X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnormal.cpp;h=09773d37489693a4854964f129002abb186b2c5b;hp=18d606b1c9f77f571a1206dddc7de7876d3cfd0c;hb=c7d9b624cb4bd5658a36fbcac2f73dbdb99edd5f;hpb=7d870583a6bf21a2ffb7b6f051b702064623892e

diff --git a/ginac/normal.cpp b/ginac/normal.cpp
index 18d606b1..09773d37 100644
--- a/ginac/normal.cpp
+++ b/ginac/normal.cpp
@@ -1268,17 +1268,19 @@ class gcdheu_failed {};
  *  polynomials and an iterator to the first element of the sym_desc vector
  *  passed in. This function is used internally by gcd().
  *
- *  @param a  first multivariate polynomial (expanded)
- *  @param b  second multivariate polynomial (expanded)
+ *  @param a  first integer multivariate polynomial (expanded)
+ *  @param b  second integer multivariate polynomial (expanded)
  *  @param ca  cofactor of polynomial a (returned), NULL to suppress
  *             calculation of cofactor
  *  @param cb  cofactor of polynomial b (returned), NULL to suppress
  *             calculation of cofactor
  *  @param var iterator to first element of vector of sym_desc structs
- *  @return the GCD as a new expression
+ *  @param res the GCD (returned)
+ *  @return true if GCD was computed, false otherwise.
  *  @see gcd
  *  @exception gcdheu_failed() */
-static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var)
+static bool heur_gcd_z(ex& res, const ex &a, const ex &b, ex *ca, ex *cb,
+	               sym_desc_vec::const_iterator var)
 {
 #if STATISTICS
 	heur_gcd_called++;
@@ -1286,7 +1288,7 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const
 
 	// Algorithm only works for non-vanishing input polynomials
 	if (a.is_zero() || b.is_zero())
-		return (new fail())->setflag(status_flags::dynallocated);
+		return false;
 
 	// GCD of two numeric values -> CLN
 	if (is_exactly_a<numeric>(a) && is_exactly_a<numeric>(b)) {
@@ -1295,7 +1297,8 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const
 			*ca = ex_to<numeric>(a) / g;
 		if (cb)
 			*cb = ex_to<numeric>(b) / g;
-		return g;
+		res = g;
+		return true;
 	}
 
 	// The first symbol is our main variable
@@ -1325,9 +1328,13 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const
 
 		// Apply evaluation homomorphism and calculate GCD
 		ex cp, cq;
-		ex gamma = heur_gcd(p.subs(x == xi, subs_options::no_pattern), q.subs(x == xi, subs_options::no_pattern), &cp, &cq, var+1).expand();
-		if (!is_exactly_a<fail>(gamma)) {
-
+		ex gamma;
+		bool found = heur_gcd_z(gamma,
+			                p.subs(x == xi, subs_options::no_pattern),
+			                q.subs(x == xi, subs_options::no_pattern),
+				        &cp, &cq, var+1);
+		if (found) {
+			gamma = gamma.expand();
 			// Reconstruct polynomial from GCD of mapped polynomials
 			ex g = interpolate(gamma, xi, x, maxdeg);
 
@@ -1338,16 +1345,83 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const
 			ex dummy;
 			if (divide_in_z(p, g, ca ? *ca : dummy, var) && divide_in_z(q, g, cb ? *cb : dummy, var)) {
 				g *= gc;
-				return g;
+				res = g;
+				return true;
 			}
 		}
 
 		// Next evaluation point
 		xi = iquo(xi * isqrt(isqrt(xi)) * numeric(73794), numeric(27011));
 	}
-	return (new fail())->setflag(status_flags::dynallocated);
+	return false;
 }
 
+/** Compute GCD of multivariate polynomials using the heuristic GCD algorithm.
+ *  get_symbol_stats() must have been called previously with the input
+ *  polynomials and an iterator to the first element of the sym_desc vector
+ *  passed in. This function is used internally by gcd().
+ *
+ *  @param a  first rational multivariate polynomial (expanded)
+ *  @param b  second rational multivariate polynomial (expanded)
+ *  @param ca  cofactor of polynomial a (returned), NULL to suppress
+ *             calculation of cofactor
+ *  @param cb  cofactor of polynomial b (returned), NULL to suppress
+ *             calculation of cofactor
+ *  @param var iterator to first element of vector of sym_desc structs
+ *  @param res the GCD (returned)
+ *  @return true if GCD was computed, false otherwise.
+ *  @see heur_gcd_z
+ *  @see gcd
+ */
+static bool heur_gcd(ex& res, const ex& a, const ex& b, ex *ca, ex *cb,
+	             sym_desc_vec::const_iterator var)
+{
+	if (a.info(info_flags::integer_polynomial) && 
+	    b.info(info_flags::integer_polynomial)) {
+		try {
+			return heur_gcd_z(res, a, b, ca, cb, var);
+		} catch (gcdheu_failed) {
+			return false;
+		}
+	}
+
+	// convert polynomials to Z[X]
+	const numeric a_lcm = lcm_of_coefficients_denominators(a);
+	const numeric ab_lcm = lcmcoeff(b, a_lcm);
+
+	const ex ai = a*ab_lcm;
+	const ex bi = b*ab_lcm;
+	if (!ai.info(info_flags::integer_polynomial))
+		throw std::logic_error("heur_gcd: not an integer polynomial [1]");
+
+	if (!bi.info(info_flags::integer_polynomial))
+		throw std::logic_error("heur_gcd: not an integer polynomial [2]");
+
+	bool found = false;
+	try {
+		found = heur_gcd_z(res, ai, bi, ca, cb, var);
+	} catch (gcdheu_failed) {
+		return false;
+	}
+	
+	// GCD is not unique, it's defined up to a unit (i.e. invertible
+	// element). If the coefficient ring is a field, every its element is
+	// invertible, so one can multiply the polynomial GCD with any element
+	// of the coefficient field. We use this ambiguity to make cofactors
+	// integer polynomials.
+	if (found)
+		res /= ab_lcm;
+	return found;
+}
+
+
+// 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);
+
+// 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);
 
 /** 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,
@@ -1360,7 +1434,7 @@ static ex heur_gcd(const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const
  *  @param check_args  check whether a and b are polynomials with rational
  *         coefficients (defaults to "true")
  *  @return the GCD as a new expression */
-ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
+ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned options)
 {
 #if STATISTICS
 	gcd_called++;
@@ -1391,150 +1465,14 @@ ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args)
 	}
 
 	// Partially factored cases (to avoid expanding large expressions)
-	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 (ca)
-			*ca = (new mul(acc_ca))->setflag(status_flags::dynallocated);
-		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;
-		}
-		if (ca)
-			*ca = part_a;
-		if (cb)
-			*cb = (new mul(acc_cb))->setflag(status_flags::dynallocated);
-		return (new mul(g))->setflag(status_flags::dynallocated);
-	}
-
+	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
-	// Input polynomials of the form poly^n are sometimes also trivial
-	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)
-
-	} else if (is_exactly_a<power>(b)) {
-		ex p = b.op(0);
-		if (p.is_equal(a)) {
-			// a = p, b = p^n, gcd = p
-			if (ca)
-				*ca = _ex1;
-			if (cb)
-				*cb = power(p, b.op(1) - 1);
-			return p;
-		}
-
-		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
-			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))
-
-			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)
-	}
+		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();
@@ -1665,41 +1603,155 @@ factored_b:
 
 	// Try heuristic algorithm first, fall back to PRS if that failed
 	ex g;
-	try {
-		g = heur_gcd(aex, bex, ca, cb, var);
-	} catch (gcdheu_failed) {
-		g = fail();
-	}
-	if (is_exactly_a<fail>(g)) {
+	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
-		g = sr_gcd(aex, bex, var);
-		if (g.is_equal(_ex1)) {
-			// Keep cofactors factored if possible
+	}
+
+	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);
+	}
+	return g;
+}
+
+// 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);
+
+	// a = p^n, b = p^m, gcd = p^min(n, m)
+	if (p.is_equal(pb)) {
+		if (exp_a < exp_b) {
 			if (ca)
-				*ca = a;
+				*ca = _ex1;
 			if (cb)
-				*cb = b;
+				*cb = power(p, exp_b - exp_a);
+			return power(p, exp_a);
 		} else {
 			if (ca)
-				divide(aex, g, *ca, false);
+				*ca = power(p, exp_a - exp_b);
 			if (cb)
-				divide(bex, g, *cb, false);
+				*cb = _ex1;
+			return power(p, exp_b);
 		}
-	} else {
-		if (g.is_equal(_ex1)) {
-			// Keep cofactors factored if possible
+	}
+
+	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;
+			// XXX: do I need to check for p_gcd = -1?
 	}
 
-	return g;
+	// 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_pow(const ex& a, const ex& b, ex* ca, ex* 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 = 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);
+
+	// a(x) = p(x)^n, gcd(p, b) = 1 ==> gcd(a, b) = 1
+	if (p_gcd.is_equal(_ex1)) {
+		if (ca)
+			*ca = a;
+		if (cb)
+			*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].
  *