#15439: sage/combinat/matrices/latin.py: isotopism method uses product of
permutations
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: permutation, combinat, latin | Merged in:
square | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by ncohen):
Yoooooooooooo !!
> Good point. I'm not sure if I want to add a `translate_from_0n_to_1n`
variable to the `Permutation` constructor (that constructor is already
quite complex, and it gets called a hell lot). But maybe we should add a
function to `sage/combinat/permutation.py` which constructs a permutation
from its "left shift by 1"?
Well... I'd say that having this exposed in the constructor would be cool,
considering that I don't even get why the permutations are on 1..n in the
first place. Accepting them on a 0..n-1 input, even to only return a 1..n
one would be cool.
But I tried to put some sense into what's happening in the combinat/
folder, and each time it crashes on a
1) We will do it some day
2) It's a good idea but it makes existing code slower (#14019 is in this
case, though wrong results are actually returned in the meantime)
3) I have to ask XXXX, which never happens
So, well. Even though the only sensible thing would be to support at least
both 0..n-1 and 1..n (why not LABELLED permutations btw ? Like
PermutationGroupElement already does ?). Even though the slightly less
sensible thing would be to give this up but to be able to relabel them
from the constructor, I think I can't hope for anything better than having
a relabeling function that I could import and use manually.
> +1 for the link. It just doesn't have much to do with the `isotopism`
method; it probably should be in the `apply_isotopism` docstring.
Right, right.
> OK, good point -- it seems that the `isotopism` method is indeed meant
to take disjoint cycles, whence the order is irrelevant. But I'm saying
"seems" because to me, too, it's far from clear from the docstring. If we
can confirm than this is what's meant, it should be rather easy to avoid
the use of `*` and probably even gain some speed this way.
Oh, I'm pretty sure that this is what is meant there. Of course nothing
checks it (we are in the combinat/ folder after all) but it was done in
the very same way in the constructor of permutations before #13742.
> For quite a long time I believed that everyone agreed `pq` would mean
"first do `q`, then `p`", apart from maybe some 19th century British
authors (who would be unreadable anyway). But it turned out that the
opposite convention is still around in Britain :(
HMmmmmmmmm `>_<`
> The `global_options` constructor is just a new way to handle these
global variables, but the global variable determining order of
multiplication is not new. I guess it's nuclear waste from the olden days
of Sage.
>
> In #15174 it surfaced that with `Permutations.global_options(mult) ==
'l2r'`, the Hecke algebra (a deformation of the symmetric group algebra)
would have its multiplication opposite of that of the symmetric group
algebra, whereas with `Permutations.global_options(mult) == 'r2l'` it
would not be an algebra at all (associativity would not hold). I believe
this has been around for ages. You've gotta love our codebase...
Nightmares. Nightmares. Why don't we have "permutations acting on right"
and "permutations acting on the left" then ? And get rid of a flag that
might break dozens of functions without anybody knowing ?
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/15439#comment:3>
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