def test_induced_sl4_representation():
M = Manifold("m004")
z_gl2 = ptolemy.CrossRatios.from_snappy_manifold(M)
z_gl4 = z_gl2.induced_representation(4)
G = M.fundamental_group()
mat = z_gl4.evaluate_word(G.relators()[0], G)
for i, row in enumerate(mat):
for j, entry in enumerate(row):
if i == j:
assert abs(entry - 1) < 1e-9
else:
assert abs(entry) < 1e-9
def cross_ratios(M):
return [ptolemys.cross_ratios() for ptolemys in ptolemy_coordinates(M)]
if __name__ == '__main__':
from snappy import Manifold
import sys
if len(sys.argv) != 2:
print("Usage: sage -python printMatrices.py CLOSED_MFD")
print()
print('Example: sage -python printMatrices.py "m004(2,3)"')
sys.exit(1)
M = Manifold(sys.argv[1])
G = M.fundamental_group()
list_z = cross_ratios(M)
for i, z in enumerate(list_z):
print("Solution %d:" % i)
nf = z['z_0000_0'].parent()
print(" Number field:", nf.defining_polynomial())
print(" Exact values:")
for g in G.generators():
print(" Generator %s:" % g)
print(z.evaluate_word(g, G))
for z_numerical in evaluate_at_roots(nf, z, precision=100):
print(" Numerical values:")
d = CrossRatios(z_numerical, manifold_thunk=lambda: M)
for g in G.generators():