first version of template works

as_covers/as_cover_class.sage

@@ -1,21 +1,18 @@
 class as_cover:
-    def __init__(self, C, list_of_fcts, branch_points = [], prec = 10):
+    def __init__(self, C, cover_template, list_of_fcts, branch_points = [], prec = 10):
         self.quotient = C
         self.functions = list_of_fcts
+        print('a')
         self.height = len(list_of_fcts)
+        print('b')
         F = C.base_ring
         self.base_ring = F
         p = C.characteristic
         self.characteristic = p
         self.prec = prec
         #group acting
-        n = self.height
+        self.height = cover_template.height
-        from itertools import product
+        self.group = cover_template.group
-        pr = [list(GF(p)) for _ in range(n)]
-        group = []
-        for a in product(*pr):
-            group += [a]
-        self.group = group
         #########
         f = C.polynomial
         m = C.exponent
@@ -25,7 +22,7 @@ class as_cover:
         self.branch_points = list(range(delta)) + branch_points
         Rxy.<x, y> = PolynomialRing(F, 2)
         Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
-
+        Rzf, zgen, fgen = cover_template.fct_field
         all_x_series = {}
         all_y_series = {}
         all_z_series = {}
@@ -40,7 +37,13 @@ class as_cover:
             n = len(list_of_fcts)
             list_of_power_series = [g.expansion(pt=pt, prec=prec) for g in list_of_fcts]
             for j in range(n):
-                power_series = list_of_power_series[j]
+                ####
+                #TUTAJ WSTAWIĆ ZMIANĘ
+                print(cover_template.fcts[j], {zgen[i] : z_series[i] for i in range(j)} | {zgen[i] : 0 for i in range(j, n)} | {fgen[i] : list_of_power_series[i] for i in range(n)})
+                power_series = Rzf(cover_template.fcts[j]).subs({zgen[i] : z_series[i] for i in range(j)} | {zgen[i] : 0 for i in range(j, n)} | {fgen[i] : list_of_power_series[i] for i in range(n)})
+                
+                ####
+                #power_series = list_of_power_series[j]
                 jump, correction, t_old, z = artin_schreier_transform(power_series, prec = prec)
                 x_series = x_series(t = t_old)
                 y_series = y_series(t = t_old)

as_covers/group.sage

@@ -1,5 +1,5 @@
 class group:
-    def __init__(self, name, elts, one, mult, inv, gens, as_gens):
+    def __init__(self, name, elts, one, mult, inv, gens):
         self.name = name
         self.elts = elts
         self.one = one
@@ -7,7 +7,6 @@ class group:
         self.inv = inv
         self.order = len(self.elts)
         self.gens = gens
-        self.as_gens = as_gens
         
     def __repr__(self):
         return self.name
@@ -25,7 +24,6 @@ class group_elt:
     def __init__(self, as_tuple, group):
         self.group = group
         self.as_tuple = as_tuple
-        self.as_gens = self.group.as_gens(as_tuple)
         
     def __repr__(self):
         return str(self.as_tuple)
@@ -62,8 +60,7 @@ def cyclic_gp(p, n):
     mult = lambda i1, i2: (i1 + i2) % (p ** n)
     inv = lambda i: (-i) % (p ** n)
     gens = [1]
-    as_gens = lambda i : [[0, i]]
+    gp = group(name, elts, one, mult, inv, gens)
-    gp = group(name, elts, one, mult, inv, gens, as_gens)
     return gp
 
 def elementary_gp(p, n):
@@ -81,8 +78,7 @@ def elementary_gp(p, n):
         e = n*[0]
         e[i] = 1
         gens += [tuple(e)]
-    as_gens = lambda i : [[j, i[j]] for j in range(n)]
+    gp = group(name, elts, one, mult, inv, gens)
-    gp = group(name, elts, one, mult, inv, gens, as_gens)
     return gp
 
 
@@ -91,9 +87,8 @@ def heisenberg(p):
     name = "Heisenberg group E(" + str(p) + "^3)"
     elts = [(i, j, k) for i in range(p) for j in range(p) for k in range(p)]
     one = 0
-    mult = lambda elt1, elt2 : ((elt1[0] + elt2[0])%p, (elt1[1] + elt2[1])%p, (-elt1[0]*elt2[1] + elt1[2] + elt2[2])%p)
+    mult = lambda elt1, elt2 : ((elt1[0] + elt2[0])%p, (elt1[1] + elt2[1])%p, (-elt1[1]*elt2[0] + elt1[2] + elt2[2])%p)
     inv = lambda elt : (p-elt[0], p-elt[1], (p - elt[2] - (p-elt[0])*(p-elt[1]))%p)
     gens = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
-    as_gens = lambda elt : [[0, elt[0]], [1, elt[1]], [2, elt[2]]]
+    gp = group(name, elts, one, mult, inv, gens)
-    gp = group(name, elts, one, mult, inv, gens, as_gens)
     return gp

as_covers/template.sage

@@ -3,7 +3,6 @@ class template:
     def __init__(self, height, field, group, fcts, gp_action):
         self.height = height
         self.group = group
-        self.fcts = fcts #RHSs of the Artin-Schreier equations
         self.gp_action = gp_action #action of the generators of the group on z[i]'s
         self.field = field
         n = height
@@ -14,9 +13,11 @@ class template:
             variable_names += 'f'+str(i)
             if i!=n-1:
                 variable_names += ','
-        R = PolynomialRing(field, 2*n, variable_names)
+        Rzf = PolynomialRing(field, 2*n, variable_names)
-        z = R.gens()[:n]
+        z = Rzf.gens()[:n]
-        f = R.gens()[n:]
+        f = Rzf.gens()[n:]
+        self.fct_field = Rzf, z, f
+        self.fcts = [Rzf(ff) for ff in fcts] #RHSs of the Artin-Schreier equations
 
 def elementary_template(p, n):
     group = elementary_gp(p, n)
@@ -34,4 +35,24 @@ def elementary_template(p, n):
     height = n
     fcts = [f[i] for i in range(n)]
     gp_action = [[z[j] + (i == j) for j in range(n)] for i in range(n)]
+    return template(height, field, group, fcts, gp_action)
+
+def heisenberg_template(p):
+    group = heisenberg(p)
+    field = GF(p)
+    variable_names = ''
+    n = 3
+    for i in range(n):
+        variable_names += 'z'+str(i)+','
+    for i in range(n):
+        variable_names += 'f'+str(i)
+        if i!=n-1:
+            variable_names += ','
+    R = PolynomialRing(field, 2*n, variable_names)
+    z = R.gens()[:n]
+    f = R.gens()[n:]
+    height = n
+    fcts = [f[i] for i in range(n)]
+    fcts[2] += (z[0] - z[1])*f[1]
+    gp_action = [[z[0] + 1, z[1], z[2] + z[1]], [z[0] + 1, z[1] + 1, z[2]], [z[0], z[1], z[2] - 1]]
     return template(height, field, group, fcts, gp_action)

init.sage

@@ -3,6 +3,8 @@ load('superelliptic/superelliptic_function_class.sage')
 load('superelliptic/superelliptic_form_class.sage')
 load('superelliptic/superelliptic_cech_class.sage')
 load('superelliptic/frobenius_kernel.sage')
+load('as_covers/group.sage')
+load('as_covers/template.sage')
 load('as_covers/as_transform.sage')
 load('as_covers/holomorphic_combinations.sage')
 load('as_covers/as_cover_class.sage')