+// Bug in reposition_dummy_indices() could result in correct expression
+// turned into one with inconsistent indices. Fixed on Aug 29, 2006
+static unsigned exam_paranoia17()
+{
+ varidx mu1(symbol("mu1"), 4);
+ varidx mu2(symbol("mu2"), 4);
+ varidx mu3(symbol("mu3"), 4);
+ varidx mu4(symbol("mu4"), 4);
+ varidx mu5(symbol("mu5"), 4);
+ varidx mu6(symbol("mu6"), 4);
+
+ exvector ev2;
+ ev2.push_back(mu3.toggle_variance());
+ ev2.push_back(mu6);
+ ev2.push_back(mu5.toggle_variance());
+ ev2.push_back(mu6.toggle_variance());
+ ev2.push_back(mu5);
+ ev2.push_back(mu3);
+ // notice: all indices are contracted ...
+
+ ex test_cycl = indexed(symbol("A"), sy_cycl(), ev2);
+ test_cycl = test_cycl.simplify_indexed();
+ // ... so there should be zero free indices in the end.
+ return test_cycl.get_free_indices().size();
+}
+
+// Bug in add::eval() could result in numeric terms not being collected into
+// the overall coefficient. Fixed first on Sep 22, 2010 and again on Dec 17 2015
+static unsigned exam_paranoia18()
+{
+ unsigned result = 0;
+
+ ex sqrt2 = sqrt(ex(2));
+ ex e1 = 1 + 2*(sqrt2+1)*(sqrt2-1);
+ if (e1.real_part() != 3) {
+ clog << "real_part(1+2*(sqrt(2)+1)*(sqrt(2)-1)) failed to evaluate to 3\n";
+ ++result;
+ }
+
+ ex sqrt3 = sqrt(ex(3));
+ ex e2 = 2 + 2*(sqrt2+1)*(sqrt2-1) - 2*(sqrt3+1)*(sqrt3-1);
+ if (e2.real_part() != 0) {
+ clog << "real_part(2+2*(sqrt(2)+1)*(sqrt(2)-1)-3*(sqrt(3)+1)*(sqrt(3)-1)) failed to evaluate to 0\n";
+ ++result;
+ }
+
+ return result;
+}
+
+// Bug in mul::conjugate when factors are evaluated at branch cuts, reported as
+// Sage bug #10964.
+static unsigned exam_paranoia19()
+{
+ symbol a("a");
+ ex e = conjugate(a*sqrt(ex(-2))*sqrt(ex(-3)));
+ ex c = a*conjugate(sqrt(ex(-2)))*conjugate(sqrt(ex(-3)));
+ if (!subs(e-c, a==42).is_zero()) {
+ clog << "subs(a*conjugate(sqrt(-2))*conjugate(sqrt(-3))-conjugate(a*sqrt(-2)*sqrt(-3)),a==42) failed to evaluate to 0\n";
+ return 1;
+ }
+ return 0;
+}
+
+// Bugs in is_polynomial (fixed 2011-05-20 and 2014-07-26).
+static unsigned exam_paranoia20()
+{
+ unsigned result = 0;
+ symbol x("x"), y("y");
+ ex e1 = sqrt(x*x+1)*sqrt(x+1);
+ if (e1.is_polynomial(x)) {
+ clog << "sqrt(x*x+1)*sqrt(x+1) is wrongly reported to be a polynomial in x\n";
+ ++result;
+ }
+ ex e2 = sqrt(Pi)*x;
+ if (!e2.is_polynomial(x)) {
+ clog << "sqrt(Pi)*x is wrongly reported to be no polynomial in x\n";
+ ++result;
+ }
+ ex e3 = sqrt(x);
+ if (!e3.is_polynomial(y)) {
+ clog << "sqrt(x) is wrongly reported to be no polynomial in y\n";
+ ++result;
+ }
+ ex e4 = (1+y)/(2+x);
+ if (e4.is_polynomial(x)) {
+ clog << "(1+y)/(2+x) is wrongly reported to be a polynomial in x\n";
+ ++result;
+ }
+ return result;
+}
+
+static unsigned is_polynomial_false_positive()
+{
+ unsigned result = 0;
+ symbol x("x"), n("n");
+ exvector nonpoly_exprs;
+ nonpoly_exprs.push_back(1/(1-x));
+ nonpoly_exprs.push_back(1/(x+1));
+ nonpoly_exprs.push_back(-1/(x-1));
+ nonpoly_exprs.push_back(1/(1-x*x));
+ nonpoly_exprs.push_back(1/(1-pow(x,n)));
+ nonpoly_exprs.push_back(x-1/(x-1));
+ for (exvector::const_iterator ep = nonpoly_exprs.begin();
+ ep != nonpoly_exprs.end(); ++ep) {
+ if (ep->is_polynomial(x)) {
+ clog << "(" << *ep << ").is_polynomial(" << x << ") "
+ "erroneously returned true" << endl;
+ ++result;
+ }
+ }
+ return result;
+}
+
+// Bug in power::expand reported by Isuru Fernando (fixed 2015-05-07).
+static unsigned exam_paranoia21()
+{
+ symbol x("x");
+ ex e = pow(x + sqrt(ex(2))*x, 2).expand();
+ if (e.nops() != 2) {
+ clog << "(x+sqrt(2)*x)^2 was wrongly expanded to " << e << "\n";
+ return 1;
+ }
+ return 0;
+}
+
+// Bug in power::expand (fixed 2015-07-18).
+static unsigned exam_paranoia22()
+{
+ symbol x("x"), y("y");
+ ex e = pow(sqrt(1+x)+y*sqrt(1+x), 2).expand();
+ if (e.nops() != 6) {
+ clog << "(sqrt(1+x)+y*sqrt(1+x))^2 was wrongly expanded to " << e << "\n";
+ return 1;
+ }
+ return 0;
+}
+
+// Bug in expairseq::evalchildren().
+static unsigned exam_paranoia23()
+{
+ unsigned result = 0;
+ symbol x("x");
+
+ epvector v1;
+ v1.push_back(expair(1, 1));
+ v1.push_back(expair(2*x, -1));
+ ex e1 = add(v1); // Should be e==1-2*x,
+ if (!e1.is_equal(1-2*x)) {
+ clog << "Failure constructing " << e1 << " from add.\n";
+ ++result;
+ }
+
+ epvector v2;
+ v2.push_back(expair(x, 1));
+ v2.push_back(expair(1,-1));
+ ex e2 = mul(v2); // Should be e==x;
+ if (!e2.is_equal(x)) {
+ clog << "Failure constructing " << e2 << " from mul.\n";
+ ++result;
+ }
+
+ return result;
+}
+
+// Bug in sqrfree_yun (fixed 2016-02-02).
+static unsigned exam_paranoia24()
+{
+ 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;
+}
+