#4115: [with patch, needs review] Double coset problems
--------------------------+-------------------------------------------------
Reporter: rlm | Owner: rlm
Type: defect | Status: new
Priority: major | Milestone: sage-3.1.3
Component: group_theory | Resolution:
Keywords: |
--------------------------+-------------------------------------------------
Comment (by rlm):
First of all, you should be using a `LinearBinaryCodeStruct` for this,
since these are linear binary codes, and the code will run much faster.
The `list` function of linear codes seemed pretty slow, so I posted
something at #4145.
Second, after playing with this for a while, I realized that GAP
permutations act on the right, which reverses the familiar multiplication:
{{{
sage: G = SymmetricGroup(20)
sage: g = G("(11,12,13,14,15,16,17)")
sage: h = G("(11,12)(13,14,15,16,17)")
sage: h^(-1)
(11,12)(13,17,16,15,14)
sage: (h^(-1))*g
(11,13)
sage: g*(h^(-1))
(12,17)
}}}
So I think the first version of your function was the correct one. With
the patches here and at #4145 applied, and with `test` defined as below, I
get nothing but `True`s for 100 trials. Without #4145, I frequently get
`False`'s. So perhaps #4145 is actually a bug fix!
{{{
def test(n):
G = SymmetricGroup(20)
g = G("(11,12,13,14,15,16,17)")
for i in range(n):
C1 = RandomLinearCode(20,10,GF(2))
C2 = C1.permuted_code(g)
CW1 = matrix(GF(2),C1.list())
CW2 = matrix(GF(2),C2.list())
B = NonlinearBinaryCodeStruct(CW1)
C = NonlinearBinaryCodeStruct(CW2)
ans = B.is_isomorphic(C)
L = [j+1 for j in ans]
h = G(L)
G1 = C1.automorphism_group_binary_code()
print i, g, h, g*(h^(-1)), g*(h^(-1)) in G1
print G1
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4115#comment:13>
SAGE <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
