Trac 29246: improve handling of easy cases in lift_to_sl2z()

src/sage/modular/arithgroup/congroup_gamma1.py

@@ -215,11 +215,11 @@ def generators(self, algorithm="farey"):
             ]
             sage: Gamma1(3).generators(algorithm="todd-coxeter")
             [
-            [1 1]  [-20   9]  [ 4  1]  [-5 -2]  [ 1 -1]  [1 0]  [1 1]  [-5  2]
-            [0 1], [ 51 -23], [-9 -2], [ 3  1], [ 0  1], [3 1], [0 1], [12 -5],
+            [1 1]  [-2  1]  [1 1]  [ 1 -1]  [1 0]  [1 1]  [-5  2]  [ 1  0]
+            [0 1], [-3  1], [0 1], [ 0  1], [3 1], [0 1], [12 -5], [-3  1],
             <BLANKLINE>
-            [ 1  0]  [ 4 -1]  [ -5   3]  [ 1 -1]  [ 7 -3]  [ 4 -1]  [ -5   3]
-            [-3  1], [ 9 -2], [-12   7], [ 3 -2], [12 -5], [ 9 -2], [-12   7]
+            [ 1 -1]  [ 1 -1]  [ 4 -1]  [ -5   3]
+            [ 3 -2], [ 3 -2], [ 9 -2], [-12   7]
             ]
         """
         if algorithm=="farey":

src/sage/modular/arithgroup/congroup_gammaH.py

@@ -470,17 +470,14 @@ def generators(self, algorithm="farey"):
             ]
             sage: GammaH(7, [2]).generators(algorithm="todd-coxeter")
             [
-            [1 1]  [-90  29]  [ 15   4]  [-10  -3]  [ 1 -1]  [1 0]  [1 1]  [-3 -1]
-            [0 1], [301 -97], [-49 -13], [  7   2], [ 0  1], [7 1], [0 1], [ 7  2],
+            [1 1]  [-13   4]  [ 15   4]  [-3 -1]  [ 1 -1]  [1 0]  [1 1]  [-3 -1]
+            [0 1], [ 42 -13], [-49 -13], [ 7  2], [ 0  1], [7 1], [0 1], [ 7  2],
             <BLANKLINE>
-            [-13   4]  [-5 -1]  [-5 -2]  [-10   3]  [ 1  0]  [ 9 -1]  [-20   7]
-            [ 42 -13], [21  4], [28 11], [ 63 -19], [-7  1], [28 -3], [-63  22],
+            [-13   4]  [-5 -1]  [-5 -2]  [-10   3]  [ 1  0]  [ 2 -1]  [1 0]
+            [ 42 -13], [21  4], [28 11], [ 63 -19], [-7  1], [ 7 -3], [7 1],
             <BLANKLINE>
-            [1 0]  [-3 -1]  [ 15  -4]  [ 2 -1]  [ 22  -7]  [-5  1]  [  8  -3]
-            [7 1], [ 7  2], [ 49 -13], [ 7 -3], [ 63 -20], [14 -3], [-21   8],
-            <BLANKLINE>
-            [11  5]  [-13  -4]
-            [35 16], [-42 -13]
+            [-3 -1]  [ 15  -4]  [ 2 -1]  [-5  1]  [  8  -3]  [11  5]  [-13  -4]
+            [ 7  2], [ 49 -13], [ 7 -3], [14 -3], [-21   8], [35 16], [-42 -13]
             ]
         """
         if algorithm=="farey":
@@ -969,14 +966,14 @@ def gamma0_coset_reps(self):
 
             sage: GammaH(108, [1,-1]).gamma0_coset_reps()
             [
-            [1 0]  [-43 -45]  [ 31  33]  [-49 -54]  [ 25  28]  [-19 -22]
-            [0 1], [108 113], [108 115], [108 119], [108 121], [108 125],
+            [1 0]  [-43  -2]  [ 31   2]  [-49  -5]  [ 25   3]  [-19  -3]
+            [0 1], [108   5], [108   7], [108  11], [108  13], [108  17],
             <BLANKLINE>
-            [-17 -20]  [ 47  57]  [ 13  16]  [ 41  52]  [  7   9]  [-37 -49]
-            [108 127], [108 131], [108 133], [108 137], [108 139], [108 143],
+            [-17  -3]  [ 47  10]  [ 13   3]  [ 41  11]  [  7   2]  [-37 -12]
+            [108  19], [108  23], [108  25], [108  29], [108  31], [108  35],
             <BLANKLINE>
-            [-35 -47]  [ 29  40]  [ -5  -7]  [ 23  33]  [-11 -16]  [ 53  79]
-            [108 145], [108 149], [108 151], [108 155], [108 157], [108 161]
+            [-35 -12]  [ 29  11]  [ -5  -2]  [ 23  10]  [-11  -5]  [ 53  26]
+            [108  37], [108  41], [108  43], [108  47], [108  49], [108  53]
             ]
         """
         from .all import SL2Z
@@ -991,8 +988,8 @@ def coset_reps(self):
 
             sage: list(Gamma1(3).coset_reps())
             [
-            [1 0]  [-1 -2]  [ 0 -1]  [-2  1]  [1 0]  [-3 -2]  [ 0 -1]  [-2 -3]
-            [0 1], [ 3  5], [ 1  0], [ 5 -3], [1 1], [ 8  5], [ 1  2], [ 5  7]
+            [1 0]  [-1  0]  [ 0 -1]  [ 0  1]  [1 0]  [-1  0]  [ 0 -1]  [ 0  1]
+            [0 1], [ 0 -1], [ 1  0], [-1  0], [1 1], [-1 -1], [ 1  2], [-1 -2]
             ]
             sage: len(list(Gamma1(31).coset_reps())) == 31**2 - 1
             True

src/sage/modular/cusps.py

@@ -751,7 +751,7 @@ def is_gamma_h_equiv(self, other, G):
             sage: G = GammaH(25,[6]) ; M = G.modular_symbols() ; M
             Modular Symbols space of dimension 11 for Congruence Subgroup Gamma_H(25) with H generated by [6] of weight 2 with sign 0 and over Rational Field
             sage: M.cusps()
-            [33/100, 1/3, 31/125, 1/4, 1/15, -7/15, 7/15, 4/15, 1/20, 3/20, 7/20, 9/20]
+            [8/25, 1/3, 6/25, 1/4, 1/15, -7/15, 7/15, 4/15, 1/20, 3/20, 7/20, 9/20]
             sage: len(M.cusps())
             12
 
@@ -896,7 +896,7 @@ def galois_action(self, t, N):
             sage: Cusp(oo).galois_action(3, 50)
             Infinity
             sage: c=Cusp(0).galois_action(3, 50); c
-            50/67
+            50/17
             sage: Gamma0(50).reduce_cusp(c)
             0
 

src/sage/modular/local_comp/liftings.py

@@ -171,7 +171,7 @@ def lift_ramified(g, p, u, n):
 
         sage: from sage.modular.local_comp.liftings import lift_ramified
         sage: lift_ramified([2,2,3,2], 3, 1, 1)
-        [5, 8, 3, 5]
+        [-1, -1, 3, 2]
         sage: lift_ramified([8,2,12,2], 3, 2, 23)
         [323, 110, -133584, -45493]
         sage: type(lift_ramified([8,2,12,2], 3, 2, 23)[0])

src/sage/modular/modsym/boundary.py

@@ -508,9 +508,9 @@ def _coerce_in_manin_symbol(self, x):
 
             sage: M = ModularSymbols(Gamma1(5), 4) ; B = M.boundary_space()
             sage: [ B(x) for x in M.basis() ]
-            [-[2/5], -[-1/5], -[1/3], -[-1/4], -[-1/4], -[-1/4]]
+            [-[2/5], -[Infinity], -[1/3], -[-1/4], -[-1/4], -[-1/4]]
             sage: [ B._coerce_in_manin_symbol(x) for x in M.manin_symbols_basis() ]
-            [-[2/5], -[-1/5], -[1/3], -[-1/4], -[-1/4], -[-1/4]]
+            [-[2/5], -[Infinity], -[1/3], -[-1/4], -[-1/4], -[-1/4]]
         """
         i = x.i
         alpha, beta = x.endpoints(self.level())

src/sage/modular/modsym/manin_symbol.pyx

@@ -343,17 +343,21 @@ cdef class ManinSymbol(Element):
             return [ZZ.one(), ZZ.zero(), ZZ.zero(), ZZ.one()]
         c = Integer(self.u)
         d = Integer(self.v)
+
+        if c == 0:
+            if d == 1:
+                return [ZZ.one(), ZZ.zero(), ZZ.zero(), ZZ.one()]
+            if d == N - 1:
+                return [Integer(-1), ZZ.zero(), ZZ.zero(), Integer(-1)]
+            c = Integer(N)
+
         g, z1, z2 = c.xgcd(d)
 
         # We're lucky: z1*c + z2*d = 1.
         if g==1:
             return [z2, -z1, c, d]
 
         # Have to try harder.
-        if c == 0:
-            c += N
-        if d == 0:
-            d += N
         m = c
 
         # compute prime-to-d part of m.

src/sage/modular/modsym/p1list.pyx

@@ -1216,20 +1216,24 @@ def lift_to_sl2z_int(int c, int d, int N):
     """
     cdef int z1, z2, g, m
 
-    if c == 0 and d == 0:
-        raise AttributeError("Element (%s, %s) not in P1." % (c,d))
+    if N == 1:
+        return [1, 0, 0, 1]
+
+    if c == 0:
+        if d == 1:
+            return [1, 0, 0, 1]
+        if d == N - 1:
+            return [-1, 0, 0, -1]
+        c = N
+
     g = arith_int.c_xgcd_int(c, d, &z1, &z2)
 
     # We're lucky: z1*c + z2*d = 1.
     if g==1:
         return [z2, -z1, c, d]
 
     # Have to try harder.
-    if c == 0:
-        c = c + N;
-    if d == 0:
-        d = d + N;
-    m = c;
+    m = c
 
     # compute prime-to-d part of m.
     while True:
@@ -1283,20 +1287,24 @@ def lift_to_sl2z_llong(llong c, llong d, int N):
     """
     cdef llong z1, z2, g, m
 
-    if c == 0 and d == 0:
-        raise AttributeError("Element (%s, %s) not in P1." % (c,d))
+    if N == 1:
+        return [1, 0, 0, 1]
+
+    if c == 0:
+        if d == 1:
+            return [1, 0, 0, 1]
+        if d == N - 1:
+            return [-1, 0, 0, -1]
+        c = N
+
     g = arith_llong.c_xgcd_longlong(c, d, &z1, &z2)
 
     # We're lucky: z1*c + z2*d = 1.
     if g==1:
         return [z2, -z1, c, d]
 
     # Have to try harder.
-    if c == 0:
-        c = c + N;
-    if d == 0:
-        d = d + N;
-    m = c;
+    m = c
 
     # compute prime-to-d part of m.
     while True:
@@ -1351,6 +1359,11 @@ def lift_to_sl2z(c, d, N):
         Traceback (most recent call last):
         ...
         NotImplementedError: N too large
+
+    TESTS::
+
+        sage: lift_to_sl2z(0, 0, 1)
+        [1, 0, 0, 1]
     """
     if N <= 46340:
         return lift_to_sl2z_int(c,d,N)