Trac #34735: some details in hyperelliptic_padic_field

URL: https://trac.sagemath.org/34735
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Lorenz Panny

Author: Release Manager

src/sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field.py

@@ -1,15 +1,15 @@
 """
 Hyperelliptic curves over a `p`-adic field
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2007 Robert Bradshaw <[email protected]>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 
 from sage.rings.all import (PowerSeriesRing, PolynomialRing, ZZ, QQ,
@@ -27,10 +27,10 @@
 class HyperellipticCurve_padic_field(hyperelliptic_generic.HyperellipticCurve_generic,
                                      ProjectivePlaneCurve_field):
 
-# The functions below were prototyped at the 2007 Arizona Winter School by
-# Robert Bradshaw and Ralf Gerkmann, working with Miljan Brakovevic and
-# Kiran Kedlaya
-# All of the below is with respect to the Monsky Washnitzer cohomology.
+    # The functions below were prototyped at the 2007 Arizona Winter School by
+    # Robert Bradshaw and Ralf Gerkmann, working with Miljan Brakovevic and
+    # Kiran Kedlaya
+    # All of the below is with respect to the Monsky Washnitzer cohomology.
 
     def local_analytic_interpolation(self, P, Q):
         """
@@ -158,7 +158,7 @@ def weierstrass_points(self):
             raise NotImplementedError()
         return [self((0,1,0))] + [self((x, 0, 1)) for x in f.roots(multiplicities=False)]
 
-    def is_in_weierstrass_disc(self,P):
+    def is_in_weierstrass_disc(self, P):
         """
         Checks if `P` is in a Weierstrass disc
 
@@ -186,12 +186,9 @@ def is_in_weierstrass_disc(self,P):
 
         - Jennifer Balakrishnan (2010-02)
         """
-        if (P[1].valuation() == 0 and P != self(0,1,0)):
-            return False
-        else:
-            return True
+        return not (P[1].valuation() == 0 and P != self(0, 1, 0))
 
-    def is_weierstrass(self,P):
+    def is_weierstrass(self, P):
         """
         Checks if `P` is a Weierstrass point (i.e., fixed by the hyperelliptic involution)
 
@@ -218,12 +215,8 @@ def is_weierstrass(self,P):
         AUTHOR:
 
         - Jennifer Balakrishnan (2010-02)
-
         """
-        if (P[1] == 0 or P[2] ==0):
-            return True
-        else:
-            return False
+        return (P[1] == 0 or P[2] == 0)
 
     def find_char_zero_weier_point(self, Q):
         """
@@ -260,7 +253,7 @@ def find_char_zero_weier_point(self, Q):
             if self.is_same_disc(P,Q):
                 return P
 
-    def residue_disc(self,P):
+    def residue_disc(self, P):
         """
         Gives the residue disc of `P`
 
@@ -306,7 +299,7 @@ def residue_disc(self,P):
         else:
             return HF(0,1,0)
 
-    def is_same_disc(self,P,Q):
+    def is_same_disc(self, P, Q):
         """
         Checks if `P,Q` are in same residue disc
 
@@ -326,10 +319,7 @@ def is_same_disc(self,P,Q):
             sage: HK.is_same_disc(Q,S)
             False
         """
-        if self.residue_disc(P) == self.residue_disc(Q):
-            return True
-        else:
-            return False
+        return self.residue_disc(P) == self.residue_disc(Q)
 
     def tiny_integrals(self, F, P, Q):
         r"""
@@ -1001,12 +991,12 @@ def newton_sqrt(self, f, x0, prec):
         - Jennifer Balakrishnan
         """
         z = x0
-        loop_prec = (log(RR(prec))/log(RR(2))).ceil()
+        loop_prec = log(RR(prec), 2).ceil()
         for i in range(loop_prec):
-            z = (z + f/z) / 2
+            z = (z + f / z) / 2
         return z
 
-    def curve_over_ram_extn(self,deg):
+    def curve_over_ram_extn(self, deg):
         r"""
         Return ``self`` over `\QQ_p(p^(1/deg))`.
 
@@ -1123,7 +1113,7 @@ def P_to_S(self, P, S):
         val = [I(S[1]) for I in integrals]
         return vector(val)
 
-    def coleman_integral_P_to_S(self,w,P,S):
+    def coleman_integral_P_to_S(self, w, P, S):
         r"""
         Given a finite Weierstrass point `P` and a point `S`
         in the same disc, computes the Coleman integral `\int_P^S w`
@@ -1168,7 +1158,7 @@ def coleman_integral_P_to_S(self,w,P,S):
         int_sing_a = int_sing(S[1])
         return int_sing_a
 
-    def S_to_Q(self,S,Q):
+    def S_to_Q(self, S, Q):
         r"""
         Given `S` a point on self over an extension field, computes the
         Coleman integrals `\{\int_S^Q x^i dx/2y \}_{i=0}^{2g-1}`
@@ -1248,13 +1238,12 @@ def S_to_Q(self,S,Q):
         b = V(L)
         M_sys = matrix(K, M_frob).transpose() - 1
         B = (~M_sys)
-        v = [c.valuation() for c in B.list()]
-        vv = min(v)
+        vv = min(c.valuation() for c in B.list())
         B = (p**(-vv)*B).change_ring(K)
         B = p**(vv)*B
         return B*(b-S_to_FS-FQ_to_Q)
 
-    def coleman_integral_S_to_Q(self,w,S,Q):
+    def coleman_integral_S_to_Q(self, w, S, Q):
         r"""
         Compute the Coleman integral `\int_S^Q w`
 
@@ -1293,7 +1282,6 @@ def coleman_integral_S_to_Q(self,w,S,Q):
         AUTHOR:
 
         - Jennifer Balakrishnan
-
         """
         import sage.schemes.hyperelliptic_curves.monsky_washnitzer as monsky_washnitzer
         K = self.base_ring()
@@ -1350,10 +1338,9 @@ def coleman_integral_from_weierstrass_via_boundary(self, w, P, Q, d):
         AUTHOR:
 
         - Jennifer Balakrishnan
-
         """
         HJ = self.curve_over_ram_extn(d)
-        S = self.get_boundary_point(HJ,P)
-        P_to_S = self.coleman_integral_P_to_S(w,P,S)
-        S_to_Q = HJ.coleman_integral_S_to_Q(w,S,Q)
+        S = self.get_boundary_point(HJ, P)
+        P_to_S = self.coleman_integral_P_to_S(w, P, S)
+        S_to_Q = HJ.coleman_integral_S_to_Q(w, S, Q)
         return P_to_S + S_to_Q