Random subquotient module elements and homomorphisms #3122
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src/Modules/ModulesGraded.jl
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| function all_partitions_in(n, k) | ||
| if k == 0 | ||
| return n == 0 ? [Int[]] : [] | ||
| end | ||
| partitions = Vector{Int}[] | ||
| for i in 0:n | ||
| for p in all_partitions_in(n - i, k - 1) | ||
| push!(partitions, [i; p]) | ||
| end | ||
| end | ||
| return partitions | ||
| end |
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This should not live here, but in src/Combinatorics as it can be applied elsewhere. One day, it can then be replaced by the implementation in experimental/JuLie/src/partitions.jl.
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Yes, I don't mind to shift it and make it available. We will also expand on it. As far as I understood JuLi does partitiions in the sorted sense. This here is what is usually called compositions. So I renamed it.
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Thanks for moving!
However, I think that this should either include a docstring as well, or shouldn't get exported (or maybe even both for now).
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For example, changing this later to ZZRingElem instead of Int would be an unnecessary breaking change, so I would rather keep this internal until an interface has been settled. (With talking to people interested in combinatorics like Uli Thiel)
Codecov Report
Additional details and impacted files@@ Coverage Diff @@
## master #3122 +/- ##
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Coverage 80.61% 80.61%
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Files 527 528 +1
Lines 70721 70766 +45
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+ Hits 57009 57051 +42
- Misses 13712 13715 +3
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src/Combinatorics/Compositions.jl
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| function weak_compositions(n, k) | ||
| if k == 0 | ||
| return n == 0 ? [Int[]] : [] |
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| return n == 0 ? [Int[]] : [] | |
| return n == 0 ? [Int[]] : Vector{Int}[] |
src/Combinatorics/Compositions.jl
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| function compositions(n, k) | ||
| if k == 0 | ||
| return n == 0 ? [Int[]] : [] |
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| return n == 0 ? [Int[]] : [] | |
| return n == 0 ? [Int[]] : Vector{Int}[] |
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Would have been better to not export this. Not sure this is compatible with the rest of the combinatorics. |
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It also has no docstring. |
Random homogeneous elements of modules, in particular random homomorphisms. Limited to finite base rings, for the moment. What is here already does what we need currently for certain constructions in algebraic geometry. We will expand on it further.