def main_poincare_1():
for (l, m, n, maxsize) in [(5, 2, 4, 4000)]:
# build the rotation group generators
a, b = [g.todisc() for g in mktriangle(l, m, n)]
cvs = Canvas()
cvs.append(Scale(2.))
disc = Disc(cvs)
z_face = 0j
z_vert = (a * b).inner_fixed()
gamma = Geodesic.construct(z_vert, (~a)(z_vert))
z_edge = gamma.z2 # midpoint
g_face = gamma.get_refl()
gamma = Geodesic.construct(z_face, z_vert)
g_edge = gamma.get_refl()
g_vert = Mobius.conjugate()
gens = [g_face, g_edge, g_vert]
gens = gens + [~g for g in gens]
G = mulclose(gens, verbose=True, maxsize=maxsize)
faces, edges, verts = [], [], []
for g in G:
faces.append(g(z_face))
edges.append(g(z_edge))
verts.append(g(z_vert))
for g in G:
disc.show_geodesic(g(z_face),
g(z_vert),
attrs=st_round + [grey.alpha(0.1)])
for g in G:
disc.show_geodesic(g(z_face), g(z_edge), attrs=st_round + [grey])
for g in G:
disc.show_geodesic(g(z_vert), g(z_edge), attrs=st_round)
# for [cl, zs] in ([green, faces], [blue, edges], [red, verts]):
for [cl, zs] in ([red, verts], ):
for z in zs:
disc.show_point(z, [cl])
disc.fini()
disc.save("poincare-rotation-%d%d%d" % (l, m, n))
def render_group(l,
m,
n,
words=[],
rels=[],
labels={},
name="output",
maxsize=1000):
# build the rotation group generators
a, b = [g.todisc() for g in mktriangle(l, m, n)]
assert (a.order()) == 10 # SL(2) not PSL(2)
assert (b.order()) == 4 # SL(2) not PSL(2)
c = (~b) * (~a)
cvs = Canvas()
cvs.append(Scale(4.))
disc = Disc(cvs)
z_face = 0j
z_vert = (a * b).inner_fixed()
gamma = Geodesic.construct(z_vert, (~a)(z_vert))
z_edge = gamma.z2 # midpoint
#z_tile = (1/3)*(z_face + z_edge + z_vert)
z_tile = (1 / 2) * (z_face + z_vert)
g_face = gamma.get_refl()
gamma = Geodesic.construct(z_face, z_vert)
g_edge = gamma.get_refl()
g_vert = Mobius.conjugate()
gens = [g_vert, ~g_vert, g_edge, ~g_edge, g_face, ~g_face]
G = mulclose(gens, verbose=True, maxsize=maxsize)
faces, edges, verts = [], [], []
for g in G:
faces.append(g(z_face))
edges.append(g(z_edge))
verts.append(g(z_vert))
#for g in G:
# disc.show_geodesic(g(z_face), g(z_vert), attrs=st_round+[grey.alpha(0.1)])
for g in G:
disc.show_geodesic(g(z_face), g(z_edge), attrs=st_round + [grey])
for g in G:
disc.show_geodesic(g(z_vert), g(z_edge), attrs=st_round)
# for [cl, zs] in ([green, faces], [blue, edges], [red, verts]):
for [cl, zs] in ([red, verts], ):
for z in zs:
disc.show_point(z, fill_attrs=[white], stroke_attrs=[black])
# ------------------------------------------------------
I = Mobius()
gens = [a, ~a, b, ~b, c, ~c]
def get(word):
g = reduce(mul, [gens[i] for i in word], I)
return g
for word in words:
g = get(word)
disc.show_point(g(z_tile), [blue.alpha(0.5)])
scale = 0.4
if labels:
for (word, label) in labels.items():
g = reduce(mul, [gens[w] for w in reversed(word)], I)
disc.show_label(g(z_tile), label, scale)
else:
for (g, label) in [
(I, r"$\star$"),
(a, r"$a$"),
(b, r"$b$"),
(c, r"$c$"),
#(c**2, r"$c^2$"),
#(c**3, r"$c^3$"),
]:
disc.show_label(g(z_tile), label, scale)
for rel in rels:
g = get(reversed(rel))
disc.show_label(g(z_tile), "I", scale)
disc.fini()
disc.save(name)
def main_bring():
# build the rotation group generators
a, b = [g.todisc() for g in mktriangle(5, 2, 5)]
disc = Disc()
z_face = 0j
z_vert = (a * b).inner_fixed()
gamma = Geodesic.construct(z_vert, (~a)(z_vert))
z_edge = gamma.z2 # midpoint
g_face = gamma.get_refl()
gamma = Geodesic.construct(z_face, z_vert)
g_edge = gamma.get_refl()
g_vert = Mobius.conjugate()
gens = [g_face, g_edge, g_vert]
gens = gens + [~g for g in gens]
G = mulclose(gens, verbose=True, maxsize=8000) # 8000 is enough
faces, edges, verts = [], [], []
for g in G:
#disc.show_geodesic(g(z_face), g(z_vert), attrs=[grey])
#disc.show_geodesic(g(z_face), g(z_edge), attrs=[grey])
faces.append(g(z_face))
edges.append(g(z_edge))
verts.append(g(z_vert))
for g in G:
disc.show_geodesic(g(z_vert), g(z_edge), attrs=st_round)
# break
#disc.show_polygon([z_face, z_edge, z_vert], st_fill=[grey])
#disc.show_point(z_vert, radius=0.1)
#disc.show_point((~a)(z_vert), radius=0.1)
#disc.show_point(z_edge, radius=0.1)
# z1, z2 = z_vert, a(z_vert)
# faces.append(0.j)
# for i in range(5):
# disc.show_geodesic(z1, z2)
# gamma = Geodesic.construct(z1, z2)
# disc.show_geodesic(0, z1)
# disc.show_geodesic(0, gamma.z2)
# edges.append(gamma.z2)
# verts.append(gamma.z0)
# #g = gamma.get_refl()
# #disc.show_point(g(0))
# z1, z2 = z2, a(z2)
for z in edges:
disc.show_qubit(z)
#for [cl, zs] in ([green, faces], [blue, edges], [red, verts]):
# for z in zs:
# disc.show_point(z, [cl])
I = Mobius()
z = 0.j
pts0 = []
for (g, label) in [
(I, "1"),
(b, "6"),
(a * b, "2"),
(a * a * b, "3"),
(a * a * a * b, "4"),
(a * a * a * a * b, "5"),
(b * a * b, "8"),
(a * b * a * b, "10"),
(a * a * b * a * b, "7"),
(a * a * a * b * a * b, "9"),
(a * a * a * a * b * a * b, "11"),
(b * a * b * a * b, "7"),
(a * b * a * b * a * b, "9"),
(a * a * b * a * b * a * b, "11"),
(a * a * a * b * a * b * a * b, "8"),
(a * a * a * a * b * a * b * a * b, "10"),
(a * b * a * a * b, "5"),
(a * a * b * a * a * b, "6"),
(a * a * a * b * a * a * b, "2"),
(a * a * a * a * b * a * a * b, "3"),
(a * a * a * a * a * b * a * a * b, "4"),
(b * a * a * a * b, "3"),
(a * b * a * a * a * b, "4"),
(a * a * b * a * a * a * b, "5"),
(a * a * a * b * a * a * a * b, "6"),
(a * a * a * a * b * a * a * a * b, "2"),
(b * a * a * a * a * b * a * b * a * b, "7"),
(a * b * a * a * a * a * b * a * b * a * b, "9"),
(a * a * b * a * a * a * a * b * a * b * a * b, "11"),
(a * a * a * b * a * a * a * a * b * a * b * a * b, "8"),
(a * a * a * a * b * a * a * a * a * b * a * b * a * b, "10"),
(b * a * a * a * a * b * a * b, "12"),
(a * b * a * a * a * a * b * a * b, "12"),
(a * a * b * a * a * a * a * b * a * b, "12"),
(a * a * a * b * a * a * a * a * b * a * b, "12"),
(a * a * a * a * b * a * a * a * a * b * a * b, "12"),
(b * a * b * a * a * a * a * b, "12"),
(a * b * a * b * a * a * a * a * b, "12"),
(a * a * b * a * b * a * a * a * a * b, "12"),
(a * a * a * b * a * b * a * a * a * a * b, "12"),
(a * a * a * a * b * a * b * a * a * a * a * b, "12"),
(b * a * a * b * a * b, "10"),
(a * b * a * a * b * a * b, "7"),
(a * a * b * a * a * b * a * b, "9"),
(a * a * a * b * a * a * b * a * b, "11"),
(a * a * a * a * b * a * a * b * a * b, "8"),
]:
z1 = g(z)
z1 = 0.98 * z1
disc.show_label(z1, label)
#pts0.append(z1)
#disc.show_point(z1, [red], radius=0.02)
disc.fini()
disc.save("brings-curve")