TropicalMinPlus is ordered wrong.

[samuelsonric]

The largest element of the TropicalMinPlus algebra is -Inf. Hence, the ordering should be the opposite of the usual one!

$$-\infty > 3 > 0 > \infty$$

[GiggleLiu]

It depends on how to define "order" here? I am happy to change the definition if you find any literature.

[samuelsonric]

Hi @GiggleLiu. Tropical semirings have a canonical partial ordering, defined by

$$x \leq y \iff x + y = y.$$

See for example, the bottom of page 6 of this standard reference:

The Maslov Dequantization, Idempotent and Tropical Mathematics

The canonical ordering of the min-plus semiring is the opposite of the usual one! Notice that the canonical ordering agrees with your definition of typemin, which is otherwise a little unintuitive.

Base.typemin(::Type{TropicalMinPlus{T}}) where T = TropicalMinPlus(posinf(T))

[GiggleLiu]

Sounds reasonable. Please feel free to make a PR, I will be happy to accept and tag a new version.

[samuelsonric]

#16

[GiggleLiu]

Bumped a patch version: JuliaRegistries/General#141673