also fix some rst issues in the doc

darmonpoints/arithgroup.py

@@ -121,15 +121,15 @@ def intersect_geodesic_arcs(x1, x2, y1, y2):
     r"""
     TESTS::
 
-    sage: from darmonpoints.arithgroup import intersect_geodesic_arcs
-    sage: intersect_geodesic_arcs(1,3,2,4)
-    1/2*I*sqrt(3) + 5/2
-    sage: print(intersect_geodesic_arcs(-1, 1, 0, AA(-1).sqrt()))
-    None
-    sage: intersect_geodesic_arcs(-1, 1, 0, 2*AA(-1).sqrt())
-    I
-    sage: intersect_geodesic_arcs(-3, 3, 2*AA(-1).sqrt(), Infinity)
-    3*I
+        sage: from darmonpoints.arithgroup import intersect_geodesic_arcs
+        sage: intersect_geodesic_arcs(1,3,2,4)
+        1/2*I*sqrt(3) + 5/2
+        sage: print(intersect_geodesic_arcs(-1, 1, 0, AA(-1).sqrt()))
+        None
+        sage: intersect_geodesic_arcs(-1, 1, 0, 2*AA(-1).sqrt())
+        I
+        sage: intersect_geodesic_arcs(-3, 3, 2*AA(-1).sqrt(), Infinity)
+        3*I
     """
     # verbose('Entering intersect_geodesic_arcs')
     e1 = geodesic_circle(x1, x2)
@@ -2744,14 +2744,14 @@ def _get_word_rep_auxiliary(self, h, check=False):
 
         Firstly, we write this as h = 1.h. Then we write h = gh', where g in Gens(G) (so we must be
         able to solve the word problem for G). Then write 1.g = zp', so that
-            h = z * p' * h'. Now iterate. We will end up with z_1 z_2 ... z_t p_0, where p_0 = id rep.
+        h = z * p' * h'. Now iterate. We will end up with z_1 z_2 ... z_t p_0, where p_0 = id rep.
 
         OUTPUT:
 
         - a list of integers in {-t,-t+1,...,t-1,t}, where the output of _generators_auxiliary is
           [a_1,...,a_t].
 
-        For example,
+        For example::
 
            h = abc in H, a,b,c in Gens(G)
            h = 1.abc

darmonpoints/arithgroup_generic.py

@@ -689,12 +689,13 @@ def cusp_reduction_table(self):
 
         Takes as input the object representing P^1(O_F/N), where F is a number field
         (that is possibly Q), and N is some ideal in the field.  Runs the following algorithm:
-                - take a remaining element C = (c:d) of P^1(O_F/N);
-                - add this to the set of cusps, declaring it to be our chosen rep;
-                - run through every translate C' = (c':d') of C under the stabiliser of infinity, and
-                        remove this translate from the set of remaining elements;
-                - store the matrix T in the stabiliser such that C' * T = C (as elements in P^1)
-                        in the dictionary, with key C'.
+
+        - take a remaining element C = (c:d) of P^1(O_F/N);
+        - add this to the set of cusps, declaring it to be our chosen rep;
+        - run through every translate C' = (c':d') of C under the stabiliser of infinity, and
+          remove this translate from the set of remaining elements;
+        - store the matrix T in the stabiliser such that C' * T = C (as elements in P^1)
+          in the dictionary, with key C'.
         """
         P = self.get_P1List()
         if hasattr(P.N(), "number_field"):

darmonpoints/cohomology_arithmetic.py

@@ -468,18 +468,19 @@ def BI(self, h, j=None):  # Returns \int_{h \Z_p} z^j \Phi\{0 \to \infy\}
         Input a 2x2 matrix h in SL2(OK) (which embeds as an element of Sigma_0(p)), and a value j.
 
         Options for j:
-            - classical case: specify a non-negative integer j. Then returns the value
-                    BI_{h,j} := Int_{h.Zp} z^j . d Phi{0 --> infty},
-                that is, the value of the distribution Phi{0 --> infty} at the function z^j x
-                the indicator function of the open set h.Zp.
-
-            - Bianchi case: specify a tuple (k,l). Then returns the value
-                    BI_{h,j} := Int_{h.(Zp x Zp)} x^k y^l . d Phi{0 --> infty},
-                that is, the value of the distribution Phi{0 --> infty} at the function x^k y^l x
-                the indicator function of the open set h.(Zp x Zp).
-
-            - do not specify j. Then returns the the distribution mu whose moments are
-                BI_{h,j}.
+
+        - classical case: specify a non-negative integer j. Then returns the value
+                BI_{h,j} := Int_{h.Zp} z^j . d Phi{0 --> infty},
+            that is, the value of the distribution Phi{0 --> infty} at the function z^j x
+            the indicator function of the open set h.Zp.
+
+        - Bianchi case: specify a tuple (k,l). Then returns the value
+                BI_{h,j} := Int_{h.(Zp x Zp)} x^k y^l . d Phi{0 --> infty},
+            that is, the value of the distribution Phi{0 --> infty} at the function x^k y^l x
+            the indicator function of the open set h.(Zp x Zp).
+
+        - do not specify j. Then returns the the distribution mu whose moments are
+            BI_{h,j}.
 
         """
         V = self.parent().coefficient_module()  ## Module V in H^1(G,V)

darmonpoints/darmonpoints.py

@@ -178,28 +178,28 @@ def darmon_point(
 
     We first need to import the module::
 
-    sage: from darmonpoints.darmonpoints import darmon_point
+        sage: from darmonpoints.darmonpoints import darmon_point
 
     A first example (Stark--Heegner point)::
 
-    sage: from darmonpoints.darmonpoints import darmon_point
-    sage: darmon_point(7,EllipticCurve('35a1'),41,20, cohomological=False, use_magma=False, use_ps_dists = True)[0]
-    Starting computation of the Darmon point
-    ...
-    -70*alpha + 449
+        sage: from darmonpoints.darmonpoints import darmon_point
+        sage: darmon_point(7,EllipticCurve('35a1'),41,20, cohomological=False, use_magma=False, use_ps_dists = True)[0]
+        Starting computation of the Darmon point
+        ...
+        -70*alpha + 449
 
     A quaternionic (Greenberg) point::
 
-    sage: darmon_point(13,EllipticCurve('78a1'),5,20) # long time # optional - magma
+        sage: darmon_point(13,EllipticCurve('78a1'),5,20) # long time # optional - magma
 
     A Darmon point over a cubic (1,1) field::
 
-    sage: F.<r> = NumberField(x^3 - x^2 - x + 2)
-    sage: E = EllipticCurve([-r -1, -r, -r - 1,-r - 1, 0])
-    sage: N = E.conductor()
-    sage: P = F.ideal(r^2 - 2*r - 1)
-    sage: beta = -3*r^2 + 9*r - 6
-    sage: darmon_point(P,E,beta,20) # long time # optional - magma
+        sage: F.<r> = NumberField(x^3 - x^2 - x + 2)
+        sage: E = EllipticCurve([-r -1, -r, -r - 1,-r - 1, 0])
+        sage: N = E.conductor()
+        sage: P = F.ideal(r^2 - 2*r - 1)
+        sage: beta = -3*r^2 + 9*r - 6
+        sage: darmon_point(P,E,beta,20) # long time # optional - magma
 
     """
     # global G, Coh, phiE, Phi, dK, J, J1, cycleGn, nn, Jlist

darmonpoints/darmonvonk.py

@@ -292,11 +292,11 @@ def darmon_vonk_point(
     r"""
     EXAMPLES ::
 
-    sage: from darmonpoints.darmonvonk import darmon_vonk_point
-    sage: J = darmon_vonk_point(5, 1, 3, 13, 60, parity='+', recognize_point='algdep',magma=magma) # optional - magma
-    #### Starting computation of the Darmon-Vonk point ####
-    ...
-    f = 7*x^2 + 11*x + 7
+        sage: from darmonpoints.darmonvonk import darmon_vonk_point
+        sage: J = darmon_vonk_point(5, 1, 3, 13, 60, parity='+', recognize_point='algdep',magma=magma) # optional - magma
+        #### Starting computation of the Darmon-Vonk point ####
+        ...
+        f = 7*x^2 + 11*x + 7
     """
     if magma is None:
         from sage.interfaces.magma import Magma

darmonpoints/findcurve.py

@@ -41,29 +41,29 @@ def find_curve(
 
     First example::
 
-    sage: from darmonpoints.findcurve import find_curve
-    sage: find_curve(5,6,30,20) # long time # optional - magma
-    # B = F<i,j,k>, with i^2 = -1 and j^2 = 3
-    ...
-    '(1, 0, 1, -289, 1862)'
+        sage: from darmonpoints.findcurve import find_curve
+        sage: find_curve(5,6,30,20) # long time # optional - magma
+        # B = F<i,j,k>, with i^2 = -1 and j^2 = 3
+        ...
+        '(1, 0, 1, -289, 1862)'
 
     A second example, now over a real quadratic::
 
-    sage: from darmonpoints.findcurve import find_curve
-    sage: F.<r> = QuadraticField(5)
-    sage: P = F.ideal(3/2*r + 1/2)
-    sage: D = F.ideal(3)
-    sage: find_curve(P,D,P*D,30,ramification_at_infinity = F.real_places()[:1]) # long time # optional - magma
-    ...
+        sage: from darmonpoints.findcurve import find_curve
+        sage: F.<r> = QuadraticField(5)
+        sage: P = F.ideal(3/2*r + 1/2)
+        sage: D = F.ideal(3)
+        sage: find_curve(P,D,P*D,30,ramification_at_infinity = F.real_places()[:1]) # long time # optional - magma
+        ...
 
     Now over a cubic of mixed signature::
 
-    sage: from darmonpoints.findcurve import find_curve
-    sage: F.<r> = NumberField(x^3 -3)
-    sage: P = F.ideal(r-2)
-    sage: D = F.ideal(r-1)
-    sage: find_curve(P,D,P*D,30) # long time # optional - magma
-    ...
+        sage: from darmonpoints.findcurve import find_curve
+        sage: F.<r> = NumberField(x^3 -3)
+        sage: P = F.ideal(r-2)
+        sage: D = F.ideal(r-1)
+        sage: find_curve(P,D,P*D,30) # long time # optional - magma
+        ...
 
     """
     config = configparser.ConfigParser()

darmonpoints/padicperiods.py

@@ -1772,13 +1772,16 @@ def find_kadziela_matrices(M, T):
     """
     The matrix M describes the relation between periods (A,B,D)^t
     and the periods (A0,B0)^t, where (A,B,D) are the periods of
-    the Teitelbaum periods, and (A0,B0) are the Darmon ones.
+    the Teitelbaum periods, and (A0,B0) are the Darmon ones. ::
+
            (A,B,D)^t = M * (A0,B0)^t
+
     The matrix T describes the action of Hecke on homology.
     That is, the first column of T describes the image of T
     on the first basis vector.
 
-    The output are matrices X and Y such that
+    The output are matrices X and Y such that::
+
          X * matrix(2,2,[A,B,B,D]) = matrix(2,2,[A0,B0,C0,D0]) * Y
 
     """

darmonpoints/schottky.py

@@ -666,23 +666,22 @@ def theta(self, prec, a, b=None, **kwargs):
 
         EXAMPLES ::
 
-        sage: from darmonpoints.schottky import *
-        sage: p = 3
-        sage: prec = 20
-        sage: working_prec = 200
-        sage: K = Qp(p,working_prec)
-        sage: g1 = matrix(K, 2, 2, [-5,32,-8,35])
-        sage: g2 = matrix(K, 2, 2, [-13,80,-8,43])
-        sage: G = SchottkyGroup(K, (g1, g2))
-        sage: a = 23
-        sage: b = 14
-        sage: z0 = K(8)
-        sage: m = 10
-        sage: Tg = G.theta_naive(m, z=z0, a=a,b=b)
-        sage: T = G.theta(prec, a, b).improve(m)
-        sage: (T(z0) / Tg - 1).valuation() > m
-        True
-
+            sage: from darmonpoints.schottky import *
+            sage: p = 3
+            sage: prec = 20
+            sage: working_prec = 200
+            sage: K = Qp(p,working_prec)
+            sage: g1 = matrix(K, 2, 2, [-5,32,-8,35])
+            sage: g2 = matrix(K, 2, 2, [-13,80,-8,43])
+            sage: G = SchottkyGroup(K, (g1, g2))
+            sage: a = 23
+            sage: b = 14
+            sage: z0 = K(8)
+            sage: m = 10
+            sage: Tg = G.theta_naive(m, z=z0, a=a,b=b)
+            sage: T = G.theta(prec, a, b).improve(m)
+            sage: (T(z0) / Tg - 1).valuation() > m
+            True
         """
         if b is not None:
             try:
@@ -771,26 +770,26 @@ def period(self, i, j, prec, **kwargs):
 
         EXAMPLES ::
 
-        sage: from darmonpoints.schottky import *
-        sage: p = 3
-        sage: prec = 10
-        sage: working_prec = 200
-        sage: K = Qp(p,working_prec)
-        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(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)
-        sage: (q00g/q00-1).valuation() > prec
-        True
-        sage: (q01g/q01-1).valuation() > prec
-        True
-        sage: (q11g/q11-1).valuation() > prec
-        True
+            sage: from darmonpoints.schottky import *
+            sage: p = 3
+            sage: prec = 10
+            sage: working_prec = 200
+            sage: K = Qp(p,working_prec)
+            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(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)
+            sage: (q00g/q00-1).valuation() > prec
+            True
+            sage: (q01g/q01-1).valuation() > prec
+            True
+            sage: (q11g/q11-1).valuation() > prec
+            True
         """
         g = len(self.generators())
         if i in ZZ: