X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnormal.cpp;h=ed036c69e2ecd9397df04b30fa8c756f4bbb7b06;hp=0cb91001a01ff427bdb353590a3a29210c99c597;hb=bb0f99d6298fccb8cf1421fa0c7463c647f543a7;hpb=7d7131d3af3de5425b7fe80b1f587740294371bc

diff --git a/ginac/normal.cpp b/ginac/normal.cpp
index 0cb91001..ed036c69 100644
--- a/ginac/normal.cpp
+++ b/ginac/normal.cpp
@@ -6,7 +6,7 @@
  *  computation, square-free factorization and rational function normalization. */
 
 /*
- *  GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2011 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
@@ -23,9 +23,6 @@
  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <algorithm>
-#include <map>
-
 #include "normal.h"
 #include "basic.h"
 #include "ex.h"
@@ -44,6 +41,10 @@
 #include "pseries.h"
 #include "symbol.h"
 #include "utils.h"
+#include "polynomial/chinrem_gcd.h"
+
+#include <algorithm>
+#include <map>
 
 namespace GiNaC {
 
@@ -672,12 +673,13 @@ bool divide(const ex &a, const ex &b, ex &q, bool check_args)
 			q = rem_i*power(ab, a_exp - 1);
 			return true;
 		}
-		for (int i=2; i < a_exp; i++) {
-			if (divide(power(ab, i), b, rem_i, false)) {
-				q = rem_i*power(ab, a_exp - i);
-				return true;
-			}
-		} // ... so we *really* need to expand expression.
+// code below is commented-out because it leads to a significant slowdown
+//		for (int i=2; i < a_exp; i++) {
+//			if (divide(power(ab, i), b, rem_i, false)) {
+//				q = rem_i*power(ab, a_exp - i);
+//				return true;
+//			}
+//		} // ... so we *really* need to expand expression.
 	}
 	
 	// Polynomial long division (recursive)
@@ -1417,11 +1419,11 @@ static bool heur_gcd(ex& res, const ex& a, const ex& b, ex *ca, ex *cb,
 
 // gcd helper to handle partially factored polynomials (to avoid expanding
 // large expressions). At least one of the arguments should be a power.
-static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb, bool check_args);
+static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb);
 
 // gcd helper to handle partially factored polynomials (to avoid expanding
 // large expressions). At least one of the arguments should be a product.
-static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb, bool check_args);
+static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb);
 
 /** Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X)
  *  and b(X) in Z[X]. Optionally also compute the cofactors of a and b,
@@ -1465,12 +1467,14 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned optio
 	}
 
 	// Partially factored cases (to avoid expanding large expressions)
-	if (is_exactly_a<mul>(a) || is_exactly_a<mul>(b))
-		return gcd_pf_mul(a, b, ca, cb, check_args);
+	if (!(options & gcd_options::no_part_factored)) {
+		if (is_exactly_a<mul>(a) || is_exactly_a<mul>(b))
+			return gcd_pf_mul(a, b, ca, cb);
 #if FAST_COMPARE
-	if (is_exactly_a<power>(a) || is_exactly_a<power>(b))
-		return gcd_pf_pow(a, b, ca, cb, check_args);
+		if (is_exactly_a<power>(a) || is_exactly_a<power>(b))
+			return gcd_pf_pow(a, b, ca, cb);
 #endif
+	}
 
 	// Some trivial cases
 	ex aex = a.expand(), bex = b.expand();
@@ -1601,183 +1605,161 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned optio
 
 	// Try heuristic algorithm first, fall back to PRS if that failed
 	ex g;
-	bool found = heur_gcd(g, aex, bex, ca, cb, var);
-	if (!found) {
+	if (!(options & gcd_options::no_heur_gcd)) {
+		bool found = heur_gcd(g, aex, bex, ca, cb, var);
+		if (found) {
+			// heur_gcd have already computed cofactors...
+			if (g.is_equal(_ex1)) {
+				// ... but we want to keep them factored if possible.
+				if (ca)
+					*ca = a;
+				if (cb)
+					*cb = b;
+			}
+			return g;
+		}
 #if STATISTICS
-		heur_gcd_failed++;
+		else {
+			heur_gcd_failed++;
+		}
 #endif
+	}
+	if (options & gcd_options::use_sr_gcd) {
 		g = sr_gcd(aex, bex, var);
-		if (g.is_equal(_ex1)) {
-			// Keep cofactors factored if possible
-			if (ca)
-				*ca = a;
-			if (cb)
-				*cb = b;
-		} else {
-			if (ca)
-				divide(aex, g, *ca, false);
-			if (cb)
-				divide(bex, g, *cb, false);
-		}
 	} else {
-		if (g.is_equal(_ex1)) {
-			// Keep cofactors factored if possible
-			if (ca)
-				*ca = a;
-			if (cb)
-				*cb = b;
-		}
+		exvector vars;
+		for (std::size_t n = sym_stats.size(); n-- != 0; )
+			vars.push_back(sym_stats[n].sym);
+		g = chinrem_gcd(aex, bex, vars);
 	}
 
+	if (g.is_equal(_ex1)) {
+		// Keep cofactors factored if possible
+		if (ca)
+			*ca = a;
+		if (cb)
+			*cb = b;
+	} else {
+		if (ca)
+			divide(aex, g, *ca, false);
+		if (cb)
+			divide(bex, g, *cb, false);
+	}
 	return g;
 }
 
-static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb, bool check_args)
-{
-	if (is_exactly_a<power>(a)) {
-		ex p = a.op(0);
-		const ex& exp_a = a.op(1);
-		if (is_exactly_a<power>(b)) {
-			ex pb = b.op(0);
-			const ex& exp_b = b.op(1);
-			if (p.is_equal(pb)) {
-				// a = p^n, b = p^m, gcd = p^min(n, m)
-				if (exp_a < exp_b) {
-					if (ca)
-						*ca = _ex1;
-					if (cb)
-						*cb = power(p, exp_b - exp_a);
-					return power(p, exp_a);
-				} else {
-					if (ca)
-						*ca = power(p, exp_a - exp_b);
-					if (cb)
-						*cb = _ex1;
-					return power(p, exp_b);
-				}
-			} else {
-				ex p_co, pb_co;
-				ex p_gcd = gcd(p, pb, &p_co, &pb_co, check_args);
-				if (p_gcd.is_equal(_ex1)) {
-					// a(x) = p(x)^n, b(x) = p_b(x)^m, gcd (p, p_b) = 1 ==>
-					// gcd(a,b) = 1
-					if (ca)
-						*ca = a;
-					if (cb)
-						*cb = b;
-					return _ex1;
-					// XXX: do I need to check for p_gcd = -1?
-				} else {
-					// there are common factors:
-					// a(x) = g(x)^n A(x)^n, b(x) = g(x)^m B(x)^m ==>
-					// gcd(a, b) = g(x)^n gcd(A(x)^n, g(x)^(n-m) B(x)^m
-					if (exp_a < exp_b) {
-						return power(p_gcd, exp_a)*
-							gcd(power(p_co, exp_a), power(p_gcd, exp_b-exp_a)*power(pb_co, exp_b), ca, cb, false);
-					} else {
-						return power(p_gcd, exp_b)*
-							gcd(power(p_gcd, exp_a - exp_b)*power(p_co, exp_a), power(pb_co, exp_b), ca, cb, false);
-					}
-				} // p_gcd.is_equal(_ex1)
-			} // p.is_equal(pb)
-
-		} else {
-			if (p.is_equal(b)) {
-				// a = p^n, b = p, gcd = p
-				if (ca)
-					*ca = power(p, a.op(1) - 1);
-				if (cb)
-					*cb = _ex1;
-				return p;
-			} 
-
-			ex p_co, bpart_co;
-			ex p_gcd = gcd(p, b, &p_co, &bpart_co, false);
-
-			if (p_gcd.is_equal(_ex1)) {
-				// a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
-				if (ca)
-					*ca = a;
-				if (cb)
-					*cb = b;
-				return _ex1;
-			} else {
-				// a(x) = g(x)^n A(x)^n, b(x) = g(x) B(x) ==> gcd(a, b) = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
-				return p_gcd*gcd(power(p_gcd, exp_a-1)*power(p_co, exp_a), bpart_co, ca, cb, false);
-			}
-		} // is_exactly_a<power>(b)
+// gcd helper to handle partially factored polynomials (to avoid expanding
+// large expressions). Both arguments should be powers.
+static ex gcd_pf_pow_pow(const ex& a, const ex& b, ex* ca, ex* cb)
+{
+	ex p = a.op(0);
+	const ex& exp_a = a.op(1);
+	ex pb = b.op(0);
+	const ex& exp_b = b.op(1);
 
-	} else if (is_exactly_a<power>(b)) {
-		ex p = b.op(0);
-		if (p.is_equal(a)) {
-			// a = p, b = p^n, gcd = p
+	// a = p^n, b = p^m, gcd = p^min(n, m)
+	if (p.is_equal(pb)) {
+		if (exp_a < exp_b) {
 			if (ca)
 				*ca = _ex1;
 			if (cb)
-				*cb = power(p, b.op(1) - 1);
-			return p;
+				*cb = power(p, exp_b - exp_a);
+			return power(p, exp_a);
+		} else {
+			if (ca)
+				*ca = power(p, exp_a - exp_b);
+			if (cb)
+				*cb = _ex1;
+			return power(p, exp_b);
 		}
+	}
 
-		ex p_co, apart_co;
-		const ex& exp_b(b.op(1));
-		ex p_gcd = gcd(a, p, &apart_co, &p_co, false);
-		if (p_gcd.is_equal(_ex1)) {
-			// b=p(x)^n, gcd(a, p) = 1 ==> gcd(a, b) == 1
+	ex p_co, pb_co;
+	ex p_gcd = gcd(p, pb, &p_co, &pb_co, false);
+	// a(x) = p(x)^n, b(x) = p_b(x)^m, gcd (p, p_b) = 1 ==> gcd(a,b) = 1
+	if (p_gcd.is_equal(_ex1)) {
 			if (ca)
 				*ca = a;
 			if (cb)
 				*cb = b;
 			return _ex1;
-		} else {
-			// there are common factors:
-			// a(x) = g(x) A(x), b(x) = g(x)^n B(x)^n ==> gcd = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
+			// XXX: do I need to check for p_gcd = -1?
+	}
 
-			return p_gcd*gcd(apart_co, power(p_gcd, exp_b-1)*power(p_co, exp_b), ca, cb, false);
-		} // p_gcd.is_equal(_ex1)
+	// there are common factors:
+	// a(x) = g(x)^n A(x)^n, b(x) = g(x)^m B(x)^m ==>
+	// gcd(a, b) = g(x)^n gcd(A(x)^n, g(x)^(n-m) B(x)^m
+	if (exp_a < exp_b) {
+		ex pg =  gcd(power(p_co, exp_a), power(p_gcd, exp_b-exp_a)*power(pb_co, exp_b), ca, cb, false);
+		return power(p_gcd, exp_a)*pg;
+	} else {
+		ex pg = gcd(power(p_gcd, exp_a - exp_b)*power(p_co, exp_a), power(pb_co, exp_b), ca, cb, false);
+		return power(p_gcd, exp_b)*pg;
 	}
 }
 
-static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb, bool check_args)
+static ex gcd_pf_pow(const ex& a, const ex& b, ex* ca, ex* cb)
 {
-	if (is_exactly_a<mul>(a)) {
-		if (is_exactly_a<mul>(b) && b.nops() > a.nops())
-			goto factored_b;
-factored_a:
-		size_t num = a.nops();
-		exvector g; g.reserve(num);
-		exvector acc_ca; acc_ca.reserve(num);
-		ex part_b = b;
-		for (size_t i=0; i<num; i++) {
-			ex part_ca, part_cb;
-			g.push_back(gcd(a.op(i), part_b, &part_ca, &part_cb, check_args));
-			acc_ca.push_back(part_ca);
-			part_b = part_cb;
-		}
+	if (is_exactly_a<power>(a) && is_exactly_a<power>(b))
+		return gcd_pf_pow_pow(a, b, ca, cb);
+
+	if (is_exactly_a<power>(b) && (! is_exactly_a<power>(a)))
+		return gcd_pf_pow(b, a, cb, ca);
+
+	GINAC_ASSERT(is_exactly_a<power>(a));
+
+	ex p = a.op(0);
+	const ex& exp_a = a.op(1);
+	if (p.is_equal(b)) {
+		// a = p^n, b = p, gcd = p
 		if (ca)
-			*ca = (new mul(acc_ca))->setflag(status_flags::dynallocated);
+			*ca = power(p, a.op(1) - 1);
 		if (cb)
-			*cb = part_b;
-		return (new mul(g))->setflag(status_flags::dynallocated);
-	} else if (is_exactly_a<mul>(b)) {
-		if (is_exactly_a<mul>(a) && a.nops() > b.nops())
-			goto factored_a;
-factored_b:
-		size_t num = b.nops();
-		exvector g; g.reserve(num);
-		exvector acc_cb; acc_cb.reserve(num);
-		ex part_a = a;
-		for (size_t i=0; i<num; i++) {
-			ex part_ca, part_cb;
-			g.push_back(gcd(part_a, b.op(i), &part_ca, &part_cb, check_args));
-			acc_cb.push_back(part_cb);
-			part_a = part_ca;
-		}
+			*cb = _ex1;
+		return p;
+	} 
+
+	ex p_co, bpart_co;
+	ex p_gcd = gcd(p, b, &p_co, &bpart_co, false);
+
+	// a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
+	if (p_gcd.is_equal(_ex1)) {
 		if (ca)
-			*ca = part_a;
+			*ca = a;
 		if (cb)
-			*cb = (new mul(acc_cb))->setflag(status_flags::dynallocated);
-		return (new mul(g))->setflag(status_flags::dynallocated);
+			*cb = b;
+		return _ex1;
+	}
+	// a(x) = g(x)^n A(x)^n, b(x) = g(x) B(x) ==> gcd(a, b) = g(x) gcd(g(x)^(n-1) A(x)^n, B(x))
+	ex rg = gcd(power(p_gcd, exp_a-1)*power(p_co, exp_a), bpart_co, ca, cb, false);
+	return p_gcd*rg;
+}
+
+static ex gcd_pf_mul(const ex& a, const ex& b, ex* ca, ex* cb)
+{
+	if (is_exactly_a<mul>(a) && is_exactly_a<mul>(b)
+		                 && (b.nops() >  a.nops()))
+		return gcd_pf_mul(b, a, cb, ca);
+
+	if (is_exactly_a<mul>(b) && (!is_exactly_a<mul>(a)))
+		return gcd_pf_mul(b, a, cb, ca);
+
+	GINAC_ASSERT(is_exactly_a<mul>(a));
+	size_t num = a.nops();
+	exvector g; g.reserve(num);
+	exvector acc_ca; acc_ca.reserve(num);
+	ex part_b = b;
+	for (size_t i=0; i<num; i++) {
+		ex part_ca, part_cb;
+		g.push_back(gcd(a.op(i), part_b, &part_ca, &part_cb, false));
+		acc_ca.push_back(part_ca);
+		part_b = part_cb;
 	}
+	if (ca)
+		*ca = (new mul(acc_ca))->setflag(status_flags::dynallocated);
+	if (cb)
+		*cb = part_b;
+	return (new mul(g))->setflag(status_flags::dynallocated);
 }
 
 /** Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].