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Coset Enumeration does not work for Mathieu group M12 #14582

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neozhaoliang opened this Issue Mar 31, 2018 · 4 comments

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neozhaoliang commented Mar 31, 2018

@valglad @luzpaz @asmeurer

A presentation of the Mathieu group M12 is

<a, b, c | a^11 = b^2 = c^2 = (ab)^3 = (ac)^3 = (bc)^10 = aabcbcaCBCB = 1>

where Bb=bB=1, cC=Cc=1.

m12

Here is the code:

    from sympy.combinatorics.free_groups import free_group
    from sympy.combinatorics.fp_groups import FpGroup, coset_enumeration_r

    F, a, b, c = free_group("a, b, c")
    f = FpGroup(F, [a**11, b**2, c**2, (a*b)**3, (a*c)**3, (b*c)**10,
                    a*a*b*c*b*c*a*c**-1*b**-1*c**-1*b**-1])
    C = coset_enumeration_r(f, [])
    C.compress()
    print(len(C.table))  # =95040

The code runs for ever and does not give the expected output 95040.

Note this is a very "tough" example for the HLT relator-based algorithm, the generated cosets are about 570000 before compression, and it should be 95040 after compression.

I wrote a simpler version of code and it gives the right output, but I don't know why sympy doesn't work ...

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luzpaz commented Mar 31, 2018

why was I CC'd on this ?

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neozhaoliang commented Mar 31, 2018

@neozhaoliang

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neozhaoliang commented Mar 31, 2018

@luzpaz OK, may be you just fixed the typos and don't understand the code ...

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valglad commented Mar 31, 2018

@gxyd Any ideas?

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