przed dodaniem ekspansji w dowolnym punkcie

sage/as_covers/as_form_class.sage

@@ -15,14 +15,14 @@ class as_form:
     def __repr__(self):
         return "(" + str(self.form)+") * dx"
     
-    def expansion_at_infty(self, i = 0):
+    def expansion_at_infty(self, place = 0):
         C = self.curve
         delta = C.nb_of_pts_at_infty
         F = C.base_ring
-        x_series = C.x_series[i]
-        y_series = C.y_series[i]
-        z_series = C.z_series[i]
-        dx_series = C.dx_series[i]
+        x_series = C.x_series[place]
+        y_series = C.y_series[place]
+        z_series = C.z_series[place]
+        dx_series = C.dx_series[place]
         n = C.height
         variable_names = 'x, y'
         for j in range(n):
@@ -98,10 +98,10 @@ class as_form:
         return superelliptic_form(C_super, Qxy(result))
 
     def residue(self, place=0):
-        return self.expansion_at_infty(i = place).residue()
+        return self.expansion_at_infty(place = place).residue()
 
     def valuation(self, place=0):
-        return self.expansion_at_infty(i = place).valuation()
+        return self.expansion_at_infty(place = place).valuation()
 
     def serre_duality_pairing(self, fct):
         AS = self.curve

sage/drafty/draft.sage

@@ -5,4 +5,10 @@ Rx.<x> = PolynomialRing(F)
 f = x^3 - x + 1
 C = superelliptic(f, m)
 C1 = patch(C)
-print(C1.crystalline_cohomology_basis())
+#print(C1.crystalline_cohomology_basis())
+g1 = C1.polynomial
+g_AS = g1(x^p - x)
+C2 = superelliptic(g_AS, 2)
+print(convert_super_into_AS(C2))
+converted = (C2.x)^4 - (C2.x)^2
+print(convert_super_fct_into_AS(converted))

sage/drafty/superelliptic_drw.sage

@@ -347,7 +347,8 @@ def de_rham_witt_lift(cech_class, prec = 50):
     aux_h2 = decom_aux_h2[0]
     aux_f = decom_aux_h2[2]
     aux_omega0 = decomposition_omega0_omega8(aux.omega, prec=prec)[0]
-    return superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
+    result = superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
+    return result.reduce()
 
 def crystalline_cohomology_basis(self, prec = 50):
     result = []

sage/init.sage

@@ -19,10 +19,12 @@ load('auxilliaries/hensel.sage')
 load('auxilliaries/linear_combination_polynomials.sage')
 ##############
 ##############
+load('drafty/convert_superelliptic_into_AS.sage')
 load('drafty/second_patch.sage')
 load('drafty/regular_on_U0.sage')
 load('drafty/lift_to_de_rham.sage')
 #load('drafty/superelliptic_cohomology_class.sage')
 load('drafty/superelliptic_drw.sage')
-load('drafty/draft.sage')
+#load('drafty/draft_klein_covers.sage')
+load('drafty/2gpcovers.sage')
 load('drafty/pole_numbers.sage')

sage/superelliptic/superelliptic_form_class.sage

@@ -140,3 +140,19 @@ class superelliptic_form:
     
     def residue(self, place = 0, prec=30):
         return self.expansion_at_infty(place = place, prec=prec)[-1]
+    
+    def reduce(self):
+        fct = self.form
+        C = self.curve
+        fct = reduction(C, fct)
+        return superelliptic_form(C, fct)
+    
+    def reduce2(self):
+        fct = self.form
+        C = self.curve
+        m = C.exponent
+        F = C.base_ring
+        Rxy.<x, y> = PolynomialRing(F, 2)
+        Fxy = FractionField(Rxy)
+        fct = reduction(C, Fxy(y^m*fct))
+        return superelliptic_form(C, fct/y^m)