https://github.com/saschatimme/tropicalsemiring.jl

Computations in the tropical semi-ring (either max or min convention)
https://github.com/saschatimme/tropicalsemiring.jl

Last synced: about 2 months ago
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Computations in the tropical semi-ring (either max or min convention)

• Host: GitHub
• URL: https://github.com/saschatimme/tropicalsemiring.jl
• Owner: saschatimme
• License: other
• Created: 2018-07-06T16:02:31.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2018-07-10T09:01:51.000Z (over 6 years ago)
• Last Synced: 2024-11-12T00:27:27.233Z (about 2 months ago)
• Language: Julia
• Homepage:
• Size: 12.7 KB
• Stars: 2
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# TropicalSemiring

[![Build Status](https://travis-ci.org/saschatimme/TropicalSemiring.jl.svg?branch=master)](https://travis-ci.org/saschatimme/TropicalSemiring.jl)

![Codecov branch][codecov-img]

This small package defines the tropical semi-ring with either the max or min convention.

With the max convention this is the semi-ring (ℝ ∪ {-∞}, ⊕, ⊙) where

⊕ is the usual multiplication and ⊙ is the usual maximum.

With the min convention this is the semi-ring (ℝ ∪ {∞}, ⊕, ⊙) where

⊕ is the usual multiplication and ⊙ is the usual minimum.

This corresponding Julia type is

```julia

Trop{MM<:Union{Min, Max}, T<:Real} <: Number

```

For the tropical addition and multiplication the usual `+` and `*` are overloaded.

```julia

julia> Trop{Max}(2) + Trop{Max}(3) == Trop{Max}(3)

true

julia> Trop{Min}(2) + Trop{Min}(3) == Trop{Min}(2)

true

julia> Trop{Min}(2) * Trop{Min}(3) == Trop{Min}(5)

true

julia> Trop{Max}(2) * Trop{Max}(3) == Trop{Max}(5)

true

```

Note that by default we use the **max convention**, i.e.,

```julia

julia> Trop(2) + Trop(3)

3

```

You can construct ±∞ by using the `inf` method

```julia

julia> inf(Max) isa Trop{Max}

true

julia> Trop{Max}(2) + inf(Max)

-∞

julia> inf(Min) isa Trop{Min}

true

julia> Trop{Min}(2) + inf(Min)

∞

# By default we have again the max convention

julia> inf() isa Trop{Max}

true

```

[codecov-img]: http://codecov.io/github/saschatimme/TropicalSemiring.jl/coverage.svg?branch=master

[codecov-url]: http://codecov.io/github/saschatimme/TropicalSemiring.jl?branch=master