ring_elem SchurRing2::from_partition(M2_arrayint part) const
{
ring_elem result;
schur_poly *f = new schur_poly;
f->coeffs.push_back(coefficientRing->one());
int len = last_nonzero(part) + 1;
f->monoms.push_back(len + 1);
for (int i=0; i<len; i++)
f->monoms.push_back(part->array[i]);
result.schur_poly_val = f;
return result;
}
// Check for identically zero polynomials using randomized polynomial identity testing
template<class R,class PerturbedT> static void
assert_last_nonzero(void(*const polynomial)(R,RawArray<const Vector<Exact<1>,PerturbedT::m>>),
R result, RawArray<const PerturbedT> X, const char* message) {
typedef Vector<Exact<1>,PerturbedT::m> EV;
const int n = X.size();
const auto Z = GEODE_RAW_ALLOCA(n,EV);
for (const int k : range(20)) {
for (int i=0;i<n;i++)
Z[i] = EV(perturbation<PerturbedT::m>(k<<10,X[i].seed()));
polynomial(result,Z);
if (last_nonzero(result)) // Even a single nonzero means we're all good
return;
}
// If we reach this point, the chance of a nonzero nonmalicious polynomial is something like (1e-5)^20 = 1e-100. Thus, we can safely assume that for the lifetime
// of this code, we will never treat a nonzero polynomial as zero. If this comes up, we can easily bump the threshold a bit further.
throw AssertionError(format("%s (there is likely a bug in the calling code), X = %s",message,str(X)));
}