, Pi), ArcTan(Divide(x, y)));
    } else {
        if (yi > 0) {
            // Pi/2 + ArcTan(x/y)
            return Plus(Times(C1D2, Pi), ArcTan(Divide(x, y)));
        }
    }
    return F.C0;
}

Example 18 with IRational

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

the class ComplexSym method quotientRemainder.

/**
 * Return the quotient and remainder as an array <code>[quotient, remainder]</code> of the
 * division of <code>IComplex</code> numbers <code>this / c2</code>.
 *
 * <p>
 * See
 *
 * <ul>
 * <li><a href="https://en.wikipedia.org/wiki/Gaussian_integer">Wikipedia - Gaussian integer</a>
 * <li><a href=
 * "http://fermatslasttheorem.blogspot.com/2005/06/division-algorithm-for-gaussian.html">Division
 * Algorithm for Gaussian Integers </a>
 * </ul>
 *
 * @param c2
 * @return the quotient and remainder as an array <code>[quotient, remainder]</code>
 */
@Override
public IComplex[] quotientRemainder(final IComplex c2) {
    final IRational re = c2.re();
    final IRational im = c2.im();
    IRational numeratorReal = // 
    fReal.multiply(re).subtract(fImaginary.multiply(im.negate()));
    IRational numeratorImaginary = // 
    fReal.multiply(im.negate()).add(re.multiply(fImaginary));
    IRational denominator = // 
    re.multiply(re).add(im.multiply(im));
    if (denominator.isZero()) {
        throw new IllegalArgumentException("Denominator can not be zero.");
    }
    IInteger divisionReal = numeratorReal.divideBy(denominator).roundExpr();
    IInteger divisionImaginary = numeratorImaginary.divideBy(denominator).roundExpr();
    IRational remainderReal = fReal.subtract(re.multiply(divisionReal)).subtract(im.multiply(divisionImaginary).negate());
    IRational remainderImaginary = fImaginary.subtract(re.multiply(divisionImaginary)).subtract(im.multiply(divisionReal));
    return new ComplexSym[] { // 
    valueOf(divisionReal, divisionImaginary), valueOf(remainderReal, remainderImaginary) };
}

Example 19 with IRational

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

the class ComplexSym method sqrtCC.

@Override
public IComplex sqrtCC() {
    // https://math.stackexchange.com/a/44414
    // this == c + d*I
    IRational c = fReal;
    IRational d = fImaginary;
    IExpr val1 = c.multiply(c).add(d.multiply(d)).sqrt();
    if (val1.isRational()) {
        IExpr a = c.add((IRational) val1).divide(F.C2).sqrt();
        if (a.isRational()) {
            IExpr val2 = ((IRational) val1).subtract(c).divide(F.C2).sqrt();
            if (val2.isRational()) {
                // Sqrt(c + d*I) -> a + b*I
                IRational b = ((IRational) val2);
                return valueOf(// 
                (IRational) a, // 
                (d.complexSign() >= 0) ? b : b.negate());
            }
        }
    }
    return null;
}

Example 20 with IRational

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

the class ComplexSym method normalize.

@Override
public INumber normalize() {
    if (fImaginary.isZero()) {
        if (fReal instanceof IFraction) {
            if (fReal.denominator().isOne()) {
                return fReal.numerator();
            }
            if (fReal.numerator().isZero()) {
                return F.C0;
            }
        }
        return fReal;
    }
    boolean evaled = false;
    IRational newRe = fReal;
    IRational newIm = fImaginary;
    if (fReal instanceof IFraction) {
        if (fReal.denominator().isOne()) {
            newRe = fReal.numerator();
            evaled = true;
        }
        if (fReal.numerator().isZero()) {
            newRe = F.C0;
            evaled = true;
        }
    }
    if (fImaginary instanceof IFraction && fImaginary.denominator().isOne()) {
        newIm = fImaginary.numerator();
        evaled = true;
    }
    return evaled ? valueOf(newRe, newIm) : this;
}