#12339: Free Groups
--------------------------------+-------------------------------------------
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:
--------------------------------+-------------------------------------------
Comment (by jlopez):
First of all, thanks for writing in this code, this is something that we
totally need to get into Sage!
I have been playing around with some finitely presented groups and found a
few oddities
{{{
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: xx = H(x)
sage: xx^5
x^5
}}}
I expected that to show 1 or `Identity`. GAP also behaves strangely on
this front.
At least equality seems to behave properly:
{{{
sage: xx^5 == H(1)
True
}}}
However, it gets completely broken when going to the group ring, which is
bad:
{{{
sage: R = GroupAlgebra(H)
sage: R(xx)^5
x^5
sage: R(xx)^5 == R(1)
False
sage: R(xx^5) == R(1)
False
}}}
Finally there are some constructions that I'd expect to work but don't,
for instance `H` is an almost dihedral group of order 20, which can be
computed in GAP but not in Sage:
{{{
sage: H.order()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
...
}}}
I haven't really read the code, but if you are wrapping the GAP code this
can be sorted out by calling the `gap.Order()`method on the underlying gap
object. Which, incidentally, also doesn't work:
{{{
sage: gap(H)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
...
sage: H._gap_()
---------------------------------------------------------------------------
TypeError
...
}}}
This last part should be very easy to fix and would probably ease wrapping
up other GAP functions.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:22>
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