Include nmod_mpoly and fmpz_mod_mpoly in factor test

src/flint/test/test_all.py

@@ -2481,41 +2481,41 @@ def test_division_matrix():
 def _all_polys():
     return [
         # (poly_type, scalar_type, is_field)
-        (flint.fmpz_poly, flint.fmpz, False),
-        (flint.fmpq_poly, flint.fmpq, True),
-        (lambda *a: flint.nmod_poly(*a, 17), lambda x: flint.nmod(x, 17), True),
+        (flint.fmpz_poly, flint.fmpz, False, flint.fmpz(0)),
+        (flint.fmpq_poly, flint.fmpq, True, flint.fmpz(0)),
+        (lambda *a: flint.nmod_poly(*a, 17), lambda x: flint.nmod(x, 17), True, flint.fmpz(17)),
         (lambda *a: flint.fmpz_mod_poly(*a, flint.fmpz_mod_poly_ctx(163)),
          lambda x: flint.fmpz_mod(x, flint.fmpz_mod_ctx(163)),
-         True),
+         True, flint.fmpz(163)),
         (lambda *a: flint.fmpz_mod_poly(*a, flint.fmpz_mod_poly_ctx(2**127 - 1)),
          lambda x: flint.fmpz_mod(x, flint.fmpz_mod_ctx(2**127 - 1)),
-         True),
+         True, flint.fmpz(2**127 - 1)),
         (lambda *a: flint.fmpz_mod_poly(*a, flint.fmpz_mod_poly_ctx(2**255 - 19)),
          lambda x: flint.fmpz_mod(x, flint.fmpz_mod_ctx(2**255 - 19)),
-         True),
+         True, flint.fmpz(2**255 - 19)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(2**127 - 1)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(2**127 - 1)),
-         True),
+         True, flint.fmpz(2**127 - 1)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(2**127 - 1, 2)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(2**127 - 1, 2)),
-         True),
+         True, flint.fmpz(2**127 - 1)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(65537)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(65537)),
-         True),
+         True, flint.fmpz(65537)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(65537, 5)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(65537, 5)),
-         True),
+         True, flint.fmpz(65537)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(11)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(11)),
-         True),
+         True, flint.fmpz(11)),
         (lambda *a: flint.fq_default_poly(*a, flint.fq_default_poly_ctx(11, 5)),
          lambda x: flint.fq_default(x, flint.fq_default_ctx(11, 5)),
-         True),
+         True, flint.fmpz(11)),
     ]
 
 
 def test_polys():
-    for P, S, is_field in _all_polys():
+    for P, S, is_field, characteristic in _all_polys():
         assert P([S(1)]) == P([1]) == P(P([1])) == P(1)
 
         assert raises(lambda: P([None]), TypeError)
@@ -2750,37 +2750,41 @@ def setbad(obj, i, val):
 
 def _all_mpolys():
     return [
-        (flint.fmpz_mpoly, flint.fmpz_mpoly_ctx.get_context, flint.fmpz, False),
-        (flint.fmpq_mpoly, flint.fmpq_mpoly_ctx.get_context, flint.fmpq, True),
+        (flint.fmpz_mpoly, flint.fmpz_mpoly_ctx.get_context, flint.fmpz, False, flint.fmpz(0)),
+        (flint.fmpq_mpoly, flint.fmpq_mpoly_ctx.get_context, flint.fmpq, True, flint.fmpz(0)),
         (
             flint.fmpz_mod_mpoly,
             lambda *args, **kwargs: flint.fmpz_mod_mpoly_ctx.get_context(*args, **kwargs, modulus=101),
             lambda x: flint.fmpz_mod(x, flint.fmpz_mod_ctx(101)),
             True,
+            flint.fmpz(101),
         ),
         (
             flint.fmpz_mod_mpoly,
             lambda *args, **kwargs: flint.fmpz_mod_mpoly_ctx.get_context(*args, **kwargs, modulus=100),
             lambda x: flint.fmpz_mod(x, flint.fmpz_mod_ctx(100)),
             False,
+            flint.fmpz(100),
         ),
         (
             flint.nmod_mpoly,
             lambda *args, **kwargs: flint.nmod_mpoly_ctx.get_context(*args, **kwargs, modulus=101),
             lambda x: flint.nmod(x, 101),
             True,
+            flint.fmpz(101),
         ),
         (
             flint.nmod_mpoly,
             lambda *args, **kwargs: flint.nmod_mpoly_ctx.get_context(*args, **kwargs, modulus=100),
             lambda x: flint.nmod(x, 100),
             False,
+            flint.fmpz(100),
         ),
     ]
 
 
 def test_mpolys():
-    for P, get_context, S, is_field in _all_mpolys():
+    for P, get_context, S, is_field, characteristic in _all_mpolys():
 
         # Division under modulo will raise a flint exception if something is not invertible, crashing the program.  We
         # can't tell before what is invertible and what is not before hand so we always raise an exception, except for
@@ -3235,7 +3239,7 @@ def test_fmpz_mpoly_vec():
 
 def _all_polys_mpolys():
 
-    for P, S, is_field in _all_polys():
+    for P, S, is_field, characteristic in _all_polys():
         x = P([0, 1])
         y = None
         assert isinstance(x, (
@@ -3245,18 +3249,18 @@ def _all_polys_mpolys():
             flint.fmpz_mod_poly,
             flint.fq_default_poly,
         ))
-        characteristic_zero = isinstance(x, (flint.fmpz_poly, flint.fmpq_poly))
-        yield P, S, [x, y], is_field, characteristic_zero
+        yield P, S, [x, y], is_field, characteristic
 
-    for P, ctx_type, S, is_field in _all_mpolys():
-        ctx = ctx_type(2, flint.Ordering.lex, ["x", "y"])
+    for P, get_context, S, is_field, characteristic in _all_mpolys():
+        ctx = get_context(2, flint.Ordering.lex, nametup=("x", "y"))
         x, y = ctx.gens()
         assert isinstance(x, (
             flint.fmpz_mpoly,
             flint.fmpq_mpoly,
+            flint.nmod_mpoly,
+            flint.fmpz_mod_mpoly,
         ))
-        characteristic_zero = isinstance(x, (flint.fmpz_mpoly, flint.fmpq_mpoly))
-        yield P, S, [x, y], is_field, characteristic_zero
+        yield P, S, [x, y], is_field, characteristic
 
 
 def test_factor_poly_mpoly():
@@ -3273,7 +3277,11 @@ def factor(p):
             assert type(m) is int
         return coeff, sorted(factors, key=lambda p: (p[1], str(p[0])))
 
-    for P, S, [x, y], is_field, characteristic_zero in _all_polys_mpolys():
+    for P, S, [x, y], is_field, characteristic in _all_polys_mpolys():
+
+        if characteristic != 0 and not characteristic.is_prime():
+            assert raises(lambda: x.factor(), DomainError)
+            continue
 
         assert factor(0*x) == (S(0), [])
         assert factor(0*x + 1) == (S(1), [])
@@ -3284,15 +3292,15 @@ def factor(p):
         assert factor(x*(x+1)) == (S(1), [(x, 1), (x+1, 1)])
         assert factor(2*(x+1)) == (S(2), [(x+1, 1)])
 
-        if characteristic_zero:
+        if characteristic == 0:
             # primitive factors over Z for Z and Q.
             assert factor(2*x+1) == (S(1), [(2*x+1, 1)])
         else:
             # monic factors over Z/pZ and GF(p^d)
             assert factor(2*x+1) == (S(2), [(x+S(1)/2, 1)])
 
         if is_field:
-            if characteristic_zero:
+            if characteristic == 0:
                 assert factor((2*x+1)/7) == (S(1)/7, [(2*x+1, 1)])
             else:
                 assert factor((2*x+1)/7) == (S(2)/7, [(x+S(1)/2, 1)])
@@ -3302,13 +3310,13 @@ def factor(p):
             assert factor(x*y+1) == (S(1), [(x*y+1, 1)])
             assert factor(x*y) == (S(1), [(x, 1), (y, 1)])
 
-            if characteristic_zero:
+            if characteristic == 0:
                 assert factor(2*x + y) == (S(1), [(2*x + y, 1)])
             else:
-                assert factor(2*x + y) == (S(1)/2, [(x + y/2, 1)])
+                assert factor(2*x + y) == (S(2), [(x + y/2, 1)])
 
             if is_field:
-                if characteristic_zero:
+                if characteristic == 0:
                     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)])

src/flint/types/fmpz_mod_mpoly.pyx

@@ -757,6 +757,12 @@ cdef class fmpz_mod_mpoly(flint_mpoly):
         fmpz_mod_mpoly_total_degree_fmpz((<fmpz> res).val, self.val, self.ctx.val)
         return res
 
+    def leading_coefficient(self):
+        if fmpz_mod_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()})"
 
@@ -846,7 +852,7 @@ cdef class fmpz_mod_mpoly(flint_mpoly):
             c = fmpz.__new__(fmpz)
             fmpz_set((<fmpz>c).val, &fac.exp[i])
 
-            res[i] = (u, c)
+            res[i] = (u, int(c))
 
         c = fmpz.__new__(fmpz)
         fmpz_set((<fmpz>c).val, fac.constant)

src/flint/types/nmod_mpoly.pyx

@@ -733,6 +733,12 @@ cdef class nmod_mpoly(flint_mpoly):
         nmod_mpoly_total_degree_fmpz((<fmpz> res).val, self.val, self.ctx.val)
         return res
 
+    def leading_coefficient(self):
+        if nmod_mpoly_is_zero(self.val, self.ctx.val):
+            return nmod(0, self.ctx.modulus())
+        else:
+            return nmod(self.coefficient(0), self.ctx.modulus())
+
     def repr(self):
         return f"{self.ctx}.from_dict({self.to_dict()})"
 
@@ -822,9 +828,9 @@ cdef class nmod_mpoly(flint_mpoly):
             c = fmpz.__new__(fmpz)
             fmpz_set((<fmpz>c).val, &fac.exp[i])
 
-            res[i] = (u, c)
+            res[i] = (u, int(c))
 
-        constant = fac.constant
+        constant = nmod(fac.constant, self.ctx.modulus())
         nmod_mpoly_factor_clear(fac, self.ctx.val)
         return constant, res