[GiNaC-devel] [PATCH] [BUGFIX] heur_gcd: handle rational polynomials, so gcd() is computed correctly.
Alexei Sheplyakov
varg at theor.jinr.ru
Thu Apr 24 15:49:53 CEST 2008
Previously heur_gcd() worked only with integer polynomials, and did not check
if the inputs are indeed integer polynomials. That lead to an endless loop or
a miscomputed gcd.
Improve heur_gcd() so it can handle rational polynomials, and add a test case.
---
check/Makefile.am | 4 ++
check/heur_gcd_bug.cpp | 39 +++++++++++++++++++
ginac/normal.cpp | 96 +++++++++++++++++++++++++++++++++++++++--------
3 files changed, 122 insertions(+), 17 deletions(-)
create mode 100644 check/heur_gcd_bug.cpp
diff --git a/check/Makefile.am b/check/Makefile.am
index 3c9182d..8d2e451 100644
--- a/check/Makefile.am
+++ b/check/Makefile.am
@@ -6,6 +6,7 @@ CHECKS = check_numeric \
check_lsolve
EXAMS = exam_paranoia \
+ exam_heur_gcd \
exam_numeric \
exam_powerlaws \
exam_inifcns \
@@ -67,6 +68,9 @@ check_lsolve_LDADD = ../ginac/libginac.la
exam_paranoia_SOURCES = exam_paranoia.cpp
exam_paranoia_LDADD = ../ginac/libginac.la
+exam_heur_gcd_SOURCES = heur_gcd_bug.cpp
+exam_heur_gcd_LDADD = ../ginac/libginac.la
+
exam_numeric_SOURCES = exam_numeric.cpp
exam_numeric_LDADD = ../ginac/libginac.la
diff --git a/check/heur_gcd_bug.cpp b/check/heur_gcd_bug.cpp
new file mode 100644
index 0000000..6fa8060
--- /dev/null
+++ b/check/heur_gcd_bug.cpp
@@ -0,0 +1,39 @@
+/**
+ * @file heur_gcd_oops.cpp Check for a bug in heur_gcd().
+ *
+ * heur_gcd() did not check if the arguments are integer polynomials
+ * (and did not convert them to integer polynomials), which lead to
+ * endless loop or (even worse) wrong result.
+ */
+#include <iostream>
+#include "ginac.h"
+using namespace GiNaC;
+using namespace std;
+
+int main(int argc, char** argv)
+{
+ cout << "checking if heur_gcd() can cope with rational polynomials. ";
+ const symbol x("x");
+ const ex _ex1(1);
+ ex a1 = x + numeric(5, 4);
+ ex a2 = x + numeric(5, 2);
+ ex b = pow(x, 2) + numeric(15, 4)*x + numeric(25, 8);
+ // note: both a1 and a2 divide b
+
+ // a2 divides b, so cofactor of a2 should be a (rational) number
+ ex ca2, cb2;
+ ex g2 = gcd(a2, b, &ca2, &cb2);
+ if (!is_a<numeric>(ca2)) {
+ cerr << "gcd(" << a2 << ", " << b << ") was miscomputed" << endl;
+ return 1;
+ }
+ ex ca1, cb1;
+ // a1 divides b, so cofactor of a1 should be a (rational) number
+ ex g1 = gcd(a1, b, &ca1, &cb1);
+ if (!is_a<numeric>(ca1)) {
+ cerr << "gcd(" << a1 << ", " << b << ") was miscomputed" << endl;
+ return 1;
+ }
+ return 0;
+}
+
diff --git a/ginac/normal.cpp b/ginac/normal.cpp
index 18d606b..e756a67 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);
@@ -1338,14 +1345,73 @@ 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;
}
@@ -1665,12 +1731,8 @@ 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)) {
+ bool found = heur_gcd(g, aex, bex, ca, cb, var);
+ if (!found) {
#if STATISTICS
heur_gcd_failed++;
#endif
--
1.5.4.2
Best regards,
Alexei
--
All science is either physics or stamp collecting.
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