Test all poly types can factor the zero poly

Author: oscarbenjamin

src/flint/test/test_all.py

@@ -3208,7 +3208,10 @@ def factor(p):
 
     for P, S, [x, y], is_field, characteristic_zero in _all_polys_mpolys():
 
+        assert factor(0*x) == (S(0), [])
+        assert factor(0*x + 1) == (S(1), [])
         assert factor(x) == (S(1), [(x, 1)])
+        assert factor(-x) == (S(-1), [(x, 1)])
         assert factor(x**2) == (S(1), [(x, 2)])
         assert factor(x*(x+1)) == (S(1), [(x, 1), (x+1, 1)])
         assert factor(2*(x+1)) == (S(2), [(x+1, 1)])
@@ -3222,10 +3225,8 @@ def factor(p):
 
         if is_field:
             if characteristic_zero:
-                # primitive factors over Z for Z and Q.
                 assert factor((2*x+1)/7) == (S(1)/7, [(2*x+1, 1)])
             else:
-                # monic factors over Z/pZ and GF(p^d)
                 assert factor((2*x+1)/7) == (S(2)/7, [(x+S(1)/2, 1)])
 
         if y is not None:
@@ -3234,12 +3235,16 @@ def factor(p):
             assert factor(x*y) == (S(1), [(x, 1), (y, 1)])
 
             if characteristic_zero:
-                # primitive factors over Z for Z and Q.
                 assert factor(2*x + y) == (S(1), [(2*x + y, 1)])
             else:
-                # monic factors over Z/pZ and GF(p^d)
                 assert factor(2*x + y) == (S(1)/2, [(x + y/2, 1)])
 
+            if is_field:
+                if characteristic_zero:
+                    assert factor((2*x+y)/7) == (S(1)/7, [(2*x+y, 1)])
+                else:
+                    assert factor((2*x+y)/7) == (S(2)/7, [(x+y/2, 1)])
+
 
 def _all_matrices():
     """Return a list of matrix types and scalar types."""

src/flint/types/fmpq_mpoly.pyx

@@ -856,6 +856,12 @@ cdef class fmpq_mpoly(flint_mpoly):
         fmpq_mpoly_total_degree_fmpz((<fmpz> res).val, self.val, self.ctx.val)
         return res
 
+    def leading_coefficient(self):
+        if fmpq_mpoly_is_zero(self.val, self.ctx.val):
+            return fmpq(0)
+        else:
+            return self.coefficient(0)
+
     def repr(self):
         return f"{self.ctx}.from_dict({self.to_dict()})"
 

src/flint/types/fmpz_mod_poly.pyx

@@ -1798,6 +1798,17 @@ cdef class fmpz_mod_poly(flint_poly):
         if not self.ctx.is_prime():
             raise NotImplementedError("factor algorithm assumes that the modulus is prime")
 
+        # XXX: fmpz_mod_poly_factor with modulus 163 crashes on the zero poly:
+        #
+        # Exception (fmpz_mod_poly_powmod_fmpz_binexp). Divide by zero
+        #
+        # We handle this special case first:
+        cdef fmpz_mod zero
+        if self.is_zero():
+            zero = fmpz_mod.__new__(fmpz_mod)
+            zero.ctx = self.ctx.mod
+            return (zero, [])
+
         fmpz_mod_poly_factor_init(fac, self.ctx.mod.val)
         if algorithm == None:
             fmpz_mod_poly_factor(fac, self.val, self.ctx.mod.val)

src/flint/types/fmpz_mpoly.pyx

@@ -838,6 +838,12 @@ cdef class fmpz_mpoly(flint_mpoly):
         fmpz_mpoly_total_degree_fmpz((<fmpz> res).val, self.val, self.ctx.val)
         return res
 
+    def leading_coefficient(self):
+        if fmpz_mpoly_is_zero(self.val, self.ctx.val):
+            return fmpz(0)
+        else:
+            return self.coefficient(0)
+
     def repr(self):
         return f"{self.ctx}.from_dict({self.to_dict()})"
 

src/flint/types/nmod_poly.pyx

@@ -235,15 +235,19 @@ cdef class nmod_poly(flint_poly):
             >>> f.leading_coefficient()
             133
         """
+        cdef ulong cu
+        cdef slong d
         cdef nmod c
 
         d = self.degree()
         if d < 0:
-            return 0
+            cu = 0
+        else:
+            cu = nmod_poly_get_coeff_ui(self.val, d)
 
         c = nmod.__new__(nmod)
         c.mod = self.val.mod
-        c.val = nmod_poly_get_coeff_ui(self.val, d)
+        c.val = cu
 
         return c