quasiuniformizer works

as_covers/as_cover_class.sage

@@ -268,13 +268,39 @@ class as_cover:
         n = self.height
         F = self.base_ring
         list_of_fcts = self.at_most_poles(threshold)
+        list_of_fcts2 = self.z + [self.x, self.y]
         for f1 in list_of_fcts:
-            for f2 in list_of_fcts:
+            for f2 in list_of_fcts2:
                 d, a, b = xgcd(f1.valuation(place), f2.valuation(place))
                 if d == 1:
                     return f1^a*f2^b
         raise ValueError("Increase threshold.")
         
+    def quasiuniformizer(self, place = 0, threshold = 10):
+        '''Return an element with valuation coprime to p.'''
+        p = self.characteristic
+        n = self.height
+        F = self.base_ring
+        rr_space = self.at_most_poles(threshold)
+        list_of_fcts = [ff for ff in rr_space if ff.valuation(place)%p != 0]
+        print(len(list_of_fcts))
+        list_of_fcts2 = [len(str(ff)) for ff in list_of_fcts]
+        i_min = list_of_fcts2.index(min(list_of_fcts2))
+        result = list_of_fcts.pop(i_min)
+        print(result)
+        flag = 1
+        while flag == 1:
+            flag = 0
+            for g in self.group.elts:
+                if result.group_action(g) == result and g != self.group.one:
+                    flag = 1
+            if flag == 1:
+                list_of_fcts2 = [len(str(ff)) for ff in list_of_fcts]
+                i_min = list_of_fcts2.index(min(list_of_fcts2))
+                result = list_of_fcts.pop(i_min)
+                print(result)
+        return result
+
     def stabilizer(self, place = 0):
         result = []
         for g in self.group.elts:
@@ -304,44 +330,51 @@ class as_cover:
                 result += [g]
         return result
 
-    def ith_ramification_gp(self, i, place = 0, uniformizer = 0):
+    def ith_ramification_gp(self, i, place = 0, quasiuniformizer = 0, threshold = 20):
         '''Find ith ramification group at place at infty of nb place.'''
         G = self.group.elts
-        if uniformizer == 0:
-            t = self.uniformizer(place)
+        p = self.characteristic
         Gi = [G[0]]
+#        list_of_fcts = self.z #[self.one/zz for zz in AS.z if zz.valuation(place) < 0]
+#        list_of_fcts += [zz^2 for zz in self.z]
+        if isinstance(quasiuniformizer, int) or isinstance(quasiuniformizer, Integer):
+            t = self.quasiuniformizer(place, threshold=threshold)
+        else:
+            t = quasiuniformizer
         for g in G:
             if g != G[0]:
                 tg = t.group_action(g)
                 v = (tg - t).valuation(place)
-                if v >= i+1:
+                if v >= i + t.valuation(place):
                     Gi += [g]
         return Gi
     
-    def ramification_jumps(self, place = 0, uniformizer = 0):
+    def ramification_jumps(self, place = 0, quasiuniformizer = 0, threshold = 20):
         '''Return list of lower ramification jumps at at place at infty of nb place.'''
-        G = self.stabilizer(place = place)
-        ramification_jps = []
+        G = self.stabilizer(place=place)
+        p = self.characteristic
+        Gi = [G[0]]
+#        list_of_fcts = self.z #[self.one/zz for zz in AS.z if zz.valuation(place) < 0]
+#        list_of_fcts += [zz^2 for zz in self.z]
+        if isinstance(quasiuniformizer, int) or isinstance(quasiuniformizer, Integer):
+            t = self.quasiuniformizer(place, threshold=threshold)
+        else:
+            t = quasiuniformizer
+        result = []
         i = 0
-        if uniformizer == 0:
-            t = self.uniformizer(place)
         while len(G) > 1:
-            print(G, i)
             Gi = [G[0]]
             for g in G:
-                print('g', g, type(g))
                 if g != G[0]:
                     tg = t.group_action(g)
-                    print('tg')
                     v = (tg - t).valuation(place)
-                    print('v')
-                    if v >= i+1:
+                    if v >= i + t.valuation(place):
                         Gi += [g]
             if len(Gi) < len(G):
-                ramification_jps += [i-1]
+                result += [i-1]
             G = Gi
             i+=1
-        return ramification_jps
+        return result
     
     def a_number(self):
         g = self.genus()

as_covers/as_function_class.sage

@@ -18,7 +18,9 @@ class as_function:
         aux = aux.numerator()
         aux = as_function(AS, aux)
         aux = aux.expansion_at_infty()
-        if aux.valuation() >= 1:
+        F = AS.base_ring
+        Rt.<t> = LaurentSeriesRing(F, default_prec=AS.prec)
+        if Rt(aux).valuation() >= 1:
             return True
         return False
 

as_covers/group.sage

@@ -88,7 +88,7 @@ def heisenberg(p):
     name = "Heisenberg group E(" + str(p) + "^3)"
     short_name = "E(p^3)"
     elts = [(i, j, k) for i in range(p) for j in range(p) for k in range(p)]
-    one = 0
+    one = elts[0]
     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)]

init.sage

@@ -31,10 +31,10 @@ load('auxilliaries/reverse.sage')
 load('auxilliaries/hensel.sage')
 load('auxilliaries/linear_combination_polynomials.sage')
 load('auxilliaries/laurent_analytic_part.sage')
-load('as_drw/witt_polynomials.sage')
-load('as_drw/as_witt.sage')
-load('as_drw/as_witt_form.sage')
-load('as_drw/as_compability.sage')
+#load('as_drw/witt_polynomials.sage')
+#load('as_drw/as_witt.sage')
+#load('as_drw/as_witt_form.sage')
+#load('as_drw/as_compability.sage')
 load('quaternion_covers/quaternion_covers.sage')
 load('quaternion_covers/quaternion_function_class.sage')
 load('quaternion_covers/quaternion_form_class.sage')