#7145: [with patch, needs review] Interval exchange transformations
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Reporter: vdelecroix | Owner: somebody
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-combinat
Component: combinatorics | Keywords:
Work_issues: | Author: Vincent Delecroix
Reviewer: | Merged:
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Changes (by vdelecroix):
* status: new => needs_review
Old description:
> This module implement Interval exchange transformations (iet) (and linear
> involutions (li)) from a combinatorial point of vue. It also makes the
> link with strata of Abelian differentials on Riemann surfaces. The three
> main objects defined in this module are:
>
> - Special kinds of permutations
> - Rauzy diagrams (oriented graph)
> - Strata of differentials
>
> There are different class of permuttations associated to iet, but all are
> constructed within a class factory:
>
> {{{
> sage: p = PermutationIET('a b c d','d c b a')
> sage: p
> a b c d
> d c b a
> sage: p.stratum()
> H(2)
> }}}
>
> The object which links those permutations to the dynamic of strata of
> differentials is the Rauzy diagram:
>
> {{{
> sage: p = PermutationIET('a b c','c b a')
> sage: d = p.rauzy_diagram()
> Rauzy diagram with 3 permutations
> }}}
New description:
This module implement Interval exchange transformations (iet) (and linear
involutions (li)) from a combinatorial point of vue. It also makes the
link with strata of Abelian differentials on Riemann surfaces. The three
main objects defined in this module are:
- Special kinds of permutations
- Rauzy diagrams (oriented graph)
- Strata of differentials
There are different class of permutations associated to iet, but all are
constructed within a class factory:
{{{
sage: p = PermutationIET('a b c d','d c b a')
sage: p
a b c d
d c b a
sage: p.stratum()
H(2)
}}}
The object which links those permutations to the dynamic (Teichmüller
flow) of strata of differentials is the Rauzy diagram:
{{{
sage: p = PermutationIET('a b c','c b a')
sage: d = p.rauzy_diagram()
Rauzy diagram with 3 permutations
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7145#comment:1>
Sage <http://www.sagemath.org>
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