#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 jlopez):
I am aware of the problem of finding a normal form for elements. My (badly
made) point is that it should be clearly documented as this is the kind of
thing that would get a student easily confused. The group algebra
comparison is a real problem, though.
Something that might be useful here would be to allow the user give some
reduction rules. In my example, it is very clear that all the group
elements can be written as `x^ay^b` for suitable `a` and `b`; in an ideal
world, I could tell Sage to simplify my elements by repeatedly using the
three rules
1. "Reduce powers of `x` modulo 5"
2. "Reduce powers of `y` modulo 4"
3. "Replace each `y^ax^b` by `x^(2a+2b)y^b`"
until none of them can be further applied. Mathematica excels at this type
of operation (reduction by pattern matching). Perhaps the combinat guys
have just the right tool for doing this, but anyway this is certainly a
matter for a follow-up ticket once we have the basic functionality
running.
The `.gap()` method didn't work for me with your patch, but maybe I didn't
use it properly, I will try again when I get home.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:24>
Sage <http://www.sagemath.org>
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