use of edu.jas.poly.GenPolynomial in project symja_android_library by axkr.
the class Algebra method partialFractionDecompositionRational.
/**
* Returns an AST with head <code>Plus</code>, which contains the partial fraction decomposition of the numerator
* and denominator parts.
*
* @param pf
* partial fraction generator
* @param parts
* @param variable
* a variable
* @return <code>F.NIL</code> if the partial fraction decomposition wasn't constructed
*/
public static IExpr partialFractionDecompositionRational(IPartialFractionGenerator pf, IExpr[] parts, ISymbol variable) {
try {
IAST variableList = F.List(variable);
IExpr exprNumerator = F.evalExpandAll(parts[0]);
IExpr exprDenominator = F.evalExpandAll(parts[1]);
ASTRange r = new ASTRange(variableList, 1);
List<IExpr> varList = r;
String[] varListStr = new String[1];
varListStr[0] = variableList.arg1().toString();
JASConvert<BigRational> jas = new JASConvert<BigRational>(varList, BigRational.ZERO);
GenPolynomial<BigRational> numerator = jas.expr2JAS(exprNumerator, false);
GenPolynomial<BigRational> denominator = jas.expr2JAS(exprDenominator, false);
// get factors
FactorAbstract<BigRational> factorAbstract = FactorFactory.getImplementation(BigRational.ZERO);
SortedMap<GenPolynomial<BigRational>, Long> sfactors = factorAbstract.baseFactors(denominator);
List<GenPolynomial<BigRational>> D = new ArrayList<GenPolynomial<BigRational>>(sfactors.keySet());
SquarefreeAbstract<BigRational> sqf = SquarefreeFactory.getImplementation(BigRational.ZERO);
List<List<GenPolynomial<BigRational>>> Ai = sqf.basePartialFraction(numerator, sfactors);
if (Ai.size() > 0) {
// IAST result = F.Plus();
pf.allocPlus(Ai.size() * 2);
pf.setJAS(jas);
if (!Ai.get(0).get(0).isZERO()) {
pf.addNonFractionalPart(Ai.get(0).get(0));
}
for (int i = 1; i < Ai.size(); i++) {
List<GenPolynomial<BigRational>> list = Ai.get(i);
int j = 0;
for (GenPolynomial<BigRational> genPolynomial : list) {
if (!genPolynomial.isZERO()) {
GenPolynomial<BigRational> Di_1 = D.get(i - 1);
pf.addSinglePartialFraction(genPolynomial, Di_1, j);
}
j++;
}
}
return pf.getResult();
}
} catch (JASConversionException e) {
if (Config.DEBUG) {
e.printStackTrace();
}
}
return F.NIL;
}
use of edu.jas.poly.GenPolynomial in project symja_android_library by axkr.
the class Algebra method factorComplex.
public static IAST factorComplex(GenPolynomial<BigRational> polyRat, JASConvert<BigRational> jas, List<IExpr> varList, ISymbol head, boolean noGCDLCM) {
TermOrder termOrder = TermOrderByName.Lexicographic;
// Object[] objects = jas.factorTerms(polyRat);
String[] vars = new String[varList.size()];
for (int i = 0; i < varList.size(); i++) {
vars[i] = varList.get(i).toString();
}
Object[] objects = JASConvert.rationalFromRationalCoefficientsFactor(new GenPolynomialRing<BigRational>(BigRational.ZERO, varList.size(), termOrder, vars), polyRat);
java.math.BigInteger gcd = (java.math.BigInteger) objects[0];
java.math.BigInteger lcm = (java.math.BigInteger) objects[1];
GenPolynomial<BigRational> poly = (GenPolynomial<BigRational>) objects[2];
ComplexRing<BigRational> cfac = new ComplexRing<BigRational>(BigRational.ZERO);
GenPolynomialRing<Complex<BigRational>> cpfac = new GenPolynomialRing<Complex<BigRational>>(cfac, 1, termOrder);
GenPolynomial<Complex<BigRational>> a = PolyUtil.complexFromAny(cpfac, poly);
FactorComplex<BigRational> factorAbstract = new FactorComplex<BigRational>(cfac);
SortedMap<GenPolynomial<Complex<BigRational>>, Long> map = factorAbstract.factors(a);
IAST result = F.ast(head);
if (!noGCDLCM) {
if (!gcd.equals(java.math.BigInteger.ONE) || !lcm.equals(java.math.BigInteger.ONE)) {
result.append(F.fraction(gcd, lcm));
}
}
GenPolynomial<Complex<BigRational>> temp;
for (SortedMap.Entry<GenPolynomial<Complex<BigRational>>, Long> entry : map.entrySet()) {
if (entry.getKey().isONE() && entry.getValue().equals(1L)) {
continue;
}
temp = entry.getKey();
result.append(F.Power(jas.complexPoly2Expr(entry.getKey()), F.integer(entry.getValue())));
}
return result;
}
use of edu.jas.poly.GenPolynomial 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));
}
}
}
}
use of edu.jas.poly.GenPolynomial in project symja_android_library by axkr.
the class Algebra method factorRational.
public static IAST factorRational(GenPolynomial<BigRational> polyRat, JASConvert<BigRational> jas, List<IExpr> varList, ISymbol head) {
Object[] objects = jas.factorTerms(polyRat);
GenPolynomial<edu.jas.arith.BigInteger> poly = (GenPolynomial<edu.jas.arith.BigInteger>) objects[2];
FactorAbstract<edu.jas.arith.BigInteger> factorAbstract = FactorFactory.getImplementation(edu.jas.arith.BigInteger.ONE);
SortedMap<GenPolynomial<edu.jas.arith.BigInteger>, Long> map;
map = factorAbstract.factors(poly);
IAST result = F.ast(head);
java.math.BigInteger gcd = (java.math.BigInteger) objects[0];
java.math.BigInteger lcm = (java.math.BigInteger) objects[1];
if (!gcd.equals(java.math.BigInteger.ONE) || !lcm.equals(java.math.BigInteger.ONE)) {
result.append(F.fraction(gcd, lcm));
}
for (SortedMap.Entry<GenPolynomial<edu.jas.arith.BigInteger>, Long> entry : map.entrySet()) {
if (entry.getKey().isONE() && entry.getValue().equals(1L)) {
continue;
}
if (entry.getValue() == 1L) {
result.append(jas.integerPoly2Expr(entry.getKey()));
} else {
result.append(F.Power(jas.integerPoly2Expr(entry.getKey()), F.integer(entry.getValue())));
}
}
return result;
}
use of edu.jas.poly.GenPolynomial in project symja_android_library by axkr.
the class Algebra method factorModulus.
public static IAST factorModulus(JASModInteger jas, ModLongRing modIntegerRing, GenPolynomial<ModLong> poly, boolean factorSquareFree) {
FactorAbstract<ModLong> factorAbstract = FactorFactory.getImplementation(modIntegerRing);
SortedMap<GenPolynomial<ModLong>, Long> map;
if (factorSquareFree) {
map = factorAbstract.squarefreeFactors(poly);
} else {
map = factorAbstract.factors(poly);
}
IAST result = F.Times();
for (SortedMap.Entry<GenPolynomial<ModLong>, Long> entry : map.entrySet()) {
GenPolynomial<ModLong> singleFactor = entry.getKey();
Long val = entry.getValue();
result.append(F.Power(jas.modLongPoly2Expr(singleFactor), F.integer(val)));
}
return result;
}
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