On Apr 17, 11:03 am, Carl Witty <[EMAIL PROTECTED]> wrote:
> On Apr 17, 6:03 am, kcrisman <[EMAIL PROTECTED]> wrote:
>
> > However, what I really want is to be able to do this dynamically and
> > to have the output be an "ordered set". Maybe an example would be
> > that I might want to list different orders of operations, so that
> > object A="exponentiation>multiplication>addition" would be my normal
> > list, but then I could have another ordering be the (wrong but
> > potentially fun) B="addition>multiplication>exponentiation", and that
> > if I wanted to then put in subtraction in B, I could infix it to be
> > B="addition>multiplication=subtraction>exponentiation" for a LOT of
> > fun.
>
> > I was thinking now that maybe just a list (which has an implicit
> > ordering and lots of functions on it) would work, but I don't know
> > that it would allow "=" between elements very easily.
>
> For tiny sets, you could use graphs. For your final example, start
> with a graph with edges "addition->multiplication",
> "multiplication->subtraction", "subtraction->multiplication", and
> "subtraction-
> >exponentiation". Then compute the transitive closure of the graph.
>
> To test whether A>B, A=B, A<B, or A and B are incomparable, just check
> whether there are edges A->B and B->A in the graph.
>
> Unfortunately the current implementation of transitive closure looks
> pretty slow, so this will currently only work for tiny sets.
>
> Carl
This was actually very helpful, though not in the way you might have
thought. I think what I might be looking for is an extension to the
Permutation_class class, as it turns out, since a permutation in that
class does give an order and allows all sorts of nifty messing with
that, including inversion etc. I'll have to look into this, or maybe
combining it with something to allow "ties", as well as trying to
figure out the easiest ways to put strings into this, probably just
sage: Permutation(['a','b','c'])
['a', 'b', 'c'].
Thanks!
Unfortunately, there is the very confusing difference between
Permutation and permutation in Sage - what's up with that? The most
unhelpful thing that happened in my session is below.
- kcrisman
sage: permutation?
Type: module
Base Class: <type 'module'>
String Form: <module 'sage.combinat.permutation' from '/
Applications/sage/local/lib/python2.5/site-packages/sage/combinat/
permutation.pyc'>
Namespace: Interactive
File: /Applications/sage/local/lib/python2.5/site-packages/
sage/combinat/permutation.py
Docstring:
Permutations
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