return 0;
}
+// Bug in sqrfree_yun (fixed 2016-02-02).
+static unsigned exam_paranoia23()
+{
+ unsigned result = 0;
+ symbol x("x");
+ ex e;
+
+ e = (x-1)*(x+1) - x*x + 1; // an unexpanded 0...
+ try {
+ ex f = sqrfree(e);
+ if (!f.is_zero()) {
+ clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+ ++result;
+ }
+ } catch (const exception &err) {
+ clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+ ++result;
+ }
+
+ e = pow(x-1,3) - expand(pow(x-1,3)); // ...still after differentiating...
+ try {
+ ex f = sqrfree(e);
+ if (!f.is_zero()) {
+ clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+ ++result;
+ }
+ } catch (const exception &err) {
+ clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+ ++result;
+ }
+
+ e = pow(x-1,4) - expand(pow(x-1,4)); // ...and after differentiating twice.
+ try {
+ ex f = sqrfree(e);
+ if (!f.is_zero()) {
+ clog << "sqrfree(" << e << ") returns " << f << " instead of 0\n";
+ ++result;
+ }
+ } catch (const exception &err) {
+ clog << "sqrfree(" << e << ") throws " << err.what() << endl;
+ ++result;
+ }
+
+ return result;
+}
+
unsigned exam_paranoia()
{
unsigned result = 0;
result += is_polynomial_false_positive(); cout << '.' << flush;
result += exam_paranoia21(); cout << '.' << flush;
result += exam_paranoia22(); cout << '.' << flush;
+ result += exam_paranoia23(); cout << '.' << flush;
return result;
}
* Yun's algorithm. Used internally by sqrfree().
*
* @param a multivariate polynomial over Z[X], treated here as univariate
- * polynomial in x.
+ * polynomial in x (needs not be expanded).
* @param x variable to factor in
* @return vector of factors sorted in ascending degree */
static exvector sqrfree_yun(const ex &a, const symbol &x)
ex w = a;
ex z = w.diff(x);
ex g = gcd(w, z);
+ if (g.is_zero()) {
+ return res;
+ }
if (g.is_equal(_ex1)) {
res.push_back(a);
return res;
ex y;
do {
w = quo(w, g, x);
+ if (w.is_zero()) {
+ return res;
+ }
y = quo(z, g, x);
z = y - w.diff(x);
g = gcd(w, z);
/** Compute a square-free factorization of a multivariate polynomial in Q[X].
*
- * @param a multivariate polynomial over Q[X]
+ * @param a multivariate polynomial over Q[X] (needs not be expanded)
* @param l lst of variables to factor in, may be left empty for autodetection
* @return a square-free factorization of \p a.
*
*/
ex sqrfree(const ex &a, const lst &l)
{
- if (is_exactly_a<numeric>(a) || // algorithm does not trap a==0
- is_a<symbol>(a)) // shortcut
+ if (is_exactly_a<numeric>(a) ||
+ is_a<symbol>(a)) // shortcuts
return a;
// If no lst of variables to factorize in was specified we have to