""" Example ladder surfaces. """
from __future__ import annotations
from typing import Tuple, Iterable
import bigger
from bigger.types import FlatTriangle
from bigger.triangulation import Triangle
from .utils import integers, extract_curve_and_test
Edge = Tuple[int, int]
[docs]def ladder() -> bigger.MCG[Edge]:
"""The infinite-genus, two-ended surface.
TODO. :("""
return NotImplemented
[docs]def spotted_ladder() -> bigger.MCG[Edge]:
"""The infinite-genus, two-ended surface.
With mapping classes:
- a_n which twists about the curve parallel to edges n and n+1
- b_n which twists about the curve which separates punctures n and n+1
- a which twists about all a_n curves simultaneously
- b which twists about all b_n curves simultaneously
- s which shifts the surface down
"""
# #---n,0---#---n,8---#
# | /| /|
# | / | / |
# n,1 n,2 n,4 n,7 n+1,0
# | / | / |
# |/ |/ |
# #---n,3---#---n,8---#
# | /|
# | / |
# n,5 n,6 n,5
# | / |
# |/ |
# #--n+1,1--#
def edges() -> Iterable[Edge]:
for x in integers():
for y in range(9):
yield x, y
def link(edge: Edge) -> tuple[Edge, bool, Edge, bool, Edge, bool, Edge, bool]:
n, k = edge
return {
0: ((n - 1, 7), False, (n - 1, 8), True, (n, 1), False, (n, 2), True),
1: ((n - 1, 5), True, (n - 1, 6), False, (n, 2), True, (n, 0), False),
2: ((n, 0), False, (n, 1), False, (n, 3), True, (n, 4), True),
3: ((n, 4), True, (n, 2), False, (n, 5), False, (n, 6), True),
4: ((n, 2), False, (n, 3), True, (n, 7), True, (n, 8), False),
5: ((n, 6), False, (n + 1, 1), True, (n, 6), True, (n, 3), False),
6: ((n, 3), False, (n, 5), False, (n + 1, 1), True, (n, 5), True),
7: ((n, 8), False, (n, 4), False, (n, 8), True, (n + 1, 0), True),
8: ((n + 1, 0), True, (n, 7), False, (n, 4), False, (n, 7), True),
}[k]
T = bigger.Triangulation.from_pos(edges, link)
def generator(name: str) -> bigger.Encoding[Edge]:
if name in ("s", "shift"):
return T.isometry(T, lambda edge: (edge[0] + 1, edge[1]), lambda edge: (edge[0] - 1, edge[1]))
curve, test = extract_curve_and_test("ab", name)
if curve == "a":
return T(lambda edge: 1 if edge[1] in {7, 8} and test(edge[0]) else 0).twist()
if curve == "b":
return T(lambda edge: 1 if edge[1] in {5, 6} and test(edge[0]) else 0).twist()
raise ValueError(f"Unknown mapping class {name}")
def layout(triangle: Triangle) -> FlatTriangle:
n, k = triangle[0].edge
return {
0: ((n + 0.25, -0.25), (n, 0.0), (n + 0.25, 0.25)),
2: ((n + 0.25, -0.25), (n + 0.25, 0.25), (n + 0.5, 0.0)),
3: ((n + 0.5, 0.0), (n + 0.25, 0.25), (n + 1.25, 0.3)),
5: ((n + 1.0, 0.05), (n + 0.5, 0.0), (n + 1.25, 0.3)),
4: ((n + 0.25, -0.25), (n + 0.5, 0.0), (n + 1.25, -0.25)),
7: ((n + 1.25, -0.25), (n + 0.5, 0.0), (n + 1.0, 0.0)),
}[k]
return bigger.MCG(T, generator, layout)
