#4115: [with patch, needs review] Double coset problems
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Reporter: rlm | Owner: rlm
Type: defect | Status: new
Priority: major | Milestone: sage-3.1.3
Component: group_theory | Resolution:
Keywords: |
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Comment (by wdj):
A couple of cool examples:-)
{{{
sage: P.<x> = PolynomialRing(GF(2),"x")
sage: g = x^3+x+1
sage: C1 = CyclicCodeFromGeneratingPolynomial(7,g); C1
Linear code of length 7, dimension 4 over Finite Field of size 2
sage: CW1 = matrix(GF(2),C1.list())
sage: C2 = HammingCode(3,GF(2)); C2
Linear code of length 7, dimension 4 over Finite Field of size 2
sage: CW2 = matrix(GF(2),C2.list())
sage: B = NonlinearBinaryCodeStruct(CW1)
sage: C = NonlinearBinaryCodeStruct(CW2)
sage: B.is_isomorphic(C)
[0, 1, 2, 6, 5, 3, 4]
}}}
{{{
sage: C1 = ExtendedQuadraticResidueCode(23,GF(2)); C1
Linear code of length 24, dimension 12 over Finite Field of size 2
sage: C2 = ExtendedBinaryGolayCode(); C2
Linear code of length 24, dimension 12 over Finite Field of size 2
sage: C1 == C2
False
sage: time CW1 = matrix(GF(2),C1.list())
CPU times: user 32.98 s, sys: 0.03 s, total: 33.01 s
Wall time: 33.12 s
sage: time CW2 = matrix(GF(2),C2.list())
CPU times: user 31.93 s, sys: 0.03 s, total: 31.95 s
Wall time: 32.05 s
sage: time B = NonlinearBinaryCodeStruct(CW1)
CPU times: user 0.19 s, sys: 0.00 s, total: 0.19 s
Wall time: 0.19 s
sage: time C = NonlinearBinaryCodeStruct(CW2)
CPU times: user 0.21 s, sys: 0.00 s, total: 0.21 s
Wall time: 0.21 s
sage: time B.is_isomorphic(C)
CPU times: user 0.22 s, sys: 0.00 s, total: 0.22 s
Wall time: 0.22 s
[0,
1,
2,
3,
4,
5,
14,
19,
23,
21,
16,
15,
18,
17,
22,
7,
11,
12,
8,
6,
10,
13,
9,
20]
sage:
}}}
This is a 24x4096 matrix!
So far so good. I'm going to try to find some more complicated examples:-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4115#comment:11>
SAGE <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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