def __mul__(self, div):
'''
Parameters
----------
div : Div
Returns
-------
Div
The intersection product of "self" and
"div" wrt. to matrix "self.int_mat".
'''
row_vec = sage_vector(sage_ZZ, self.e_lst).row()
col_vec = sage_vector(sage_ZZ, div.e_lst).column()
mat = self.int_mat
v = row_vec * mat * col_vec
return v[0][0]
def mat_mul(self, M):
'''
Parameters
----------
M : sage_matrix
A matrix with self.rank() columns.
Returns
-------
Div
Returns a "Div" object that is a result of
applying the linear transformation corresponding
to "M" to itself.
'''
v = sage_vector(self.e_lst).column()
return Div((M * v).list())
def __sub__(self, div):
v = sage_vector(sage_ZZ, self.e_lst) - sage_vector(sage_ZZ, div.e_lst)
return Div(list(v))
def __add__(self, div):
v = sage_vector(sage_ZZ, self.e_lst) + sage_vector(sage_ZZ, div.e_lst)
return Div(list(v))
def set_attributes(self, level=9):
'''
Sets attributes of this object, depending
on the input level.
For constructing a classification we instantiate
many DPLattice objects. This method allows us
to minimize the number of attributes that computed
(thus we use lazy evaluation).
Parameter
---------
self: DPLattice
At least self.M, self.Md_lst and self.d_lst
should be initialized.
level : int
A non-negative number.
'''
# M, Md_lst and d_lst are set.
if self.m1_lst == None:
all_m1_lst = get_divs(get_ak(self.get_rank()), 1, -1, True)
self.m1_lst = get_indecomp_divs(all_m1_lst, self.d_lst)
if level < 1: return
if self.fam_lst == None:
all_fam_lst = get_divs(get_ak(self.get_rank()), 2, 0, True)
self.fam_lst = get_indecomp_divs(all_fam_lst, self.d_lst)
if level < 2: return
if self.real_d_lst == None:
self.real_d_lst = [d for d in self.d_lst if d.mat_mul(self.M) == d]
if level < 3: return
if self.real_m1_lst == None:
self.real_m1_lst = [
m1 for m1 in self.m1_lst if m1.mat_mul(self.M) == m1
]
if level < 4: return
if self.real_fam_lst == None:
self.real_fam_lst = [
f for f in self.fam_lst if f.mat_mul(self.M) == f
]
if level < 5: return
if self.or_lst == None:
self.or_lst = []
for m2 in get_divs(get_ak(self.get_rank()), 0, -2, True):
if [m2 * d for d in self.d_lst] == len(self.d_lst) * [0]:
self.or_lst += [m2]
if level < 6: return
if self.sr_lst == None:
V = sage_VectorSpace(sage_QQ, self.get_rank())
W = V.subspace([d.e_lst for d in self.d_lst])
self.sr_lst = []
for m2 in get_divs(get_ak(self.get_rank()), 0, -2, True):
if sage_vector(m2.e_lst) in W:
self.sr_lst += [m2]
if level < 7: return
if self.type == None:
self.type = get_dynkin_type(self.d_lst)
if level < 8: return
if self.Mtype == None:
self.Mtype = get_dynkin_type(self.Md_lst)
if level < 9: return
if self.G == None:
self.G = get_ext_graph(self.d_lst + self.m1_lst, self.M)