Dear tableaux users,

I have (finally!) posted a patch on the queue for trac #9265. This
converts the file tableau.py to use the modern Parent/Element model with
categories. Some highlights:

************

* Tableau_class no longer exists. If you want to test if something is a
Tableau, you should use 'isinstance(x, Tableau)'. To create a tableau
from a list of lists 'x', use 'Tableau(x)' (or some of the alternative
forms below.)

* There now exist classes Tableau, SemistandardTableau, and
StandardTableau. SemistandardTableau is new. So, in particular, one can
do 'SemistandardTableau(x)', and this will raise an error if x is not
weakly increasing in rows and strictly increasing in columns. Perhaps
some areas of sage which currently use Tableau could be changed to use
SemistandardTableau, but I made no effort in this patch to do this.

* One can also create tableau objects by first creating the appropriate
parent. For example,

sage: S = SemistandardTableaux([3,2], max_entry = 3)
sage: t = S([[1, 1, 1], [2, 3]])
sage: t.parent()
Semistandard tableaux of shape [3, 2] and maximum entry 3

* The Tableaux classes are not iterable, since the elements of a tableau
can be any object whatsoever. However, all classes of semistandard
tableaux are now iterable, except for the most general class.

sage: S = SemistandardTableaux()
sage: S[12]
NotImplementedError

sage: S = SemistandardTableaux(max_entry=3)
sage: S[12]
[[2], [3]]

***********************

If you use tableaux, I would appreciate it if you could take a look at
this patch and provide a partial (or full!) review on #9265. In
particular, I'm happy to take suggestions for more doc or tests.

Thanks,
Jason

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