#12339: Free Groups
------------------------------------------------------------------+---------
       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):

 For what it's worth, I get the same error [comment:61 as above] on
 sage.math. A simpler example:
 {{{
 sage: G.<e0> = FreeGroup()
 sage: relns_G = [e0^2]
 sage: H.<e0, e1> = FreeGroup()
 sage: relns_H = [e0^2, e1]
 sage: G2 = G / relns_G
 sage: H2 = H / relns_H
 sage: G2.simplified()
 Finitely presented group < e0 | e0^2 >
 sage: H2.simplified()
 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
 
/scratch/palmieri/sage-5.5.rc0/local/lib/libcsage.so(print_backtrace+0x31)[0x7f5a11f63207]
 
/scratch/palmieri/sage-5.5.rc0/local/lib/libcsage.so(sigdie+0x14)[0x7f5a11f63239]
 
/scratch/palmieri/sage-5.5.rc0/local/lib/libcsage.so(sage_signal_handler+0x216)[0x7f5a11f62e16]
 /lib/libpthread.so.0[0x7f5a171797d0]
 [0x7f58e53e47d0]

 ------------------------------------------------------------------------
 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.
 ------------------------------------------------------------------------
 }}}
 It looks like the issue is using the same generator names for `G` and `H`:
 if I change it so `H` is defined by `H.<f0, f1> = FreeGroup()`, I don't
 get this problem. I think this needs to be dealt with, and a doctest needs
 to be added verifying that it has been dealt with.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:63>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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