Improve heur_gcd() so it can handle rational polynomials, and add a test case.

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.

[A.Sheplyakov]

diff --git a/check/Makefile.am b/check/Makefile.am
index 3c9182d0fb46868e0b024f9e5ad8bbcf7e040f5b..8d2e451e29768b04973ae3341fcb837ce2fdddcd 100644 (file)
--- a/check/Makefile.am
+++ b/check/Makefile.am
@@ -6,6 +6,7 @@ CHECKS = check_numeric \
         check_lsolve 
 
 EXAMS = exam_paranoia \
         check_lsolve 
 
 EXAMS = exam_paranoia \

+       exam_heur_gcd \

        exam_numeric \
        exam_powerlaws  \
        exam_inifcns \
        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_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
 
 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 (file)
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 18d606b1c9f77f571a1206dddc7de7876d3cfd0c..e756a677d429e6d564ff0211ddcb9556ab2a1f55 100644 (file)
--- 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().
  *
  *  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
  *  @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() */
  *  @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++;
 {
 #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())
 
        // 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)) {
 
        // 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;
                        *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
        }
 
        // 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;
 
                // 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);
 
                        // 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;
                        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));
        }
                        }
                }
 
                // 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 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
 #if STATISTICS
                heur_gcd_failed++;
 #endif