/**
* Calculate the result array <code>
* [ poly1.divide(gcd(poly1, poly2)), poly2.divide(gcd(poly1, poly2)) ]</code> if the given
* expressions <code>poly1</code> and <code>poly2</code> are univariate polynomials with equal
* variable name.
*
* @param poly1 univariate polynomial
* @param poly2 univariate polynomial
* @return <code>null</code> if the expressions couldn't be converted to JAS polynomials
*/
public static IExpr[] cancelGCD(IExpr poly1, IExpr poly2) throws JASConversionException {
try {
ExprVariables eVar = new ExprVariables(poly1);
eVar.addVarList(poly2);
if (!eVar.isSize(1)) {
// gcd only possible for univariate polynomials
return null;
}
ASTRange r = new ASTRange(eVar.getVarList(), 1);
JASConvert<BigRational> jas = new JASConvert<BigRational>(r.toList(), BigRational.ZERO);
GenPolynomial<BigRational> p1 = jas.expr2JAS(poly1);
GenPolynomial<BigRational> p2 = jas.expr2JAS(poly2);
GenPolynomial<BigRational> gcd = p1.gcd(p2);
IExpr[] result = new IExpr[2];
if (gcd.isONE()) {
result[0] = jas.rationalPoly2Expr(p1);
result[1] = jas.rationalPoly2Expr(p2);
} else {
result[0] = jas.rationalPoly2Expr(p1.divide(gcd));
result[1] = jas.rationalPoly2Expr(p2.divide(gcd));
}
return result;
} catch (Exception e) {
if (Config.SHOW_STACKTRACE) {
e.printStackTrace();
}
}
return null;
}
/**
* GenPolynomial polynomial squarefree factorization.
*
* @param A GenPolynomial.
* @return [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i
* squarefree.
*/
@Override
public SortedMap<GenPolynomial<C>, Long> baseSquarefreeFactors(GenPolynomial<C> A) {
SortedMap<GenPolynomial<C>, Long> sfactors = new TreeMap<GenPolynomial<C>, Long>();
if (A == null || A.isZERO()) {
return sfactors;
}
GenPolynomialRing<C> pfac = A.ring;
if (A.isConstant()) {
C coeff = A.leadingBaseCoefficient();
// System.out.println("coeff = " + coeff + " @ " + coeff.factory());
SortedMap<C, Long> rfactors = squarefreeFactors(coeff);
// System.out.println("rfactors,const = " + rfactors);
if (rfactors != null && rfactors.size() > 0) {
for (Map.Entry<C, Long> me : rfactors.entrySet()) {
C c = me.getKey();
if (!c.isONE()) {
GenPolynomial<C> cr = pfac.getONE().multiply(c);
Long rk = me.getValue(); // rfactors.get(c);
sfactors.put(cr, rk);
}
}
} else {
sfactors.put(A, 1L);
}
return sfactors;
}
if (pfac.nvar > 1) {
throw new IllegalArgumentException(
this.getClass().getName() + " only for univariate polynomials");
}
C ldbcf = A.leadingBaseCoefficient();
if (!ldbcf.isONE()) {
A = A.divide(ldbcf);
SortedMap<C, Long> rfactors = squarefreeFactors(ldbcf);
// System.out.println("rfactors,ldbcf = " + rfactors);
if (rfactors != null && rfactors.size() > 0) {
for (Map.Entry<C, Long> me : rfactors.entrySet()) {
C c = me.getKey();
if (!c.isONE()) {
GenPolynomial<C> cr = pfac.getONE().multiply(c);
Long rk = me.getValue(); // rfactors.get(c);
sfactors.put(cr, rk);
}
}
} else {
GenPolynomial<C> f1 = pfac.getONE().multiply(ldbcf);
// System.out.println("gcda sqf f1 = " + f1);
sfactors.put(f1, 1L);
}
ldbcf = pfac.coFac.getONE();
}
GenPolynomial<C> T0 = A;
long e = 1L;
GenPolynomial<C> Tp;
GenPolynomial<C> T = null;
GenPolynomial<C> V = null;
long k = 0L;
long mp = 0L;
boolean init = true;
while (true) {
// System.out.println("T0 = " + T0);
if (init) {
if (T0.isConstant() || T0.isZERO()) {
break;
}
Tp = PolyUtil.<C>baseDeriviative(T0);
T = engine.baseGcd(T0, Tp);
T = T.monic();
V = PolyUtil.<C>basePseudoDivide(T0, T);
// System.out.println("iT0 = " + T0);
// System.out.println("iTp = " + Tp);
// System.out.println("iT = " + T);
// System.out.println("iV = " + V);
// System.out.println("const(iV) = " + V.isConstant());
k = 0L;
mp = 0L;
init = false;
}
if (V.isConstant()) {
mp = pfac.characteristic().longValue(); // assert != 0
// T0 = PolyUtil.<C> baseModRoot(T,mp);
T0 = baseRootCharacteristic(T);
logger.info("char root: T0 = " + T0 + ", T = " + T);
if (T0 == null) {
// break;
T0 = pfac.getZERO();
}
e = e * mp;
init = true;
continue;
}
k++;
if (mp != 0L && k % mp == 0L) {
T = PolyUtil.<C>basePseudoDivide(T, V);
System.out.println("k = " + k);
// System.out.println("T = " + T);
k++;
}
GenPolynomial<C> W = engine.baseGcd(T, V);
W = W.monic();
GenPolynomial<C> z = PolyUtil.<C>basePseudoDivide(V, W);
// System.out.println("W = " + W);
// System.out.println("z = " + z);
V = W;
T = PolyUtil.<C>basePseudoDivide(T, V);
// System.out.println("V = " + V);
// System.out.println("T = " + T);
if (z.degree(0) > 0) {
if (ldbcf.isONE() && !z.leadingBaseCoefficient().isONE()) {
z = z.monic();
logger.info("z,monic = " + z);
}
sfactors.put(z, (e * k));
}
}
// look, a stupid error:
// if ( !ldbcf.isONE() ) {
// GenPolynomial<C> f1 = sfactors.firstKey();
// long e1 = sfactors.remove(f1);
// System.out.println("gcda sqf c = " + c);
// f1 = f1.multiply(c);
// //System.out.println("gcda sqf f1e = " + f1);
// sfactors.put(f1,e1);
// }
logger.info("exit char root: T0 = " + T0 + ", T = " + T);
return sfactors;
}