Fix integer partitions

[jessebett]

This would close #79 #80 and #81.

Solution is due to @simonschoelly.

Note that integer_partitions is still implemented, but now just collects partitions(n::Int). However, this implementation now returns the partitions in reverse order as before, so this would be a breaking change! Probably best to just remove integer_partitions

Also, partitions(0) now correctly returns the set containing the empty set and is the same as what's returned by integer_partitions(0), which was not the case before.

[codecov-io]

Codecov Report

Merging #82 into master will increase coverage by 18.72%. The diff coverage is 100%.

@@             Coverage Diff             @@
##           master      #82       +/-   ##
===========================================
+ Coverage   75.51%   94.23%   +18.72%     
===========================================
  Files           7        7               
  Lines         637      503      -134     
===========================================
- Hits          481      474        -7     
+ Misses        156       29      -127

Impacted Files	Coverage Δ
src/partitions.jl	97.43% <100%> (+21.72%)	:arrow_up:
src/numbers.jl	100% <0%> (+14.66%)	:arrow_up:
src/combinations.jl	80.64% <0%> (+15.98%)	:arrow_up:
src/multinomials.jl	88.88% <0%> (+16.16%)	:arrow_up:
src/permutations.jl	97.64% <0%> (+17.06%)	:arrow_up:
src/youngdiagrams.jl	93.93% <0%> (+19.24%)	:arrow_up:
src/factorials.jl	100% <0%> (+23.07%)	:arrow_up:

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[mschauer]

@jessebett

[mschauer]

What do we do with this? Can we make this non-breaking?

[jessebett]

@mschauer sorry this was lost in my github notifications. To answer your question, I don't know how to make it non-breaking. Not sure why integer_partitions was ever implemented in the first place, let alone to have a completely different behaviour than partitions(n::Int) (referring to the reversed order, not the iterator vs array).

So, seems to me this should be a breaking change to remove the integer_partitions. I am not familiar with the preferred procedure for this, but we could give it a deprecation notice and also have it call collect(reverse(partitions(n::Int))) in the back-end?

[mschauer]

I would opt for deprecate it and keep it doing what it did before instead of collecting partitions(n::Int)

[jessebett]

Agreed.