X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fpolynomial%2Fremainder.cpp;fp=ginac%2Fpolynomial%2Fremainder.cpp;h=3f29e82569010863a7a8b28cf1f1352767fd668c;hp=0000000000000000000000000000000000000000;hb=faf8c206bdcd01eee758103d56b83a634f787e7a;hpb=ac8c33efafa1c9f62db040db0d974f47229960b8

diff --git a/ginac/polynomial/remainder.cpp b/ginac/polynomial/remainder.cpp
new file mode 100644
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+++ b/ginac/polynomial/remainder.cpp
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+/** @file remainder.h
+ *
+ *  Functions calculating remainders. */
+
+/*
+ *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ *
+ *  This program is free software; you can redistribute it and/or modify
+ *  it under the terms of the GNU General Public License as published by
+ *  the Free Software Foundation; either version 2 of the License, or
+ *  (at your option) any later version.
+ *
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU General Public License for more details.
+ *
+ *  You should have received a copy of the GNU General Public License
+ *  along with this program; if not, write to the Free Software
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+ */
+
+#include "remainder.h"
+#include "ring_traits.h"
+#include "upoly_io.h"
+#include "debug.h"
+
+namespace GiNaC {
+
+/**
+ * @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.
+ */
+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();
+}
+
+} // namespace GiNaC