#6750: [with spkg, needs review] New version of optional Group Cohomology spkg
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Reporter: SimonKing | Owner: SimonKing
Type: enhancement | Status: assigned
Priority: major | Milestone:
Component: optional packages | Keywords: cohomology ring p-group
Reviewer: | Author: Simon King
Merged: |
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Comment(by SimonKing):
Thanks to Mikael Vejdemo Johansson, I detected another bug in the
computation of restricted Massey powers. In this example (cohomology of
C_4 times C_4), the answers of COHO.massey_products() and of
COCH.massey_power() were inconsistent.
It is fixed, and used as a doc test, as follows:
{{{
sage: tmp_root = tmp_filename()
sage: from pGroupCohomology import CohomologyRing
sage: CohomologyRing.set_user_db(tmp_root)
sage: H = CohomologyRing.user_db(16,2)
sage: H.make()
sage: x,a,b,c,d = H.gens()
sage: c
c_1_0, a 1-Cochain in H^*(SmallGroup(16,2); GF(2))
sage: d
c_1_1, a 1-Cochain in H^*(SmallGroup(16,2); GF(2))
sage: H.cochain_to_polynomial(c.massey_power())
0, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))
sage: H.cochain_to_polynomial(d.massey_power())
0, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))
sage: H.cochain_to_polynomial(c.massey_power(2))
c_2_1, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))
sage: H.cochain_to_polynomial(d.massey_power(2))
c_2_2, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))
}}}
According to Mikael, this is what he expected (but in the previous
version, a null cocycle was returned). The result is consistent with the
set-valued Massey products:
{{{
sage: sorted(list(H.massey_products(c,c,c,c)))
[c_2_1, a 2-Cochain in H^*(SmallGroup(16,2); GF(2)),
c_2_1+c_1_0*c_1_1, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))]
sage: sorted(list(H.massey_products(d,d,d,d)))
[c_2_2, a 2-Cochain in H^*(SmallGroup(16,2); GF(2)),
c_2_2+c_1_0*c_1_1, a 2-Cochain in H^*(SmallGroup(16,2); GF(2))]
}}}
The example that I gave previously (a degree 3 cocycle of
SmallGroup(27,3)) is still in accordance with theoretical results, it did
not change.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6750#comment:38>
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