/** @file normal.h
*
- * Functions for polynomial quotient and remainder, GCD and LCM computation
- * and square-free factorization. */
+ * This file defines several functions that work on univariate and
+ * multivariate polynomials and rational functions.
+ * These functions include polynomial quotient and remainder, GCD and LCM
+ * computation, square-free factorization and rational function normalization. */
-#ifndef NORMAL_H
-#define NORMAL_H
+/*
+ * GiNaC Copyright (C) 1999-2020 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 "ex.h"
+#ifndef GINAC_NORMAL_H
+#define GINAC_NORMAL_H
-class symbol;
+#include "lst.h"
+
+namespace GiNaC {
+
+/**
+ * Flags to control the behavior of gcd() and friends
+ */
+struct gcd_options
+{
+ enum {
+ /**
+ * Usually GiNaC tries heuristic GCD first, because typically
+ * it's much faster than anything else. Even if heuristic
+ * algorithm fails, the overhead is negligible w.r.t. cost
+ * of computing the GCD by some other method. However, some
+ * people dislike it, so here's a flag which tells GiNaC
+ * to NOT use the heuristic algorithm.
+ */
+ no_heur_gcd = 2,
+ /**
+ * GiNaC tries to avoid expanding expressions when computing
+ * GCDs. This is a good idea, but some people dislike it.
+ * Hence the flag to disable special handling of partially
+ * factored polynomials. DON'T SET THIS unless you *really*
+ * know what are you doing!
+ */
+ no_part_factored = 4,
+ /**
+ * By default GiNaC uses modular GCD algorithm. Typically
+ * it's much faster than PRS (pseudo remainder sequence)
+ * algorithm. This flag forces GiNaC to use PRS algorithm
+ */
+ use_sr_gcd = 8
+
+ };
+};
+class ex;
+class symbol;
// Quotient q(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
-extern ex quo(const ex &a, const ex &b, const symbol &x, bool check_args = true);
+extern ex quo(const ex &a, const ex &b, const ex &x, bool check_args = true);
// Remainder r(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
-extern ex rem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
+extern ex rem(const ex &a, const ex &b, const ex &x, bool check_args = true);
+
+// Decompose rational function a(x)=N(x)/D(x) into Q(x)+R(x)/D(x) with degree(R, x) < degree(D, x)
+extern ex decomp_rational(const ex &a, const ex &x);
-// Pseudo-remainder of polynomials a(x) and b(x) in Z[x]
-extern ex prem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
+// Pseudo-remainder of polynomials a(x) and b(x) in Q[x]
+extern ex prem(const ex &a, const ex &b, const ex &x, bool check_args = true);
+
+// Pseudo-remainder of polynomials a(x) and b(x) in Q[x]
+extern ex sprem(const ex &a, const ex &b, const ex &x, bool check_args = true);
// Exact polynomial division of a(X) by b(X) in Q[X] (quotient returned in q), returns false when exact division fails
extern bool divide(const ex &a, const ex &b, ex &q, bool check_args = true);
// Polynomial GCD in Z[X], cofactors are returned in ca and cb, if desired
-extern ex gcd(const ex &a, const ex &b, ex *ca = NULL, ex *cb = NULL, bool check_args = true);
+extern ex gcd(const ex &a, const ex &b, ex *ca = nullptr, ex *cb = nullptr,
+ bool check_args = true, unsigned options = 0);
// Polynomial LCM in Z[X]
extern ex lcm(const ex &a, const ex &b, bool check_args = true);
// Square-free factorization of a polynomial a(x)
-extern ex sqrfree(const ex &a, const symbol &x);
+extern ex sqrfree(const ex &a, const lst &l = lst());
+
+// Square-free partial fraction decomposition of a rational function a(x)
+extern ex sqrfree_parfrac(const ex & a, const symbol & x);
+
+// Collect common factors in sums.
+extern ex collect_common_factors(const ex & e);
+
+// Resultant of two polynomials e1,e2 with respect to symbol s.
+extern ex resultant(const ex & e1, const ex & e2, const ex & s);
+
+} // namespace GiNaC
-#endif
+#endif // ndef GINAC_NORMAL_H