package org.matheclipse.core.polynomials;
import static org.matheclipse.core.expression.F.ArcTan;
import static org.matheclipse.core.expression.F.C1;
import static org.matheclipse.core.expression.F.C1D2;
import static org.matheclipse.core.expression.F.C2;
import static org.matheclipse.core.expression.F.C4;
import static org.matheclipse.core.expression.F.CN1;
import static org.matheclipse.core.expression.F.CN1D2;
import static org.matheclipse.core.expression.F.Integrate;
import static org.matheclipse.core.expression.F.Log;
import static org.matheclipse.core.expression.F.Plus;
import static org.matheclipse.core.expression.F.Power;
import static org.matheclipse.core.expression.F.Times;
import org.matheclipse.core.convert.JASConvert;
import org.matheclipse.core.expression.F;
import org.matheclipse.core.interfaces.IAST;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.core.interfaces.IFraction;
import org.matheclipse.core.interfaces.IInteger;
import org.matheclipse.core.interfaces.ISymbol;
import edu.jas.arith.BigInteger;
import edu.jas.arith.BigRational;
import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.Monomial;
/**
* Generator to integrate a rational polynomial by partial fraction
*
*/
public class PartialFractionIntegrateGenerator implements IPartialFractionGenerator {
IAST result;
JASConvert jas;
ISymbol x;
public PartialFractionIntegrateGenerator(ISymbol x) {
this.result = F.Plus();
this.x = x;
}
public void setJAS(JASConvert jas) {
this.jas = jas;
}
@Override
public IAST getResult() {
return result;
}
@Override
public void addNonFractionalPart(GenPolynomial genPolynomial) {
IExpr temp = F.eval(jas.poly2Expr(genPolynomial, null));
if (temp.isAST()) {
((IAST) temp).addEvalFlags(IAST.IS_DECOMPOSED_PARTIAL_FRACTION);
}
result.add(F.Integrate(temp, x));
}
@Override
public void addSinglePartialFraction(GenPolynomial genPolynomial, GenPolynomial 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 genPolynomial2 = ((GenPolynomial) objects[2])
.multiply(edu.jas.arith.BigInteger.valueOf(gcd));
if (genPolynomial2.isONE()) {
GenPolynomial 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.add(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.add(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.add(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.add(F.Times(F.C2, temp, F.ArcTan(Times(ax2Plusb, temp))));
}
}
} else {
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()) {
// JavaForm[B*Log[p*x+q]/p]
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.add(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.add(F.eval(temp));
} else {
temp = F.eval(F.Times(jas.poly2Expr(genPolynomial), F.Power(jas.poly2Expr(Di_1), F.integer(j * (-1L)))));
if (!temp.equals(F.C0)) {
if (temp.isAST()) {
((IAST) temp).addEvalFlags(IAST.IS_DECOMPOSED_PARTIAL_FRACTION);
}
result.add(F.Integrate(temp, x));
}
}
}
}
/**
* Check if the polynomial has maximum degree 2 in 1 variable and return the
* coefficients.
*
* @param poly
* @return null if the polynomials degree > 2 and number of
* variables <> 1
*/
public static boolean isQuadratic(GenPolynomial poly, BigRational[] result) {
if (poly.degree() <= 2 && poly.numberOfVariables() == 1) {
result[0] = BigRational.ZERO;
result[1] = BigRational.ZERO;
result[2] = BigRational.ZERO;
for (Monomial monomial : poly) {
BigRational coeff = monomial.coefficient();
ExpVector exp = monomial.exponent();
for (int i = 0; i < exp.length(); i++) {
result[(int) exp.getVal(i)] = coeff;
}
}
return true;
}
return false;
}
/**
* Check if the polynomial has maximum degree 2 in 1 variable and return the
* coefficients.
*
* @param poly
* @return null if the polynomials degree > 2 and number of
* variables <> 1
*/
public static boolean isQuadratic(GenPolynomial poly, BigInteger[] result) {
if (poly.degree() <= 2 && poly.numberOfVariables() == 1) {
result[0] = BigInteger.ZERO;
result[1] = BigInteger.ZERO;
result[2] = BigInteger.ZERO;
for (Monomial monomial : poly) {
BigInteger coeff = monomial.coefficient();
ExpVector exp = monomial.exponent();
for (int i = 0; i < exp.length(); i++) {
result[(int) exp.getVal(i)] = coeff;
}
}
return true;
}
return false;
}
}
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