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

Example 21 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 StringBuilder buf, final IComplex c, final int precedence) {
    if (c.isImaginaryUnit()) {
        buf.append("i ");
        return;
    }
    if (c.isNegativeImaginaryUnit()) {
        if (precedence > plusPrec) {
            buf.append("\\left( ");
        }
        buf.append(" - i ");
        if (precedence > plusPrec) {
            buf.append("\\right) ");
        }
        return;
    }
    if (precedence > plusPrec) {
        buf.append("\\left( ");
    }
    IRational re = c.getRealPart();
    IRational im = c.getImaginaryPart();
    if (!re.isZero()) {
        convertInternal(buf, re, 0);
        if (im.compareInt(0) >= 0) {
            buf.append(" + ");
        } else {
            buf.append(" - ");
            im = im.negate();
        }
    }
    convertInternal(buf, im, 0);
    // InvisibleTimes
    buf.append("\\,");
    buf.append("i ");
    if (precedence > plusPrec) {
        buf.append("\\right) ");
    }
}

Example 22 with IRational

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

the class Algebra method fractionalPartsRational.

/**
 * Split the expression into numerator and denominator parts, by separating positive and negative
 * powers.
 *
 * @param arg
 * @return the numerator and denominator expression
 */
public static IExpr[] fractionalPartsRational(final IExpr arg) {
    if (arg.isFraction()) {
        IFraction fr = (IFraction) arg;
        IExpr[] parts = new IExpr[2];
        parts[0] = fr.numerator();
        parts[1] = fr.denominator();
        return parts;
    } else if (arg.isComplex()) {
        IRational re = ((IComplex) arg).getRealPart();
        IRational im = ((IComplex) arg).getImaginaryPart();
        if (re.isFraction() || im.isFraction()) {
            IExpr[] parts = new IExpr[2];
            parts[0] = re.numerator().times(im.denominator()).add(im.numerator().times(re.denominator()).times(F.CI));
            parts[1] = re.denominator().times(im.denominator());
            return parts;
        }
        return null;
    }
    return fractionalParts(arg, false);
}

Example 23 with IRational

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

the class Algebra method factorTermsPlus.

/**
 * Factor out a rational number which may be a factor in every sub-expression of <code>plus
 * </code>.
 *
 * @param plusAST
 * @param engine
 * @return {@link F#NIL} if the factor couldn't be found
 */
/* package private */
static IExpr factorTermsPlus(IAST plusAST, EvalEngine engine) {
    IRational gcd1 = null;
    if (plusAST.arg1().isRational()) {
        gcd1 = (IRational) plusAST.arg1();
    } else if (plusAST.arg1().isTimes() && plusAST.arg1().first().isRational()) {
        gcd1 = (IRational) plusAST.arg1().first();
    }
    if (gcd1 == null) {
        return F.NIL;
    }
    for (int i = 2; i < plusAST.size(); i++) {
        IRational gcd2 = null;
        if (plusAST.get(i).isRational()) {
            gcd2 = (IRational) plusAST.get(i);
        } else if (plusAST.get(i).isTimes() && plusAST.get(i).first().isRational()) {
            gcd2 = (IRational) plusAST.get(i).first();
        }
        if (gcd2 == null) {
            return F.NIL;
        }
        final IExpr gcd12 = engine.evaluate(F.GCD(gcd1, gcd2));
        if (gcd12.isRational() && !gcd12.isOne()) {
            gcd1 = (IRational) gcd12;
        } else {
            return F.NIL;
        }
    }
    if (gcd1.isMinusOne()) {
        return F.NIL;
    }
    return engine.evaluate(F.Times(gcd1, F.Expand(F.Times(gcd1.inverse(), plusAST))));
}

Example 24 with IRational

use of org.matheclipse.core.interfaces.IRational 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;
    if (symbol != null && (!symbol.isVariable() || symbol.isProtected())) {
        // Cannot assign to raw object `1`.
        throw new ArgumentTypeException(IOFunctions.getMessage("setraw", F.list(symbol), EvalEngine.get()));
    }
    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.isQuantity()) {
                    return new QuantityIterator(symbol, (IQuantity) upperLimit);
                } else if (upperLimit.isReal()) {
                    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 (upperLimit.isList()) {
                    if (variable != null) {
                        if (!variable.isVariable() || variable.isProtected()) {
                            // Cannot assign to raw object `1`.
                            throw new ArgumentTypeException(IOFunctions.getMessage("setraw", F.list(variable), EvalEngine.get()));
                        }
                    } else {
                        // Raw object `1` cannot be used as an iterator.
                        throw new ArgumentTypeException(IOFunctions.getMessage("itraw", F.list(list.arg1()), EvalEngine.get()));
                    }
                    return new ExprListIterator(variable, (IAST) upperLimit, evalEngine);
                }
                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.isQuantity() && upperLimit.isQuantity()) {
                    return new QuantityIterator(symbol, (IQuantity) lowerLimit, (IQuantity) upperLimit);
                } else if (lowerLimit.isReal() && upperLimit.isReal()) {
                    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.isQuantity() && upperLimit.isQuantity() && step.isQuantity()) {
                    return new QuantityIterator(symbol, (IQuantity) lowerLimit, (IQuantity) upperLimit, (IQuantity) step);
                } else if (lowerLimit.isReal() && upperLimit.isReal() && step.isReal()) {
                    return new ISignedNumberIterator(variable, (ISignedNumber) lowerLimit, (ISignedNumber) upperLimit, (ISignedNumber) step);
                }
                break;
            default:
                lowerLimit = null;
                upperLimit = null;
                step = null;
                variable = null;
        }
        return new ExprIterator(variable, lowerLimit, upperLimit, step, fNumericMode, evalEngine);
    } catch (LimitException le) {
        throw le;
    } catch (ArgumentTypeException atex) {
        throw atex;
    } catch (RuntimeException rex) {
        throw new ClassCastException();
    } finally {
        evalEngine.setNumericMode(localNumericMode);
    }
}

Example 25 with IRational

use of org.matheclipse.core.interfaces.IRational 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 position the position of the list in the argument sequence, for printing an error if
 *        list cannot be converted into an iterator form
 * @param engine the evaluation engine
 * @return the iterator
 */
public static IIterator<IExpr> create(final IAST list, int position, 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();
        int iterationLimit = evalEngine.getIterationLimit();
        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();
                        if (iUpperLimit > iterationLimit && iterationLimit > 0) {
                            IterationLimitExceeded.throwIt(iUpperLimit, upperLimit);
                        }
                        return new IntIterator(variable, 1, iUpperLimit, 1);
                    } catch (ArithmeticException ae) {
                    // 
                    }
                } else if (upperLimit.isRational()) {
                    try {
                        int iUpperLimit = ((IRational) upperLimit).floor().toInt();
                        if (iUpperLimit > iterationLimit && iterationLimit > 0) {
                            IterationLimitExceeded.throwIt(iUpperLimit, upperLimit);
                        }
                        return new RationalIterator(variable, F.C1, (IRational) upperLimit, F.C1);
                    } catch (ArithmeticException ae) {
                    // 
                    }
                } else if (upperLimit.isQuantity()) {
                    return new QuantityIterator(variable, (IQuantity) upperLimit);
                } else if (upperLimit.isReal()) {
                    return new ISignedNumberIterator(variable, F.C1, (ISignedNumber) upperLimit, F.C1);
                }
                if (!list.arg1().isVariable()) {
                    throw new ArgumentTypeException(IOFunctions.getMessage("vloc", F.list(list.arg1()), EvalEngine.get()));
                }
                break;
            case 3:
                lowerLimit = F.C1;
                upperLimit = evalEngine.evalWithoutNumericReset(list.arg2());
                step = F.C1;
                if (list.arg1() instanceof ISymbol) {
                    ISymbol sym = (ISymbol) list.arg1();
                    if (!sym.isVariable() || sym.isProtected()) {
                        // Cannot assign to raw object `1`.
                        throw new ArgumentTypeException(IOFunctions.getMessage("setraw", F.list(sym), EvalEngine.get()));
                    }
                    variable = sym;
                } else {
                    // Raw object `1` cannot be used as an iterator.
                    throw new ArgumentTypeException(IOFunctions.getMessage("itraw", F.list(list.arg1()), EvalEngine.get()));
                }
                if (upperLimit.isList()) {
                    return new ExprListIterator(variable, (IAST) upperLimit, evalEngine);
                }
                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.isQuantity()) {
                    return new QuantityIterator(variable, (IQuantity) upperLimit);
                } else if (upperLimit.isReal()) {
                    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()) {
                    ISymbol sym = (ISymbol) list.arg1();
                    if (!sym.isVariable() || sym.isProtected()) {
                        // Cannot assign to raw object `1`.
                        throw new ArgumentTypeException(IOFunctions.getMessage("setraw", F.list(sym), EvalEngine.get()));
                    }
                    variable = sym;
                } else {
                    // Raw object `1` cannot be used as an iterator.
                    throw new ArgumentTypeException(IOFunctions.getMessage("itraw", F.list(list.arg1()), EvalEngine.get()));
                }
                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.isQuantity() && upperLimit.isQuantity()) {
                    return new QuantityIterator(variable, (IQuantity) lowerLimit, (IQuantity) upperLimit);
                } else if (lowerLimit.isReal() && upperLimit.isReal()) {
                    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) {
                    ISymbol sym = (ISymbol) list.arg1();
                    if (!sym.isVariable() || sym.isProtected()) {
                        // Cannot assign to raw object `1`.
                        throw new ArgumentTypeException(IOFunctions.getMessage("setraw", F.list(sym), EvalEngine.get()));
                    }
                    variable = sym;
                } else {
                    // Raw object `1` cannot be used as an iterator.
                    throw new ArgumentTypeException(IOFunctions.getMessage("itraw", F.list(list.arg1()), EvalEngine.get()));
                }
                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.isQuantity() && upperLimit.isQuantity() && step.isQuantity()) {
                    return new QuantityIterator(variable, (IQuantity) lowerLimit, (IQuantity) upperLimit, (IQuantity) step);
                } else if (lowerLimit.isReal() && upperLimit.isReal() && step.isReal()) {
                    return new ISignedNumberIterator(variable, (ISignedNumber) lowerLimit, (ISignedNumber) upperLimit, (ISignedNumber) step);
                }
                break;
            default:
                // Argument `1` at position `2` does not have the correct form for an iterator.
                String str = IOFunctions.getMessage("itform", F.list(list, F.ZZ(position)), EvalEngine.get());
                throw new ArgumentTypeException(str);
        }
        return new ExprIterator(variable, lowerLimit, upperLimit, step, fNumericMode, evalEngine);
    } catch (LimitException le) {
        throw le;
    } catch (ArgumentTypeException atex) {
        throw atex;
    } catch (RuntimeException rex) {
        // Argument `1` at position `2` does not have the correct form for an iterator.
        String str = IOFunctions.getMessage("itform", F.list(list, F.ZZ(position)), EvalEngine.get());
        throw new ArgumentTypeException(str);
    } finally {
        evalEngine.setNumericMode(localNumericMode);
    }
}