Added coordinates computation in h0

vector_bundle/function_field_utility.py

@@ -1013,4 +1013,4 @@ def full_rank_matrix_in_completion(mat, place=None, pi=None):
             row = [exps[i][j].coefficient(vals[i] + ell) for j in range(s)]
             N = insert_row(N, (i+1)*(ell+1) - 1, row)
         ell += 1
-    return N
+    return N, Kp, vals

vector_bundle/vector_bundle.py

@@ -144,6 +144,9 @@ class VectorBundle(SageObject):
         else:
             self._vector_bundle_from_data(function_field, ideals,
                                         g_finite,g_infinite)
+        self._h0_matrix = None
+        self._h0_Kp = None
+        self._h0_vs = None
 
     def __hash__(self):
         return hash((tuple(self._ideals),
@@ -949,7 +952,7 @@ class VectorBundle(SageObject):
         dual_matrix = matrix([h1_dual_bundle._matrix_to_vector(mat)
                               for mat in h1_dual]).transpose()
         zero_rows = [i for i, row in enumerate(dual_matrix) if row == 0]
-        n_matrix = function_field_utility.full_rank_matrix_in_completion(
+        n_matrix, _, _  = function_field_utility.full_rank_matrix_in_completion(
                 dual_matrix,
                 place_0,
                 pi_0)
@@ -1043,6 +1046,36 @@ class VectorBundle(SageObject):
                 for mat in ext_dual]
         return ext_group.extension(form)
 
+    def coordinates_in_h0(self, f):
+        r"""
+        Return a vector of coordinates of ``f`` in the basis returned
+        by ``self.h0()``
+
+        EXAMPLES ::
+            
+            sage: from vector_bundle import VectorBundle
+            sage: F.<x> = FunctionField(GF(7))
+            sage: R.<y> = F[]
+            sage: K.<y> = F.extension(y^2 - x^3 - x)
+            sage: ideals = [P.prime_ideal() for P in K.places_finite()[:2]]
+            sage: g_finite = matrix([[1,1 / (x**5 + y)],[2, y]])
+            sage: g_infinite = matrix([[x, 1], [2, y**3]])
+            sage: V = VectorBundle(K, ideals, g_finite, g_infinite)
+            sage: h0 = V.h0()
+            sage: v = sum([i*e for i, e in enumerate(h0)])
+            sage: V.coordinates_in_h0(v)
+            (0, 1, 2, 3, 4, 5)
+        """
+        if self._h0_matrix is None:
+            mat = matrix(self._function_field, self.h0()).transpose()
+            self._h0_matrix, self._h0_Kp, self._h0_vs =\
+                    function_field_utility.full_rank_matrix_in_completion(mat)
+        ell = self._h0_matrix.nrows() // self.rank()
+        series = [self._h0_Kp(c) for c in f]
+        v = vector(sum([[s.coefficient(val + j) for j in range(ell)]
+                        for s, val in zip(series, self._h0_vs)],[]))
+        return self._h0_matrix.solve_right(v)
+                            
     def _isomorphism_to_large_field(self, other, proba=10^-20):
         r"""
         Return an isomorphism from self to other if it exists and None otherwise.
@@ -1052,6 +1085,7 @@ class VectorBundle(SageObject):
         ``len(self.end().h0())``.
         """
 
+
     def isomorphism_to(self, other):
         r"""
         Return an isomorphism from self to other if it exists and None otherwise