corrected as_transform at non-totally ramified pts

as_covers/as_form_class.sage

@@ -202,14 +202,21 @@ def artin_schreier_transform(power_series, prec = 10):
         power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
     jump = max(-(power_series.valuation()), 0)
     try:
-        T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
+        if jump != 0:
+            T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
     except:
         print("no ", str(jump), "-th root; divide by", power_series.list()[0])
         return (jump, power_series.list()[0])
-    T_rev = new_reverse(T, prec = prec)
-    t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
-    z = 1/t^(jump) + Rt(correction)(t = t_old)
-    return(jump, correction, t_old, z)
+    if jump != 0:
+        T_rev = new_reverse(T, prec = prec)
+        t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
+        z = 1/t^(jump) + Rt(correction)(t = t_old)
+        return(jump, correction, t_old, z)
+    if jump == 0:
+        aux = t^p - t
+        z = new_reverse(aux, prec = prec)
+        z = z(t = power_series)
+        return(0, correction, t, z)
 
 
 def are_forms_linearly_dependent(set_of_forms):

drafty/draft2.sage

@@ -1,10 +1,10 @@
 p = 3
-F = GF(3)
+F = GF(3^2, 'a')
 Rx.<x> = PolynomialRing(F)
-P1 = superelliptic(x^2 + 1, 1)
+P1 = superelliptic(x^2 + 1, 2)
 fct1 = (P1.x)^2
 fct2 = fct1 + (P1.x)/(P1.y - P1.x)
 fct3 = (P1.x)^4
-C = heisenberg_cover(P1, [fct1, fct2, fct3], prec=300)
+C = heisenberg_cover(P1, [1/2*fct1, fct2, fct3], prec=300)
 print(C)
-a, b, c = heisenberg_group_action_matrices_holo(C)
+a1, b1, c1 = heisenberg_group_action_matrices_holo(C)

heisenberg_covers/heisenberg_form_class.sage

@@ -225,15 +225,21 @@ def artin_schreier_transform(power_series, prec = 10):
         power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
     jump = max(-(power_series.valuation()), 0)
     try:
-        T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
+        if jump != 0:
+            T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
     except:
         print("no ", str(jump), "-th root; divide by", power_series.list()[0])
         return (jump, power_series.list()[0])
-    T_rev = new_reverse(T, prec = prec)
-    t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
-    z = 1/t^(jump) + Rt(correction)(t = t_old)
-    return(jump, correction, t_old, z)
-
+    if jump != 0:
+        T_rev = new_reverse(T, prec = prec)
+        t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
+        z = 1/t^(jump) + Rt(correction)(t = t_old)
+        return(jump, correction, t_old, z)
+    if jump == 0:
+        aux = t^p - t
+        z = new_reverse(aux, prec = prec)
+        z = z(t = power_series)
+        return(0, correction, t, z)
 
 def are_forms_linearly_dependent(set_of_forms):
     from sage.rings.polynomial.toy_variety import is_linearly_dependent

quaternion_covers/quaternion_form_class.sage

@@ -221,14 +221,21 @@ def artin_schreier_transform(power_series, prec = 10):
         power_series = power_series - (coeff*t^(-p*M) - coeff.nth_root(p)*t^(-M))
     jump = max(-(power_series.valuation()), 0)
     try:
-        T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
+        if jump != 0:
+            T = nth_root2((power_series)^(-1), jump, prec=prec) #T is defined by power_series = 1/T^m
     except:
         print("no ", str(jump), "-th root; divide by", power_series.list()[0])
         return (jump, power_series.list()[0])
-    T_rev = new_reverse(T, prec = prec)
-    t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
-    z = 1/t^(jump) + Rt(correction)(t = t_old)
-    return(jump, correction, t_old, z)
+    if jump != 0:
+        T_rev = new_reverse(T, prec = prec)
+        t_old = T_rev(t^p/nth_root2(1 - t^((p-1)*jump), jump, prec=prec))
+        z = 1/t^(jump) + Rt(correction)(t = t_old)
+        return(jump, correction, t_old, z)
+    if jump == 0:
+        aux = t^p - t
+        z = new_reverse(aux, prec = prec)
+        z = z(t = power_series)
+        return(0, correction, t, z)
 
 
 def are_forms_linearly_dependent(set_of_forms):