def _adjust_bounds(self):
# TODO: take into account vertex_min_degree
if self._fmax is None:
if self._emax is None:
raise ValueError("'fmax' or 'emax' must be set")
self._fmax = 2*self._emax
if self._vmax is None:
if self._emax is None:
raise ValueError("'vmax' or 'emax' must be set")
self._vmax = 2*self._emax
if self._emax is None:
# e = 2g - 2 + v + f
self._emax = 2*(self._gmax-1) - 2 + (self._vmax-1) + (self._fmax-1) + 1
# v, e, f, g
# -2 + v - e + f + 2g = 0
from sage.geometry.polyhedron.constructor import Polyhedron
P = Polyhedron(ieqs=[
(-self._vmin, 1, 0, 0, 0),
(self._vmax-1, -1, 0, 0, 0),
(-self._emin, 0, 1, 0, 0),
(self._emax-1, 0, -1, 0, 0),
(-self._fmin, 0, 0, 1, 0),
(self._fmax-1, 0, 0, -1, 0),
(-self._gmin, 0, 0, 0, 1),
(self._gmax-1, 0, 0, 0, -1)],
eqns = [(-2, 1, -1, 1, 2)])
if P.is_empty():
raise ValueError('conditions lead to an empty set')
half = QQ((1,2))
self._vmin, self._vmax = minmax([v[0] for v in P.vertices_list()])
self._vmin = self._vmin.floor()
self._vmax = (self._vmax + half).ceil()
self._emin, self._emax = minmax([v[1] for v in P.vertices_list()])
self._emin = self._emin.floor()
self._emax = (self._emax + half).ceil()
self._fmin, self._fmax = minmax([v[2] for v in P.vertices_list()])
self._fmin = self._fmin.floor()
self._fmax = (self._fmax + half).ceil()
self._gmin, self._gmax = minmax([v[3] for v in P.vertices_list()])
self._gmin = self._gmin.floor()
self._gmax = (self._gmax + half).ceil()
def _adjust_bounds(self):
r"""
TESTS::
sage: from surface_dynamics import FatGraphs
sage: FatGraphs(g=0, nv_max=4, vertex_min_degree=3)
Traceback (most recent call last):
...
ValueError: infinitely many fat graphs
sage: FatGraphs(g=0, nf_max=4, vertex_min_degree=3)
FatGraphs(g=0, nf_min=2, nf_max=4, ne_min=1, ne_max=4, nv_min=1, nv_max=3, vertex_min_degree=3)
sage: F = FatGraphs(g=0, nv=2, ne=1, nf=2)
sage: F
EmptySet
sage: F.cardinality_and_weighted_cardinality()
(0, 0)
sage: FatGraphs(ne=0).list()
[FatGraph('()', '()', '()')]
sage: FatGraphs(ne=1).list()
[FatGraph('(0,1)', '(0,1)', '(0)(1)'),
FatGraph('(0)(1)', '(0,1)', '(0,1)')]
sage: FatGraphs(ne=2).list()
[FatGraph('(0,1,2,3)', '(0,2)(1,3)', '(0,1,2,3)'),
FatGraph('(0,2,1)(3)', '(0,1)(2,3)', '(0,2,3)(1)'),
FatGraph('(0,2)(1,3)', '(0,1)(2,3)', '(0,3)(1,2)'),
FatGraph('(0,3,2,1)', '(0,1)(2,3)', '(0,2)(1)(3)'),
FatGraph('(0,2)(1)(3)', '(0,1)(2,3)', '(0,1,2,3)')]
"""
# variable order: v, e, f, g
from sage.geometry.polyhedron.constructor import Polyhedron
eqns = [(-2, 1, -1, 1, 2)] # -2 + v - e + f + 2g = 0
ieqs = [
(-self._vmin, 1, 0, 0, 0), # -vim + v >= 0
(-self._emin, 0, 1, 0, 0), # -emin + e >= 0
(-self._fmin, 0, 0, 1, 0), # -fmin + f >= 0
(-self._gmin, 0, 0, 0, 1), # -gmin + g >= 0
(0, -self._vertex_min_degree, 2, 0, 0)
] # -v_min_degree*v + 2e >= 0
if self._vmax is not None:
ieqs.append((self._vmax - 1, -1, 0, 0, 0)) # v < vmax
if self._emax is not None:
ieqs.append((self._emax - 1, 0, -1, 0, 0)) # e < emax
if self._fmax is not None:
ieqs.append((self._fmax - 1, 0, 0, -1, 0)) # f < fmax
if self._gmax is not None:
ieqs.append((self._gmax - 1, 0, 0, 0, -1)) # g < gmax
P = Polyhedron(ieqs=ieqs, eqns=eqns, ambient_dim=4, base_ring=QQ)
if P.is_empty():
self._vmin = self._vmax = 1
self._emin = self._emax = 0
self._fmin = self._fmax = 1
self._gmin = self._gmax = 0
self._vertex_min_degree = 0
return
if not P.is_compact():
raise ValueError('infinitely many fat graphs')
half = QQ((1, 2))
self._vmin, self._vmax = minmax([v[0] for v in P.vertices_list()])
self._vmin = self._vmin.floor()
self._vmax = (self._vmax + half).ceil()
self._emin, self._emax = minmax([v[1] for v in P.vertices_list()])
self._emin = self._emin.floor()
self._emax = (self._emax + half).ceil()
self._fmin, self._fmax = minmax([v[2] for v in P.vertices_list()])
self._fmin = self._fmin.floor()
self._fmax = (self._fmax + half).ceil()
self._gmin, self._gmax = minmax([v[3] for v in P.vertices_list()])
self._gmin = self._gmin.floor()
self._gmax = (self._gmax + half).ceil()
