tropical determinant via Hungarian method

[micjoswig]

The previous implementation (via Leibniz' rule) was not useful. It is now replaced via polymake's implementation of the Hungarian method.

To see the difference, here are two computations with v.1.1.1:

julia> @time det(matrix(tropical_semiring(), rand(0:9, 100, 100)))
ERROR: OverflowError: 100 is too large to look up in the table; consider using `factorial(big(100))` instead
Stacktrace:
 [1] factorial_lookup
   @ ./combinatorics.jl:19 [inlined]
 [2] factorial
   @ ./combinatorics.jl:27 [inlined]
 [3] AbstractAlgebra.Generic.AllPerms(n::Int64)
   @ AbstractAlgebra.Generic ~/.julia/packages/AbstractAlgebra/EYoda/src/generic/GenericTypes.jl:57
 [4] iterate
   @ ~/.julia/packages/AbstractAlgebra/EYoda/src/generic/PermGroups.jl:634 [inlined]
 [5] det(A::AbstractAlgebra.Generic.MatSpaceElem{TropicalSemiringElem{typeof(min)}})
   @ Oscar ~/.julia/packages/Oscar/38HwK/src/TropicalGeometry/matrix.jl:35
 [6] macro expansion
   @ ./timing.jl:279 [inlined]
 [7] top-level scope
   @ ./REPL[10]:1

julia> @time Polymake.tropical.tdet(matrix(tropical_semiring(), rand(0:9, 100, 100)))
  0.016758 seconds (328.42 k allocations: 3.419 MiB, 22.80% compilation time)
pm::TropicalNumber<pm::Min, pm::Rational>
0

[YueRen]

A very welcome change!

[micjoswig]

@danteluber please have a look

code overhauled, will start new review once tests are through

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.01%. Comparing base (71c1f3e) to head (7d0e8c7).
Report is 10 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3943      +/-   ##
==========================================
+ Coverage   84.00%   84.01%   +0.01%     
==========================================
  Files         592      592              
  Lines       81624    81672      +48     
==========================================
+ Hits        68566    68616      +50     
+ Misses      13058    13056       -2     

Files	Coverage Δ
src/TropicalGeometry/matrix.jl	100.00% <100.00%> (ø)

... and 18 files with indirect coverage changes

[YueRen]

Everything looks great. Thanks for this very useful feature!