def __call__(self, hmult, vmult):
r"""
INPUT:
- ``hmult`` -- multiplicities of the horizontal twists
- ``vmult`` -- multiplicities of the vertical twists
"""
if len(hmult) != self._num_hcyls or len(vmult) != self._num_vcyls:
raise ValueError("invalid input lengths")
E = self._E
H = E * diagonal_matrix(vmult)
V = E.transpose() * diagonal_matrix(hmult)
if self._num_hcyls < self._num_vcyls:
F = H * V
else:
F = V * H
p = F.charpoly()
assert F.nrows() == F.ncols() == min(
[self._num_hcyls, self._num_vcyls])
pf = max(p.roots(AA, False))
mp = pf.minpoly()
if mp.degree() == 1:
K = QQ
pf = QQ(pf)
else:
fwd, bck, q = do_polred(pf.minpoly())
im_gen = fwd(pf)
K = NumberField(q, 'a', embedding=im_gen)
pf = bck(K.gen())
# Compute widths of the cylinders via Perron-Frobenius
if self._num_hcyls < self._num_vcyls:
hcirc = (F - pf).right_kernel_matrix()
assert hcirc.nrows() == 1
assert hcirc.ncols() == self._num_hcyls
hcirc = hcirc[0]
assert all(x > 0 for x in hcirc)
vcirc = V * hcirc
c = 1
d = pf
else:
vcirc = (F - pf).right_kernel_matrix()
assert vcirc.nrows() == 1
assert vcirc.ncols() == self._num_vcyls
vcirc = vcirc[0]
assert all(x > 0 for x in vcirc)
hcirc = H * vcirc
d = 1
c = pf
# Solve linear systems to get heights
h = [hcirc[i] * hmult[i] / c for i in range(self._num_hcyls)]
v = [vcirc[i] * vmult[i] / d for i in range(self._num_vcyls)]
C = ConvexPolygons(K)
P = []
for i in range(self._o.nb_squares()):
hi = h[self._hcycles[i]]
vi = v[self._vcycles[i]]
P.append(C(edges=[(vi, 0), (0, hi), (-vi, 0), (0, -hi)]))
surface = Surface_list(base_ring=K)
for p in P:
surface.add_polygon(p)
r = self._o.r_tuple()
u = self._o.u_tuple()
for i in range(self._o.nb_squares()):
surface.set_edge_pairing(i, 1, r[i], 3)
surface.set_edge_pairing(i, 0, u[i], 2)
surface.set_immutable()
return TranslationSurface(surface)
