using next in isogeny plotting

Author: fchapoton

src/sage/schemes/elliptic_curves/isogeny_class.py

@@ -434,60 +434,71 @@ def graph(self):
         elif n == 2:
             # one edge, two vertices.  We align horizontally and put
             # the lower number on the left vertex.
-            G.set_pos(pos={0:[-0.5,0],1:[0.5,0]})
+            G.set_pos(pos={0: [-0.5, 0], 1: [0.5, 0]})
         else:
             maxdegree = max(max(N))
             if n == 3:
                 # o--o--o
-                centervert = [i for i in range(3) if max(N.row(i)) < maxdegree][0]
+                centervert = next(i for i in range(3) if max(N.row(i)) < maxdegree)
                 other = [i for i in range(3) if i != centervert]
-                G.set_pos(pos={centervert:[0,0],other[0]:[-1,0],other[1]:[1,0]})
+                G.set_pos(pos={centervert: [0, 0], other[0]: [-1, 0], other[1]: [1, 0]})
             elif maxdegree == 4:
                 # o--o<8
-                centervert = [i for i in range(4) if max(N.row(i)) < maxdegree][0]
+                centervert = next(i for i in range(4) if max(N.row(i)) < maxdegree)
                 other = [i for i in range(4) if i != centervert]
-                G.set_pos(pos={centervert:[0,0],other[0]:[0,1],other[1]:[-0.8660254,-0.5],other[2]:[0.8660254,-0.5]})
+                G.set_pos(pos={centervert: [0, 0], other[0]: [0, 1],
+                               other[1]: [-0.8660254, -0.5], other[2]: [0.8660254, -0.5]})
             elif maxdegree == 27:
                 # o--o--o--o
                 centers = [i for i in range(4) if list(N.row(i)).count(3) == 2]
-                left = [j for j in range(4) if N[centers[0],j] == 3 and j not in centers][0]
-                right = [j for j in range(4) if N[centers[1],j] == 3 and j not in centers][0]
-                G.set_pos(pos={left:[-1.5,0],centers[0]:[-0.5,0],centers[1]:[0.5,0],right:[1.5,0]})
+                left = next(j for j in range(4) if N[centers[0], j] == 3 and j not in centers)
+                right = next(j for j in range(4) if N[centers[1], j] == 3 and j not in centers)
+                G.set_pos(pos={left: [-1.5, 0], centers[0]: [-0.5, 0],
+                               centers[1]: [0.5, 0], right: [1.5, 0]})
             elif n == 4:
                 # square
-                opp = [i for i in range(1,4) if not N[0,i].is_prime()][0]
-                other = [i for i in range(1,4) if i != opp]
-                G.set_pos(pos={0:[1,1],other[0]:[-1,1],opp:[-1,-1],other[1]:[1,-1]})
+                opp = next(i for i in range(1, 4) if not N[0, i].is_prime())
+                other = [i for i in range(1, 4) if i != opp]
+                G.set_pos(pos={0: [1, 1], other[0]: [-1, 1],
+                               opp: [-1, -1], other[1]: [1, -1]})
             elif maxdegree == 8:
                 # 8>o--o<8
                 centers = [i for i in range(6) if list(N.row(i)).count(2) == 3]
-                left = [j for j in range(6) if N[centers[0],j] == 2 and j not in centers]
-                right = [j for j in range(6) if N[centers[1],j] == 2 and j not in centers]
-                G.set_pos(pos={centers[0]:[-0.5,0],left[0]:[-1,0.8660254],left[1]:[-1,-0.8660254],centers[1]:[0.5,0],right[0]:[1,0.8660254],right[1]:[1,-0.8660254]})
+                left = [j for j in range(6) if N[centers[0], j] == 2 and j not in centers]
+                right = [j for j in range(6) if N[centers[1], j] == 2 and j not in centers]
+                G.set_pos(pos={centers[0]: [-0.5, 0], left[0]: [-1, 0.8660254],
+                               left[1]: [-1, -0.8660254], centers[1]: [0.5, 0],
+                               right[0]: [1, 0.8660254], right[1]: [1, -0.8660254]})
             elif maxdegree == 18:
                 # two squares joined on an edge
                 centers = [i for i in range(6) if list(N.row(i)).count(3) == 2]
-                top = [j for j in range(6) if N[centers[0],j] == 3]
-                bl = [j for j in range(6) if N[top[0],j] == 2][0]
-                br = [j for j in range(6) if N[top[1],j] == 2][0]
-                G.set_pos(pos={centers[0]:[0,0.5],centers[1]:[0,-0.5],top[0]:[-1,0.5],top[1]:[1,0.5],bl:[-1,-0.5],br:[1,-0.5]})
+                top = [j for j in range(6) if N[centers[0], j] == 3]
+                bl = next(j for j in range(6) if N[top[0], j] == 2)
+                br = next(j for j in range(6) if N[top[1], j] == 2)
+                G.set_pos(pos={centers[0]: [0, 0.5], centers[1]: [0, -0.5],
+                               top[0]: [-1, 0.5], top[1]: [1, 0.5],
+                               bl: [-1, -0.5], br: [1, -0.5]})
             elif maxdegree == 16:
                 # tree from bottom, 3 regular except for the leaves.
                 centers = [i for i in range(8) if list(N.row(i)).count(2) == 3]
-                center = [i for i in centers if len([j for j in centers if N[i,j] == 2]) == 2][0]
+                center = next(i for i in centers if len([j for j in centers if N[i, j] == 2]) == 2)
                 centers.remove(center)
-                bottom = [j for j in range(8) if N[center,j] == 2 and j not in centers][0]
-                left = [j for j in range(8) if N[centers[0],j] == 2 and j != center]
-                right = [j for j in range(8) if N[centers[1],j] == 2 and j != center]
-                G.set_pos(pos={center:[0,0],bottom:[0,-1],centers[0]:[-0.8660254,0.5],centers[1]:[0.8660254,0.5],left[0]:[-0.8660254,1.5],right[0]:[0.8660254,1.5],left[1]:[-1.7320508,0],right[1]:[1.7320508,0]})
+                bottom = next(j for j in range(8) if N[center, j] == 2 and j not in centers)
+                left = [j for j in range(8) if N[centers[0], j] == 2 and j != center]
+                right = [j for j in range(8) if N[centers[1], j] == 2 and j != center]
+                G.set_pos(pos={center: [0, 0], bottom: [0, -1], centers[0]: [-0.8660254, 0.5],
+                               centers[1]: [0.8660254, 0.5], left[0]: [-0.8660254, 1.5],
+                               right[0]: [0.8660254, 1.5], left[1]: [-1.7320508, 0], right[1]: [1.7320508, 0]})
             elif maxdegree == 12:
                 # tent
                 centers = [i for i in range(8) if list(N.row(i)).count(2) == 3]
-                left = [j for j in range(8) if N[centers[0],j] == 2]
+                left = [j for j in range(8) if N[centers[0], j] == 2]
                 right = []
                 for i in range(3):
-                    right.append([j for j in range(8) if N[centers[1],j] == 2 and N[left[i],j] == 3][0])
-                G.set_pos(pos={centers[0]:[-0.75,0],centers[1]:[0.75,0],left[0]:[-0.75,1],right[0]:[0.75,1],left[1]:[-1.25,-0.75],right[1]:[0.25,-0.75],left[2]:[-0.25,-0.25],right[2]:[1.25,-0.25]})
+                    right.append(next(j for j in range(8) if N[centers[1], j] == 2 and N[left[i], j] == 3))
+                G.set_pos(pos={centers[0]: [-0.75, 0], centers[1]: [0.75, 0], left[0]: [-0.75, 1],
+                               right[0]: [0.75, 1], left[1]: [-1.25, -0.75], right[1]: [0.25, -0.75],
+                               left[2]: [-0.25, -0.25], right[2]: [1.25, -0.25]})
         G.set_vertices(D)
         G.relabel(list(range(1, n + 1)))
         return G