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[ginac.git] / ginac / normal.h

diff --git a/ginac/normal.h b/ginac/normal.h
index 879e0d4d452cfec697c630f58d7e47024d7187c1..eb579d6b4cb5aa3ebf181b02cd9f56e0269c0387 100644 (file)
--- a/ginac/normal.h
+++ b/ginac/normal.h
@@ -1,10 +1,12 @@
 /** @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. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 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
@@ -18,34 +20,89 @@
  *
  *  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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#ifndef NORMAL_H
-#define NORMAL_H
+#ifndef GINAC_NORMAL_H
+#define GINAC_NORMAL_H
+
+#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