Added mainly cosmetic changes

darmonpoints/padicperiods.py

@@ -35,14 +35,14 @@ def precompute_powers(p, q, N):
         pdict[2 * i] = q * pdict[2 * i - 2]
     for i in range(1, N + 2):
         idx = i**2 - i
-        if not pdict.has_key(idx):
+        if idx not in pdict.keys():
             pdict[idx] = pdict[2 * i - 2] * pdict[idx - 2 * i + 2]
     return pdict
 
 
 # Theta functions of (25) in Teitelbaum's
 # and also the other theta functions that we need to compute the lambda's according to the formulas (23)
-# We sum terms until we get the result to the accuracy prec. When deciding the set of indicies over which we sum, we have made several simplifications that probably cause that we sum more terms than strictly needed for that accuracy, but this probably won't be an issue...
+# We sum terms until we get the result to the accuracy prec. When deciding the set of indices over which we sum, we have made several simplifications that probably cause that we sum more terms than strictly needed for that accuracy, but this probably won't be an issue...
 def Thetas(p1, p2, p3, q1, q2, q3, prec=None):
     if prec is None:
         prec = 2 * p1.parent().precision_cap()
@@ -921,7 +921,7 @@ def find_igusa_invariants_from_AB(A, B, T, scaling, prec, **kwargs):
     phi = kwargs.get("phi", lambda x: Qp(p, prec)(x))
     mat_coeffs_range = kwargs.get("mat_coeffs_range", 3)
     base = kwargs.setdefault("base", QQ)
-    if kwargs.has_key("list_I10"):
+    if "list_I10" in kwargs.keys():
         list_I10 = kwargs["list_I10"]
         kwargs["list_I10_padic"] = [phi(o) for o in list_I10]
     # matlists = kwargs.get('matlists',generate_matlists(Lambdalist,mat_coeffs_range))
@@ -1057,9 +1057,9 @@ def find_igusa_invariants(
 
 
 def check_generic(xvec, prec, data, **kwargs):
-    if kwargs.has_key("cheatjs"):
+    if "cheatjs" in kwargs.keys():
         return check_cheatjs(xvec, prec, data, **kwargs)
-    elif kwargs.has_key("list_I10"):
+    elif "list_I10" in kwargs.keys():
         return check_absoluteinvs(xvec, prec, data, **kwargs) + check_listI10(
             xvec, prec, data, **kwargs
         )
@@ -1499,7 +1499,7 @@ def guess_equation(
             K0 = Qq(Pnrm**2, prec, names="s")
             A = K0(take_to_Qp(Pnrm**Aval * Alog.exp() * Amul))
             B = K0(take_to_Qp(Pnrm**Bval * Blog.exp() * Bmul))
-            if not param_dict.has_key("list_I10"):
+            if "list_I10" not in param_dict.keys():
                 param_dict["list_I10"] = generate_listI10(
                     G.F, G.ideal_p * G.discriminant * G.level
                 )

darmonpoints/schottky.py

@@ -17,7 +17,7 @@
 from sage.structure.richcmp import richcmp
 from sage.structure.sage_object import SageObject
 from sage.structure.unique_representation import UniqueRepresentation
-
+from sage.misc.latex import latex
 from .divisors import Divisors, DivisorsElement
 from .meromorphic import *
 
@@ -220,23 +220,37 @@ def improve_one(self):
 
     def _repr_(self):
         a, b = self.a, self.b
+        if b is None:
+            try:
+                lst = a.as_list_of_differences()
+                if len(lst) == 1:
+                    a, b = lst[0]
+            except AttributeError:
+                pass
         try:
-            a = self.a.lift()
-            b = self.b.lift()
+            a = a.lift()
+            b = b.lift()
         except AttributeError:
             pass
         return f"Θ(z;{a},{b})_{{{self.m}}}"
 
     def _latex_(self):
         a, b = self.a, self.b
+        if b is None:
+            try:
+                lst = a.as_list_of_differences()
+                if len(lst) == 1:
+                    a, b = lst[0]
+            except AttributeError:
+                pass
         try:
-            a = self.a.rational_reconstruction()
-            b = self.b.rational_reconstruction()
+            a = a.lift()
+            b = b.lift()
         except AttributeError:
             pass
         try:
-            a = self.a.lift()
-            b = self.b.lift()
+            a = a.rational_reconstruction()
+            b = b.rational_reconstruction()
         except AttributeError:
             pass
         return f"\\Theta(z;{latex(a)},{latex(b)})_{{{latex(self.m)}}}"
@@ -261,7 +275,11 @@ def evaluate(self, z, recursive=True):
             )
         return ans
 
-    def eval_derivative(self, z):
+    def eval_derivative(self, z, recursive=True):
+        if recursive and not G.in_fundamental_domain(z, closure=True):
+            raise NotImplementedError("Recursivity not implemented for derivative")
+        if isinstance(z, DivisorsElement):
+            return prod(self.eval_derivative(P, recursive=recursive) ** n for P, n in z)
         v0 = self.val(z)
         Fnz = {}
         for ky, F in self.Fn.items():
@@ -309,6 +327,9 @@ def generators(self):
     def inverse_generators(self):
         return self._inverse_generators
 
+    def _repr_(self):
+        return "Schottky group with %s generators"%len(self.generators())
+
     def enumerate_group_elements(self, length):
         return enumerate_group_elements(
             self._generators, self._inverse_generators, length
@@ -693,6 +714,7 @@ def find_equivalent_divisor(self, D):
 
     def theta(self, prec, a=ZZ(0), b=ZZ(1), **kwargs):
         r"""
+        Compute the Theta function
 
         EXAMPLES ::
 
@@ -718,11 +740,21 @@ def theta(self, prec, a=ZZ(0), b=ZZ(1), **kwargs):
         DK = Divisors(K)
         gens = self.generators()
         D0 = DK(a) - DK(b)
+        s = kwargs.pop("s", None)
+        if s is not None:
+            D0 += s * D0
         D = self.find_equivalent_divisor(D0)
-        return ThetaOC(self, a=D, b=None, prec=prec, **kwargs).improve(prec)
+        ans = ThetaOC(self, a=D, b=None, prec=prec, **kwargs)
+        improve = kwargs.pop("improve", True)
+        if improve:
+            ans = ans.improve(prec)
+        return ans
 
     @cached_method
     def u_function(self, gamma, prec, a=None, **kwargs):
+        r"""
+        Compute u_gamma
+        """
         K = self.base_ring()
         DK = Divisors(K)
         if a is None:
@@ -735,7 +767,7 @@ def u_function(self, gamma, prec, a=None, **kwargs):
     @cached_method
     def period(self, i, j, prec, **kwargs):
         r"""
-        Computes the (i,j)-entry of the period matrix.
+        Compute the (i,j)-entry of the period matrix.
 
         EXAMPLES ::
 
@@ -747,9 +779,9 @@ def period(self, i, j, prec, **kwargs):
         sage: h1 = matrix(K, 2, 2, [-5,32,-8,35])
         sage: h2 = matrix(K, 2, 2, [-13,80,-8,43])
         sage: G = SchottkyGroup(K, (h1,h2))
-        sage: q00g = G.period_naive(prec, 0, 0)
-        sage: q01g = G.period_naive(prec, 0, 1)
-        sage: q11g = G.period_naive(prec, 1, 1)
+        sage: q00g = G.period_naive(0, 0, prec)
+        sage: q01g = G.period_naive(0, 1, prec)
+        sage: q11g = G.period_naive(1, 1, prec)
         sage: q00 = G.period(0,0, prec)
         sage: q01 = G.period(0,1, prec)
         sage: q11 = G.period(1,1, prec)
@@ -776,7 +808,7 @@ def period(self, i, j, prec, **kwargs):
         verbose(f"{den = }")
         return num / den
 
-    def period_naive(self, prec, i, j, **kwargs):
+    def period_naive(self, i, j, prec, **kwargs):
         g1 = self.generators()[i]
         g2 = self.generators()[j]
         z1 = self.find_point(g1)