Examples with ExprMonomial org.matheclipse.core.polynomials.longexponent.ExprMonomial used on opensource projects

Example 1 with ExprMonomial

use of org.matheclipse.core.polynomials.longexponent.ExprMonomial in project symja_android_library by axkr.

the class RootsFunctions method nthComplexRoot.

/**
 * Solve polynomials of the form <code>a * x^n + b == 0</code>.
 *
 * @param n
 * @param polynomial
 * @return
 */
private static IASTAppendable nthComplexRoot(int n, ExprPolynomial polynomial) {
    IExpr coefficientN = C0;
    IExpr coefficient0 = C0;
    for (ExprMonomial monomial : polynomial) {
        IExpr coefficient = monomial.coefficient();
        long lExp = monomial.exponent().getVal(0);
        if (lExp == n) {
            coefficientN = coefficient;
        } else if (lExp == 0) {
            coefficient0 = coefficient;
        } else {
            return F.NIL;
        }
    }
    if (coefficientN.isZero() || coefficient0.isZero()) {
        return F.NIL;
    }
    EvalEngine engine = EvalEngine.get();
    IExpr a = engine.evaluate(F.Divide(F.Negate(coefficient0), coefficientN));
    if (a.isNumber()) {
        // z = r*(Cos(θ)+I*Sin(θ))
        IAST z = ((INumber) a).toPolarCoordinates();
        IExpr r = z.arg1();
        IExpr theta = z.arg2();
        IRational fraction = F.fraction(1, n);
        IExpr f1 = F.Power(r, fraction);
        IASTAppendable result = F.ListAlloc(n);
        for (int k = 0; k < n; k++) {
            IAST argCosSin = F.Times(fraction, F.Plus(theta, F.Times(F.ZZ(k + k), S.Pi)));
            IAST f2 = F.Plus(F.Cos(argCosSin), F.Times(F.CI, F.Sin(argCosSin)));
            result.append(F.Times(f1, f2));
        }
        return result;
    }
    return F.NIL;
}

Example 2 with ExprMonomial

use of org.matheclipse.core.polynomials.longexponent.ExprMonomial in project symja_android_library by axkr.

the class RootsFunctions method unitPolynomial.

/**
 * Solve polynomials of the form <code>a * x^varDegree + b == 0</code>
 *
 * @param varDegree
 * @param polynomial
 * @return
 */
private static IASTAppendable unitPolynomial(int varDegree, ExprPolynomial polynomial) {
    IExpr a = C0;
    IExpr b = C0;
    for (ExprMonomial monomial : polynomial) {
        IExpr coeff = monomial.coefficient();
        long lExp = monomial.exponent().getVal(0);
        if (lExp == varDegree) {
            a = coeff;
        } else if (lExp == 0) {
            b = coeff;
        } else {
            return F.NIL;
        }
    }
    if (a.isZero() || b.isZero()) {
        return F.NIL;
    }
    boolean isNegative = false;
    IExpr rhsNumerator = EvalEngine.get().evaluate(b.negate());
    // EvalEngine.get().evaluate(F.Divide(F.C1, a));
    IExpr rhsDenominator = a;
    if ((varDegree & 0x0001) == 0x0001) {
        // odd
        IExpr zNumerator;
        if (rhsNumerator.isTimes()) {
            IASTMutable temp = ((IAST) rhsNumerator).mapThread(F.Power(F.Slot1, F.fraction(1, varDegree)), 1);
            if (rhsNumerator.first().isNegative()) {
                isNegative = true;
                temp.set(1, rhsNumerator.first().negate());
            }
            zNumerator = EvalEngine.get().evaluate(temp);
        } else {
            if (rhsNumerator.isNegative()) {
                isNegative = true;
                rhsNumerator = rhsNumerator.negate();
            }
            zNumerator = EvalEngine.get().evaluate(F.Power(rhsNumerator, F.fraction(1, varDegree)));
        }
        IExpr zDenominator;
        if (rhsDenominator.isTimes()) {
            IASTMutable temp = ((IAST) rhsDenominator).mapThread(F.Power(F.Slot1, F.fraction(-1, varDegree)), 1);
            if (rhsDenominator.first().isNegative()) {
                isNegative = !isNegative;
                temp.set(1, rhsDenominator.first().negate());
            }
            zDenominator = EvalEngine.get().evaluate(temp);
        } else {
            if (rhsDenominator.isNegative()) {
                isNegative = !isNegative;
                rhsDenominator = rhsDenominator.negate();
            }
            zDenominator = EvalEngine.get().evaluate(F.Power(rhsDenominator, F.fraction(-1, varDegree)));
        }
        IASTAppendable result = F.ListAlloc(varDegree);
        for (int i = 0; i < varDegree; i++) {
            if (isNegative) {
                result.append(F.Times(F.Power(F.CN1, i + 1), F.Power(F.CN1, F.fraction(i, varDegree)), zNumerator, zDenominator));
            } else {
                result.append(F.Times(F.Power(F.CN1, i), F.Power(F.CN1, F.fraction(i, varDegree)), zNumerator, zDenominator));
            }
        }
        return result;
    } else {
        // even
        IExpr zNumerator;
        if (rhsNumerator.isTimes()) {
            IExpr temp = ((IAST) rhsNumerator).mapThread(F.Power(F.Slot1, F.fraction(1, varDegree)), 1);
            zNumerator = EvalEngine.get().evaluate(temp);
        } else {
            zNumerator = EvalEngine.get().evaluate(F.Power(rhsNumerator, F.fraction(1, varDegree)));
        }
        IExpr zDenominator;
        if (rhsDenominator.isTimes()) {
            IExpr temp = ((IAST) rhsDenominator).mapThread(F.Power(F.Slot1, F.fraction(-1, varDegree)), 1);
            zDenominator = EvalEngine.get().evaluate(temp);
        } else {
            zDenominator = EvalEngine.get().evaluate(F.Power(rhsDenominator, F.fraction(-1, varDegree)));
        }
        IASTAppendable result = F.ListAlloc(varDegree);
        long size = varDegree / 2;
        // isNegative?1:0;
        int k = 0;
        for (int i = 1; i <= size; i++) {
            result.append(F.Times(F.CN1, F.Power(F.CN1, F.fraction(k, varDegree)), zNumerator, zDenominator));
            result.append(F.Times(F.Power(F.CN1, F.fraction(k, varDegree)), zNumerator, zDenominator));
            k += 2;
        }
        return result;
    }
}

Example 3 with ExprMonomial

use of org.matheclipse.core.polynomials.longexponent.ExprMonomial in project symja_android_library by axkr.

the class RootsFunctions method rootsOfQuadraticPolynomial.

/**
 * Solve a polynomial with degree <= 2.
 *
 * @param polynomial the polynomial
 * @return <code>F.NIL</code> if no evaluation was possible.
 */
private static IASTAppendable rootsOfQuadraticPolynomial(ExprPolynomial polynomial) {
    long varDegree = polynomial.degree(0);
    if (polynomial.isConstant()) {
        return F.ListAlloc(1);
    }
    IExpr a;
    IExpr b;
    IExpr c;
    IExpr d;
    IExpr e;
    if (varDegree <= 2) {
        IEvalStepListener listener = EvalEngine.get().getStepListener();
        if (listener != null) {
            IASTAppendable temp = listener.rootsOfQuadraticPolynomial(polynomial);
            if (temp.isPresent()) {
                return temp;
            }
        }
        // solve quadratic equation:
        a = C0;
        b = C0;
        c = C0;
        d = C0;
        e = C0;
        for (ExprMonomial monomial : polynomial) {
            IExpr coeff = monomial.coefficient();
            long lExp = monomial.exponent().getVal(0);
            if (lExp == 4) {
                a = coeff;
            } else if (lExp == 3) {
                b = coeff;
            } else if (lExp == 2) {
                c = coeff;
            } else if (lExp == 1) {
                d = coeff;
            } else if (lExp == 0) {
                e = coeff;
            } else {
                throw new ArithmeticException("Roots::Unexpected exponent value: " + lExp);
            }
        }
        IASTAppendable result = QuarticSolver.quarticSolve(a, b, c, d, e);
        if (result.isPresent()) {
            result = (IASTAppendable) QuarticSolver.sortASTArguments(result);
            return result;
        }
    }
    return F.NIL;
}

Example 4 with ExprMonomial

use of org.matheclipse.core.polynomials.longexponent.ExprMonomial in project symja_android_library by axkr.

the class PolynomialExample method main.

public static void main(String[] args) {
    try {
        ExprEvaluator util = new ExprEvaluator();
        IExpr expr = util.eval("x^2+y+a*x+b*y+c");
        System.out.println(expr.toString());
        final IAST variables = F.List(F.symbol("x"), F.symbol("y"));
        ExprPolynomialRing ring = new ExprPolynomialRing(ExprRingFactory.CONST, variables, variables.argSize(), ExprTermOrderByName.Lexicographic, false);
        ExprPolynomial poly = ring.create(expr);
        System.out.println(poly.toString());
        // x degree
        System.out.println(poly.degree(0));
        // y degree
        System.out.println(poly.degree(1));
        // show internal structure:
        System.out.println(poly.coefficientRules());
        System.out.println();
        for (ExprMonomial monomial : poly) {
            System.out.println(monomial.toString());
        }
    } catch (SyntaxError e) {
        // catch Symja parser errors here
        System.out.println(e.getMessage());
    } catch (MathException me) {
        // catch Symja math errors here
        System.out.println(me.getMessage());
    } catch (Exception e) {
        e.printStackTrace();
    } catch (final StackOverflowError soe) {
        System.out.println(soe.getMessage());
    } catch (final OutOfMemoryError oome) {
        System.out.println(oome.getMessage());
    }
}

Example 5 with ExprMonomial

use of org.matheclipse.core.polynomials.longexponent.ExprMonomial in project symja_android_library by axkr.

the class ExprEvaluatorTest method testStringEval003.

public void testStringEval003() {
    try {
        ExprEvaluator util = new ExprEvaluator();
        IExpr expr = util.eval("x^2+y+a*x+b*y+c");
        assertEquals("c+a*x+x^2+y+b*y", expr.toString());
        final IAST variables = F.List(F.symbol("x"), F.symbol("y"));
        ExprPolynomialRing ring = new ExprPolynomialRing(ExprRingFactory.CONST, variables, variables.argSize(), ExprTermOrderByName.Lexicographic, false);
        ExprPolynomial poly = ring.create(expr);
        assertEquals("x^2 + a x + ( 1+b ) y + c ", poly.toString());
        // x degree
        assertEquals(2, poly.degree(0));
        // y degree
        assertEquals(1, poly.degree(1));
        // show internal structure:
        assertEquals("{{2,0}->1,{1,0}->a,{0,1}->1+b,{0,0}->c}", poly.coefficientRules().toString());
        System.out.println(poly.coefficientRules());
        for (ExprMonomial monomial : poly) {
            System.out.println(monomial.toString());
        }
    } catch (SyntaxError e) {
        // catch Symja parser errors here
        System.out.println(e.getMessage());
    } catch (MathException me) {
        // catch Symja math errors here
        System.out.println(me.getMessage());
    } catch (Exception e) {
        e.printStackTrace();
    } catch (final StackOverflowError soe) {
        System.out.println(soe.getMessage());
    } catch (final OutOfMemoryError oome) {
        System.out.println(oome.getMessage());
    }
}