Hi Andrew and Travis,

Thanks for your work on this!

> I am reviewing Travis' patch #13605 which is great as it implements some 
> needed improvements. I have a few minor issues which I think shouldn't be 
> decided between just the two of us -- apologies if I
> am being too precious here!
> 
> Only fans of partitions are likely to be interested in what follows. Please 
> let me know what you think of the following:
> 
>  1. Travis has created two new files, partition_options.py and 
> tableau_options.py, in the sage/combinat directory. *
> 
>     Question*: is this cluttering the file space too much?
> 
>     Given the number of partition and tableau files floating around already 
> perhaps it would have been better to have sage/combinat/partition and 
> sage/combinat/tableau directories from the start.
>     Changing this now would be a deprecation nightmare, however. In any case, 
> I do think that we should think twice when creating new files.
> 
>     With regards to partition_options and tableau_options I think there are 
> three obvious alternatives:
>       * keep them as separate files (as done currently)
>       * move them into partition.py and tableau.py, respectively
>         (argument against: the both affect classes outside of these files)
>       * create a separate options.py file which contains all of the global 
> options.
> 
> 
>     In the long term, it would be good to come up a with a general mechanism 
> to streamline the way options work for optionable classes.

Why would the move of all files related to partitions to a directory
/combinat/partitions/ result into deprecations? For example, crystals are
in a directory, but the user does not know that. The user just says

sage: CrystalsOfTableaux

All you would need to do is to change the all.py files to point Partitions
to the right file, but I think the user interface would not change at all.
I hope I am not wrong! If this is the case, then I would be in favor in
creating a new directory.

>  2. Similarly, there are now separate entries in the manual for partition and 
> tableau options (actually, the latter doesn't exist yet). This is probably 
> OK, however, I think it would work better if
>     there was a section in the reference manual for "Partitions and partition 
> like objects" which would have Partitions, Partition options, 
> PartitionTuples, etc as subheadings.
> 
>     *Question*: should we reorganise partitions in the manual?

Yes!

>  3. Some more mundane questions:
> 
>       * The patch provides two options "convention" and "notation" both of 
> which are for choosing between the English and French conventions for drawing 
> Young diagrams and tableaux. I don't see any
>         value in having two names for the same thing. I suggest dropping 
> "notation".
> 
>         *Question*: should we use "convention", "notation" or both?
> 
>         Btw, this is a shared option for partitions and tableaux.

I would vote to only use "convention".

>       * The new display option allows the following behaviour in sage:
> 
>         sage: Partitions().options(display="compact")
>         sage: Partition([4,4,3,3,2,1,1])
>         1^2,2,3^2,4^2
>         sage: mu=Partition([4,4,3,3,2,1,1])
>         sage: Partitions().options(display="compact"); mu
>         1^2,2,3^2,4^2
>         sage: Partitions().options(display="compact_high"); mu
>         4^2,3^2,2,1^2
>         sage: Partitions().options(display="exp"); mu
>         1^2, 2, 3^2, 4^2
>         sage: Partitions().options(display="exp_high"); mu
>         4^2, 3^2, 2, 1^2
> 
>         I always read the parts of partitions in weakly decreasing order so 
> the defaults for "compact" and "exp" look wrong: I would prefer to make the 
> default behaviour display weakling decreasing
>         sequences here and having compact_low and exp_low options.
> 
>         Note: Travis prefers the current behaviour - although the "compact" 
> option currently available in  5.5 is equivalent to compact_high above.
> 
>         *Question*: should the default for these options be weakling 
> decreasing or weakly increasing?

I do not have Stanley's enumerative combinatorics under hand, but I think we
should use the convention he uses in his book as the default.

Best,

Anne

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