one more test and a try in charpoly

Author: edgarcosta

src/sage/schemes/cyclic_covers/charpoly_frobenius.py

@@ -1,3 +1,10 @@
+r"""
+
+Computation of the Frobenius polynomial using Newton's identities
+
+"""
+
+
 # *****************************************************************************
 #  Copyright (C) 2018 Edgar Costa <[email protected]>
 #  Distributed under the terms of the GNU General Public License (GPL)
@@ -186,7 +193,11 @@ def charpoly_frobenius(frob_matrix, charpoly_prec, p, weight, a=1, known_factor=
 
     """
     assert known_factor[-1] == 1
-    cp = frob_matrix.change_ring(ZZ).charpoly().list()
+    try:
+        cp = frob_matrix.change_ring(ZZ).charpoly().list()
+    except ValueError:
+        # the given matrix wasn't integral
+        cp = frob_matrix.charpoly().change_ring(ZZ).list()
     assert len(charpoly_prec) == len(cp) - (len(known_factor) - 1)
     assert cp[-1] == 1
 

src/sage/schemes/cyclic_covers/cycliccover_finite_field.py

@@ -1,6 +1,13 @@
 r"""
+
 Cyclic covers over a finite field
 
+The most interesting feature is computation of Frobenius matrix on
+Monsky-Washnitzer cohomology and the Frobenius polynomial.
+
+REFERENCES::
+ - [ABCMT2019]_
+
 EXAMPLES::
 
     sage: p = 13
@@ -52,7 +59,7 @@
 # *****************************************************************************
 #  Copyright (C) 2018   Vishal Arul <[email protected]>,
 #                       Alex Best <[email protected]>,
-#                       Edgar Costa <[email protected].edu>,
+#                       Edgar Costa <edgarc@mit.edu>,
 #                       Richard Magner <[email protected]>,
 #                       Nicholas Triantafillou <[email protected]>
 #  Distributed under the terms of the GNU General Public License (GPL)
@@ -1054,6 +1061,7 @@ def _frobenius_matrix_p(N0):
 
         self._init_frob(N)
         FrobP = _frobenius_matrix_p(self._N0)
+        assert N == self._N0 or N is None
         if self._n == 1:
             return FrobP
         else:
@@ -1064,6 +1072,7 @@ def _frobenius_matrix_p(N0):
                     [[entry.frobenius() for entry in row] for row in current]
                 )
                 total = total * current
+            total = matrix([[elt.add_bigoh(self._N0) for elt in row] for row in total])
             return total
 
     @cached_method
@@ -1073,7 +1082,6 @@ def frobenius_polynomial(self):
 
         EXAMPLES:
 
-
         Hyperelliptic curves::
 
             sage: p = 11
@@ -1173,6 +1181,34 @@ def frobenius_polynomial(self):
             x^12 + 299994*x^10 + 37498500015*x^8 + 2499850002999980*x^6 + 93742500224997000015*x^4 + 1874812507499850001499994*x^2 + 15623125093747500037499700001
 
 
+        TESTS::
+
+            sage: for _ in range(5): # long time
+            ....:     fail = False
+            ....:     p = random_prime(500, lbound=5)
+            ....:     for i in range(1, 4):
+            ....:         F = GF(p**i)
+            ....:         Fx = PolynomialRing(F, 'x')
+            ....:         b = F.random_element()
+            ....:         while b == 0:
+            ....:            b = F.random_element()
+            ....:         E = EllipticCurve(F, [0, b])
+            ....:         C1 = CyclicCover(3, Fx([-b, 0, 1]))
+            ....:         C2 = CyclicCover(2, Fx([b, 0, 0, 1]))
+            ....:         frob = [elt.frobenius_polynomial() for elt in [E, C1, C2]]
+            ....:         if len(set(frob)) != 1:
+            ....:             E
+            ....:             C1
+            ....:             C2
+            ....:             frob
+            ....:             fail = True
+            ....:             break
+            ....:     if fail:
+            ....:       break
+            ....: else:
+            ....:     True
+            True
+
 
         """
         self._init_frob()