本文整理汇总了Python中sage.graphs.graph.Graph.is_forest方法的典型用法代码示例。如果您正苦于以下问题：Python Graph.is_forest方法的具体用法？Python Graph.is_forest怎么用？Python Graph.is_forest使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sage.graphs.graph.Graph的用法示例。
在下文中一共展示了Graph.is_forest方法的1个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: _finite_recognition
# 需要导入模块: from sage.graphs.graph import Graph [as 别名]
# 或者: from sage.graphs.graph.Graph import is_forest [as 别名]
def _finite_recognition(self):
"""
Return ``True`` if and only if the type is finite.
This is an auxiliary function used during the initialisation.
EXAMPLES:
Some infinite ones::
sage: F = CoxeterGroups().Finite()
sage: W = CoxeterGroup([[1,3,2],[3,1,-1],[2,-1,1]])
sage: W in F # indirect doctest
False
sage: W = CoxeterGroup([[1,-1,-1],[-1,1,-1],[-1,-1,1]])
sage: W in F # indirect doctest
False
Some finite ones::
sage: CoxeterGroup(['D',4], base_ring=QQ) in F # indirect doctest
True
sage: CoxeterGroup(['H',4]) in F # indirect doctest
True
"""
# First, we build the Coxeter graph of the group, without the
# edge labels.
coxeter_matrix = self._matrix
n = ZZ(coxeter_matrix.nrows())
G = Graph([(i, j) for i in range(n) for j in range(i)
if coxeter_matrix[i, j] not in [1, 2]])
# Coxeter graphs of finite Coxeter groups are forests
if not(G.is_forest()):
return False
comps = G.connected_components()
finite = True
# The group is finite if and only if for every connected
# component ``comp`` of its Coxeter graph, the submatrix of
# the Coxeter matrix corresponding to ``comp`` is one of the
# type-A,B,D,E,F,H,I matrices (up to permutation). So we
# shall check this condition on every ``comp``.
for comp in comps:
l = len(comp)
if l == 1:
# Any `1 \times 1` Coxeter matrix gives a finite group.
continue # A1
elif l == 2:
# A dihedral group is finite iff there is no `\infty`
# in its Coxeter matrix.
c0, c1 = comp
if coxeter_matrix[c0, c1] > 0:
continue # I2
return False
elif l == 3:
# The `3`-node case. The finite groups to check for
# here are `A_3`, `B_3` and `H_3`.
c0, c1, c2 = comp
s = sorted([coxeter_matrix[c0, c1],
coxeter_matrix[c0, c2],
coxeter_matrix[c1, c2]])
if s[1] == 3 and s[2] in [3, 4, 5]:
continue # A3, B3, H3
return False
elif l == 4:
# The `4`-node case. The finite groups to check for
# here are `A_4`, `B_4`, `D_4`, `F_4` and `H_4`.
c0, c1, c2, c3 = comp
u = [coxeter_matrix[c0, c1],
coxeter_matrix[c0, c2],
coxeter_matrix[c0, c3],
coxeter_matrix[c1, c2],
coxeter_matrix[c1, c3],
coxeter_matrix[c2, c3]]
s = sorted(u)
# ``s`` is the list of all off-diagonal entries of
# the ``comp``-submatrix of the Coxeter matrix,
# sorted in increasing order.
if s[3:5] == [3, 3]:
if s[5] == 3:
continue # A4, D4
if s[5] in [4, 5]:
u0 = u[0] + u[1] + u[2]
u1 = u[0] + u[3] + u[4]
u2 = u[1] + u[3] + u[5]
u3 = u[2] + u[4] + u[5]
ss = sorted([u0, u1, u2, u3])
if ss in [[7, 7, 9, 9], [7, 8, 8, 9],
[7, 8, 9, 10]]:
continue # F4, B4, H4
return False
else:
# The case of `l \geq 5` nodes. The finite
# groups to check for here are `A_l`, `B_l`, `D_l`,
# and `E_l` (for `l = 6, 7, 8`).
# Checking that the Coxeter matrix of the subgroup
# corresponding to the vertices ``comp`` has all its
# off-diagonal entries equal to 2, 3 or at most once 4
found_a_4 = False
for j in range(l):
#.........这里部分代码省略.........