Hello,
I do have a question linked to categorification of sage.combinat.words
(trac #12224), Subwords (trac #10534) and graded sets (trac #10193).
For object like integer partition, compositions or words, it make
sense to take slices. In the current implementation we do have quite
different behavior for slices and parents
{{{
sage: p = Partition([3,2,2,1])
sage: type(p[1:5])
<type 'list'>
sage: p.parent()
Partitions of the integer 8
sage: c = Composition([1,3,2,1,3])
sage: type(c[1:5])
<type 'list'>
sage: c.parent()
Compositions of non-negative integers
sage: w = Word([1,3,3,1,2,1])
sage: type(w[1:5])
<class 'sage.combinat.words.word.FiniteWord_list'>
sage: w.parent()
Free monoid over {1, 2, 3} # this is the new implementation!!
}}}
Note that for partitions, slice with negative step is not defined. I
would like that p[1:5] returns a partition and p[5:1:-1] returns an
error (or a list).
For such objects, it is possible to consider factors, subwords,
shuffle product... but it is quite hard to have a common
implementation for all of them (shuffle product needs to work for
compositions and words). It would be nice to have a sort of protocol
for sliceable elements in Sage in order to allow functorial
construction as Subwords or ShuffleProduct.
* Do we need that a slice like p[1:5] returns an object of the "same family" ?
* Is it interesting to make "Subwords(Partition([3,2,1,1]))" work ?
* What should be the default parent of Partition([3,2,1]),
Composition([3,2,3,1]) or Word([1,2,1,2,3]) ? We have many choices. As
an example, for Partition([3,2,1]) have four natural parents
* partitions
* partitions of 6
* partitions of length 3
* partitions of 6 of length 3
* Does slice make sense for other Sage objects ?
Best,
Vincent
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