#20477: reduced words in complex reflection group
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: complex reflection groups, | Merged in:
reduced words | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by stumpc5):
The typical ways of getting elements in the group are
1. iterating through the group
2. "from_reduced_word" and "from_reduced_word_in_reflections"
3. getting special elements such as "a_coxeter_element"
I believe whenever we know a reduced word Red(w) (in simples S or in all
reflections R) *a priori*, we should store that information.
concerning 1)
- if the user is interested in Red_S(w), then she should use an
iterator that generates the group (as we already do) breadth first from S,
and store all Red_S(w) along the way. Similarly for R: if you are
interested in Red_R(w), you should use a breadth first iterator from R and
store all Red_R(w).
- this way, you get the info you want from the iterator for free
without actually computing a reduced word from scratch.
concerning 2) same as for 1, store info you have, and only compute the
other. This might be a problem (in case you give a word is S/R and want a
word in R/S), but you usually do not create tons of elements from words.
concerning 3) in this case, it is likely that you have to compute words
explicitly.
Overall, I think the most common case will be (1) and we can treat that
without actually computing reduced words.
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Ticket URL: <http://trac.sagemath.org/ticket/20477#comment:1>
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