#12339: Free Groups
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Reporter: mmarco | Owner: joyner
Type: enhancement | Status: needs_review
Priority: minor | Milestone:
Component: group theory | Resolution:
Keywords: free groups | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Miguel Marco | Merged in:
Dependencies: | Stopgaps:
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Comment (by mmarco):
Gap doesn't try to reduce elements of finitely presented groups to normal
form because, in general, it is an undecideable problem. The package kbmag
has some algorithms to look for confluent rewriting systems and automatic
structures, which would allow a normal form reduction in some cases. I
have thought about including this in my code, but since it deppends on an
external package (which is not even in the optional gap_packes spkg) i
would prefear to tackle that in an external spkg that would include also
kbmag.
I don't know why comparison doesn't work in the group algebra. I should
take a look at the group algebra code to see what is going on.
To compute the order of a group, use the .size method. You will either get
an answer or exhaust the system memory, kill the internal gap session, and
get a mess. You can even get an expression as symmetric group.
In your example:
{{{
sage: G = FreeGroup("x,y")
sage: G.inject_variables()
Defining x, y
sage: H = G.quotient([x^5, y^4, y*x*y^3*x^3])
sage: H.size()
20
sage: H.permutation_group()
Permutation Group with generators
[(1,2,6,9,3)(4,12,10,7,13)(5,15,8,11,16)(14,18,20,19,17),
(1,4,14,5)(2,7,17,8)(3,10,18,11)(6,12,19,16)(9,13,20,15)]
}}}
Finally, the method .gap() gives you the gap representation of the objects
(that is, an object of the class sage.interfaces.gap.GapElement). So if
you want to call some gap function foo on one of this objects, you just
need to call something like H.gap().foo() .
Maybe i should write a comprehensive documentation. That's another item on
the to-do list.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:23>
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