IMO permutations should maintain the following invariant: for any vector
v,
isequal(map(i -> getindex(v,i), collect(permutations(1:length(v)))),
collect(permutations(v)))
Bringing equality and uniqueness into the issue disposes of this
property, which is desirable in many applications.
Best,
Tamas
On Mon, Nov 23 2015, Glen O <gjo1...@gmail.com> wrote:
> Logically, the same definition being used by "unique" would be applied,
> unless specified otherwise (which should also be available for unique -
> it's silly that you can't specify the level of inequality necessary for
> uniqueness).
>
> Incidentally, in the example you gave, unique gives
> [0.0,-0.0,NaN,Foo(),Bar(NaN),Bar(NaN)]
>
> On Monday, 23 November 2015 05:08:12 UTC+10, Tamas Papp wrote:
>>
>> Also, "unique" permutations require a notion of equality, and which is
>> hard to define in general (classic essay is [1], about Common Lisp,
>> but applies to Julia mutatis mutandis). At least Julia has bits types
>> for numbers, which makes life a bit easier.
>>
>> Whether one picks is, isequal, or == for comparison, it easy to come up
>> with cases which go against user expectations (at least for some
>> users). For example, given
>>
>> type Foo end
>> type Bar x end
>>
>> what should be the unique permutations of
>>
>> [0.0,-0.0,NaN,NaN,Foo(),Foo(),Bar(NaN),Bar(NaN)]
>>
>> ?
>>
>> Best,
>>
>> Tamas
>>
>> [1] http://www.nhplace.com/kent/PS/EQUAL.html
>>
>> On Sun, Nov 22 2015, Ratan Sur <ratan...@gmail.com <javascript:>> wrote:
>>
>> > I think julia more than other languages has a tendency to stick with
>> > mathematical consistency over some user preferences, which is good. For
>> > that reason, I would be in favor of permutations remaining as is but
>> having
>> > multiset_permutations renamed to something more intuitive, like
>> > uniqueperms, or unique_permutations.
>> >
>> > On Sun, Nov 22, 2015 at 2:16 AM Glen O <gjo...@gmail.com <javascript:>>
>> wrote:
>> >
>> >> While it is true that an interpretation of arrays is multisets, that's
>> not
>> >> the only reasonable interpretation. And while the strict interpretation
>> of
>> >> "permutations" suggests it should include duplicates, you have to
>> consider
>> >> what the user would most likely expect it to do. Most would think that
>> a
>> >> list of the permutations would include unique permutations only.
>> >>
>> >> So perhaps both functionalities should be available in the same
>> function
>> >> with a keyword argument. At the very least, the description of the
>> function
>> >> should directly inform the user that it's going to give duplicate
>> >> permutations if the array contains repeat elements.
>> >>
>> >> On Saturday, 21 November 2015 04:24:51 UTC+10, Jiahao Chen wrote:
>> >>>
>> >>> The current behavior of permutations is correct and should not be
>> >>> changed. Combinatorially, arrays are multisets, not sets, since they
>> allow
>> >>> for duplicate entries, so it is correct to produce what look like
>> identical
>> >>> permutations. The redundancy is important for operations that can be
>> >>> expressed as sums over all permutations.
>> >>>
>> >>> Combinatorics.jl currently provides multiset_permutations for
>> generating
>> >>> only distinct permutations:
>> >>>
>> >>>
>> >>>
>> https://github.com/JuliaLang/Combinatorics.jl/blob/3c08c9af9ebeaa54589e939c0cf2e652ef4ca6a0/test/permutations.jl#L24-L25
>> >>>
>> >>
>>
>>
