#12339: Free Groups
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Reporter: mmarco |
Owner: joyner
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.5
Component: group theory |
Resolution:
Keywords: free groups, finitely presented groups, braids | Work
issues:
Report Upstream: N/A |
Reviewers: Volker Braun
Authors: Miguel Marco | Merged
in:
Dependencies: #6391, #13687, #13588 |
Stopgaps:
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Comment (by jhpalmieri):
Good, the patch from #13588 fixes things. Thanks.
I'm running into another problem, which I found by working on #13254. I'm
not sure what the issue is: two different presentations for the same
group? Anyway, I'm getting a segfault, at least on OS X 10.8:
{{{
sage: G.<e0, e1, e2, e3, e4, e5, e6, e7, e8, e9> = FreeGroup()
sage: rels = [e6, e5, e3, e9, e4*e7^-1*e6, e9*e7^-1*e0, e0*e1^-1*e2,
e5*e1^-1*e8, e4*e3^-1*e8, e2]
sage: G.quotient(rels)
Finitely presented group < e0, e1, e2, e3, e4, e5, e6, e7, e8, e9 | e6,
e5, e3, e9, e4*e7^-1*e6, e9*e7^-1*e0, e0*e1^-1*e2, e5*e1^-1*e8,
e4*e3^-1*e8, e2 >
sage: G.quotient(rels).simplified()
Finitely presented group < e0 | e0^2 >
sage: H.<e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14,
e15, e16, e17, e18, e19, e20, e21, e22, e23, e24, e25, e26, e27, e28, e29,
e30, e31, e32, e33, e34, e35, e36, e37, e38, e39, e40> = FreeGroup()
sage: rels = [e31*e20^-1*e23, e6, e4*e8^-1*e37, e24*e5^-1*e33,
e36*e38^-1*e4, e35, e7*e25^-1*e24, e27*e5^-1*e23, e25, e26*e13^-1*e40,
e3*e37^-1*e40, e31*e14^-1*e15, e28*e20^-1*e5, e21, e10*e20^-1*e34,
e18*e34^-1*e23, e32*e13^-1*e37, e39*e34^-1*e21, e32*e26^-1*e3, e38, e28,
e27, e3, e13*e12^-1*e33, e26, e1, e15, e36*e29^-1*e1, e31, e35*e9^-1*e8,
e11*e9^-1*e37, e10*e11^-1*e6, e25*e16^-1*e17, e17*e33^-1*e19, e32,
e39*e25^-1*e8, e9, e28*e9^-1*e24, e14, e19, e6*e16^-1*e2, e34,
e38*e27^-1*e3, e0*e21^-1*e23, e38*e29^-1*e2, e1*e21^-1*e19, e39*e18^-1*e0,
e26*e30^-1*e15, e18*e16^-1*e15, e10*e14^-1*e16, e30, e35*e14^-1*e1,
e37*e22^-1*e33, e6*e34^-1*e22, e8, e35*e11^-1*e4, e32*e12^-1*e22,
e29*e5^-1*e19, e24*e29^-1*e17, e13*e30^-1*e17, e36*e27^-1*e0, e7, e24,
e11*e14^-1*e2, e12, e11*e20^-1*e22, e40*e15^-1*e17, e36*e5^-1*e21,
e28*e31^-1*e27, e4*e0^-1*e3, e30*e12^-1*e19, e39, e7*e16^-1*e29,
e18*e25^-1*e40, e22, e0*e8^-1*e40, e9*e20^-1*e33, e4*e1^-1*e2,
e10*e31^-1*e18, e7*e6^-1*e38]
sage: H.quotient(rels)
Finitely presented group < e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, e10,
e11, e12, e13, e14, e15, e16, e17, e18, e19, e20, e21, e22, e23, e24, e25,
e26, e27, e28, e29, e30, e31, e32, e33, e34, e35, e36, e37, e38, e39, e40
| e31*e20^-1*e23, e6, e4*e8^-1*e37, e24*e5^-1*e33, e36*e38^-1*e4, e35,
e7*e25^-1*e24, e27*e5^-1*e23, e25, e26*e13^-1*e40, e3*e37^-1*e40,
e31*e14^-1*e15, e28*e20^-1*e5, e21, e10*e20^-1*e34, e18*e34^-1*e23,
e32*e13^-1*e37, e39*e34^-1*e21, e32*e26^-1*e3, e38, e28, e27, e3,
e13*e12^-1*e33, e26, e1, e15, e36*e29^-1*e1, e31, e35*e9^-1*e8,
e11*e9^-1*e37, e10*e11^-1*e6, e25*e16^-1*e17, e17*e33^-1*e19, e32,
e39*e25^-1*e8, e9, e28*e9^-1*e24, e14, e19, e6*e16^-1*e2, e34,
e38*e27^-1*e3, e0*e21^-1*e23, e38*e29^-1*e2, e1*e21^-1*e19, e39*e18^-1*e0,
e26*e30^-1*e15, e18*e16^-1*e15, e10*e14^-1*e16, e30, e35*e14^-1*e1,
e37*e22^-1*e33, e6*e34^-1*e22, e8, e35*e11^-1*e4, e32*e12^-1*e22,
e29*e5^-1*e19, e24*e29^-1*e17, e13*e30^-1*e17, e36*e27^-1*e0, e7, e24,
e11*e14^-1*e2, e12, e11*e20^-1*e22, e40*e15^-1*e17, e36*e5^-1*e21,
e28*e31^-1*e27, e4*e0^-1*e3, e30*e12^-1*e19, e39, e7*e16^-1*e29,
e18*e25^-1*e40, e22, e0*e8^-1*e40, e9*e20^-1*e33, e4*e1^-1*e2,
e10*e31^-1*e18, e7*e6^-1*e38 >
sage: H.quotient(rels).simplified() # should be Finitely presented group <
e0 | e0^2 >
Exception RuntimeError: "Error, no method found! For debugging hints type
?Recovery from NoMethodFound\nError, no 1st choice method found for `<' on
2 arguments\n" in 'sage.libs.gap.util.error_handler' ignored
------------------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component of Sage has a bug
in it and is not properly wrapped with sig_on(), sig_off(). You might
want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate.
------------------------------------------------------------------------
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:61>
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