-/**
- * @brief Polynomial remainder for univariate polynomials over fields
- *
- * Given two univariate polynomials \f$a, b \in F[x]\f$, where F is
- * a finite field (presumably Z/p) computes the remainder @a r, which is
- * defined as \f$a = b q + r\f$. Returns true if the remainder is zero
- * and false otherwise.
- */
-static bool
-remainder_in_field(umodpoly& r, const umodpoly& a, const umodpoly& b)
-{
- typedef cln::cl_MI field_t;
-
- if (degree(a) < degree(b)) {
- r = a;
- return false;
- }
- // The coefficient ring is a field, so any 0 degree polynomial
- // divides any other polynomial.
- if (degree(b) == 0) {
- r.clear();
- return true;
- }
-
- r = a;
- const field_t b_lcoeff = lcoeff(b);
- for (std::size_t k = a.size(); k-- >= b.size(); ) {
-
- // r -= r_k/b_n x^{k - n} b(x)
- if (zerop(r[k]))
- continue;
-
- field_t qk = div(r[k], b_lcoeff);
- bug_on(zerop(qk), "division in a field yield zero: "
- << r[k] << '/' << b_lcoeff);
-
- // Why C++ is so off-by-one prone?
- for (std::size_t j = k, i = b.size(); i-- != 0; --j) {
- if (zerop(b[i]))
- continue;
- r[j] = r[j] - qk*b[i];
- }
- bug_on(!zerop(r[k]), "polynomial division in field failed: " <<
- "r[" << k << "] = " << r[k] << ", " <<
- "r = " << r << ", b = " << b);
-
- }
-
- // Canonicalize the remainder: remove leading zeros. Give a hint
- // to canonicalize(): we know degree(remainder) < degree(b)
- // (because the coefficient ring is a field), so
- // c_{degree(b)} \ldots c_{degree(a)} are definitely zero.
- std::size_t from = degree(b) - 1;
- canonicalize(r, from);
- return r.empty();
-}