holomorphic differentials for non totally ramified covers

as_covers/as_cover_class.sage

@@ -175,8 +175,10 @@ class as_cover:
 
         forms = holomorphic_combinations(S)
         
-        for pt in self.branch_points[1:]:
+        for i in range(delta):
-            forms = [(omega, omega.expansion(pt=pt)) for omega in forms]
+            for g in self.fiber(place = i):
+                if i!=0 or g != self.group.one:
+                    forms = [(omega, omega.group_action(g).expansion_at_infty(i)) for omega in forms]
                     forms = holomorphic_combinations(forms)
         
         if len(forms) < self.genus():
@@ -184,6 +186,7 @@ class as_cover:
             raise ValueError("Increase threshold.")
             #return holomorphic_differentials_basis(self, threshold = threshold + 1)
         if len(forms) > self.genus():
+            print(len(forms), forms)
             raise ValueError("Increase precision.")
         return forms
     
@@ -545,6 +548,13 @@ class as_cover:
         F = AS.base_ring
         return as_group_action_matrices(F, basis, AS.group.gens, basis = basis)
     
+    def group_action_matrices_poly(AS, mult, basis=0, threshold=10):
+        n = AS.height
+        if basis == 0:
+            basis = AS.holo_polydifferentials_basis(mult = mult, threshold=threshold)
+        F = AS.base_ring
+        return as_group_action_matrices(F, basis, AS.group.gens, basis = basis)    
+    
     def group_action_matrices_dR(AS, basis = 0, threshold=8):
         n = AS.height
         if basis == 0:
@@ -589,11 +599,9 @@ class as_cover:
                     S += [(eta, eta_exp)]
 
         forms = holomorphic_combinations_fcts(S, pole_orders[(0, self.group.one)])
-        print('iteration')
         for i in range(delta):
             for g in self.fiber(place = i):
                 if i!=0 or g != self.group.one:
-                    print('iteration')
                     forms = [(omega, omega.group_action(g).expansion_at_infty(place = i)) for omega in forms]
                     forms = holomorphic_combinations_fcts(forms, pole_orders[(i, g)])
         return forms

as_covers/as_form_class.sage

@@ -88,10 +88,8 @@ class as_form:
         # We need to have only polynomials to use monomial_coefficients in linear_representation_polynomials,
         # and sometimes basis elements have denominators. Thus we multiply by them.
         denom = LCM([denominator(omega.form) for omega in basis])
-        print(denom, basis, '\n')
         basis = [denom*omega for omega in basis]
         self_with_no_denominator = denom*self
-        print(self_with_no_denominator.form, [omega.form for omega in basis])
         return linear_representation_polynomials(Rxyz(self_with_no_denominator.form), [Rxyz(omega.form) for omega in basis])
 
     def trace(self, super=True):

as_covers/as_polyforms.sage

@@ -14,6 +14,11 @@ class as_polyform:
     def expansion_at_infty(self, place):
         return self.form.expansion_at_infty(place=place)*(self.curve.dx.expansion_at_infty(place=place))^(self.mult)
     
+    def reduce(self):
+        AS = self.curve
+        reduced = self.form.reduce()
+        return as_polyform(reduced, self.mult)
+    
     def coordinates(self, basis = 0):
         """Find coordinates of the given holomorphic form self in terms of the basis forms in a list holo."""
         AS = self.curve
@@ -24,7 +29,8 @@ class as_polyform:
         # and sometimes basis elements have denominators. Thus we multiply by them.
         denom = LCM([denominator(omega.form.function) for omega in basis])
         basis = [denom*omega.form.function for omega in basis]
-        self_with_no_denominator = denom*self.form.function
+        self_reduced = self.reduce()
+        self_with_no_denominator = denom*self_reduced.form.function
         return linear_representation_polynomials(Rxyz(self_with_no_denominator), [Rxyz(omega) for omega in basis])
     
     def group_action(self, elt):
@@ -69,7 +75,7 @@ def as_canonical_ideal(AS, n, threshold=8):
     g = AS.genus()
     RxyzQ, Rxyz, x, y, z = AS.fct_field
     from itertools import product
-    B1 = as_symmetric_power_basis(AS, n, threshold = 8)
+    B1 = as_symmetric_power_basis(AS, n, threshold = threshold)
     B2 = AS.holo_polydifferentials_basis(n, threshold = threshold)
     g = AS.genus()
     r = len(B2)

as_covers/holomorphic_combinations.sage

@@ -41,7 +41,6 @@ def holomorphic_combinations_mixed(S):
     Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
     RtQ = FractionField(Rt)
     minimal_valuation = min([g[1].valuation() for g in S])
-    print(minimal_valuation)
     if minimal_valuation >= 0:
         return [s[0] for s in S]
     list_of_lists = [] #to będzie lista złożona z list współczynników część nieholomorficznych rozwinięcia form z S