non-totally ramified pts and holo diffs - first try

drafty/draft2.sage

@@ -7,4 +7,6 @@ fct2 = fct1 + (P1.x)/(P1.y - P1.x)
 fct3 = (P1.x)^4
 C = heisenberg_cover(P1, [1/2*fct1, fct2, fct3], prec=300)
 print(C)
-a1, b1, c1 = heisenberg_group_action_matrices_holo(C)
+B = C.holomorphic_differentials_basis()
+print("Computed basis")
+a1, b1, c1 = heisenberg_group_action_matrices_holo(C, basis = B)

heisenberg_covers/heisenberg_covers.sage

@@ -146,7 +146,19 @@ class heisenberg_cover:
         if len(forms) < self.genus():
             print("I haven't found all forms, only ", len(forms), " of ", self.genus())
             return holomorphic_differentials_basis(self, threshold = threshold + 1)
+        
         if len(forms) > self.genus():
+            forms1 = []
+            for omega in forms:
+                flag = 1
+                for g in self.group:
+                    for i in range(self.nb_of_pts_at_infty):
+                        if omega.group_action(g).valuation(i) < 0:
+                            flag = 0
+                if flag == 1:
+                    forms1 += [omega]
+            if len(forms1) == self.genus():
+                return forms1
             raise ValueError("Increase precision.")
         return forms
     

heisenberg_covers/heisenberg_form_class.sage

@@ -84,6 +84,8 @@ class heisenberg_form:
     def group_action(self, elt):
         AS = self.curve
         RxyzQ, Rxyz, x, y, z = AS.fct_field
+        if elt == (0, 0, 0):
+            return self
         if elt == (1, 0, 0):
             sub_list = {x : x, y : y} | {z[0] : z[0] + 1, z[1] : z[1], z[2]: z[2] + z[1]}
             g = self.form

heisenberg_covers/heisenberg_function_class.sage

@@ -120,6 +120,8 @@ class heisenberg_function:
     def group_action(self, elt):
         AS = self.curve
         RxyzQ, Rxyz, x, y, z = AS.fct_field
+        if elt == (0, 0, 0):
+            return self
         if elt == (1, 0, 0):
             sub_list = {x : x, y : y} | {z[0] : z[0] + 1, z[1] : z[1], z[2]: z[2] + z[1]}
             g = self.function