# Sylvester.AbstractAlgebra 0.2.3

.NET Standard 2.0 .NET Framework 4.5
There is a newer version of this package available.
See the version list below for details.
`dotnet add package Sylvester.AbstractAlgebra --version 0.2.3`
`NuGet\Install-Package Sylvester.AbstractAlgebra -Version 0.2.3`
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package.
`<PackageReference Include="Sylvester.AbstractAlgebra" Version="0.2.3" />`
For projects that support PackageReference, copy this XML node into the project file to reference the package.
`paket add Sylvester.AbstractAlgebra --version 0.2.3`
`#r "nuget: Sylvester.AbstractAlgebra, 0.2.3"`
#r directive can be used in F# Interactive, C# scripting and .NET Interactive. Copy this into the interactive tool or source code of the script to reference the package.
```// Install Sylvester.AbstractAlgebra as a Cake Addin

// Install Sylvester.AbstractAlgebra as a Cake Tool
#tool nuget:?package=Sylvester.AbstractAlgebra&version=0.2.3```

## Sylvester.AbstractAlgebra

The Sylvester abstract algebra library contains types and operations for rigorously defining abstract algebra structures and concepts.

``````// Use the Sylvester abstract algebra package
Paket.Package["Sylvester.AbstractAlgebra"]

open System
open System.Linq
open Sylvester
``````

### Morphisms

``````// Define a custom symbol type S with a (+) operator and zero
// We could just also use plain strings
type S = S of string with
static member (+) (S l, S r) = S (l + r)
static member Zero = S ""

// Define an infinite sequence of L strings
let Sym = infiniteSeq ((+) 65 >> Char.ConvertFromUtf32 >> S)
Sym
``````
``````// Define a monoid using our set and + operator and zero element
let L = Monoid(Sym, (+), S.Zero)
L
``````
``````seq
[(S "A", S "B", S "AB"); (S "B", S "C", S "BC"); (S "C", S "D", S "CD");
(S "D", S "E", S "DE"); ...]
``````
``````// Create 2 S values
let a, b = S "Nancy", S "Drew"
a + b
``````
``````S "NancyDrew"
``````
``````// Create a L morphism using the PadLeft string function
let Pad = Morph(L, fun l -> let (S s) = l in S(s.PadLeft 20))
``````
``````S "               Nancy"
``````
``````// Is pad a homomorphism?
``````
``````S "               Nancy                Drew"
``````
``````pad (a + b)
``````
``````S "           NancyDrew"
``````
``````pad a + pad b = pad (a + b)
``````
``````false
``````

### Rings

``````Zpos
``````
``````seq [(0, 1, 1); (1, 2, 3); (2, 3, 5); (3, 4, 7); ...]
``````

### Subsets

``````let s = seq{1..6} |> Set.ofSubsets
s
``````
``````Seq
[|Empty; Seq [|1|]; Seq [|2|]; Seq [|1; 2|]; Seq [|3|]; Seq [|1; 3|];
Seq [|2; 3|]; Seq [|1; 2; 3|]; Seq [|4|]; Seq [|1; 4|]; Seq [|2; 4|];
Seq [|1; 2; 4|]; Seq [|3; 4|]; Seq [|1; 3; 4|]; Seq [|2; 3; 4|];
Seq [|1; 2; 3; 4|]; Seq [|5|]; Seq [|1; 5|]; Seq [|2; 5|]; Seq [|1; 2; 5|];
Seq [|3; 5|]; Seq [|1; 3; 5|]; Seq [|2; 3; 5|]; Seq [|1; 2; 3; 5|];
Seq [|4; 5|]; Seq [|1; 4; 5|]; Seq [|2; 4; 5|]; Seq [|1; 2; 4; 5|];
Seq [|3; 4; 5|]; Seq [|1; 3; 4; 5|]; Seq [|2; 3; 4; 5|];
Seq [|1; 2; 3; 4; 5|]; Seq [|6|]; Seq [|1; 6|]; Seq [|2; 6|];
Seq [|1; 2; 6|]; Seq [|3; 6|]; Seq [|1; 3; 6|]; Seq [|2; 3; 6|];
Seq [|1; 2; 3; 6|]; Seq [|4; 6|]; Seq [|1; 4; 6|]; Seq [|2; 4; 6|];
Seq [|1; 2; 4; 6|]; Seq [|3; 4; 6|]; Seq [|1; 3; 4; 6|]; Seq [|2; 3; 4; 6|];
Seq [|1; 2; 3; 4; 6|]; Seq [|5; 6|]; Seq [|1; 5; 6|]; Seq [|2; 5; 6|];
Seq [|1; 2; 5; 6|]; Seq [|3; 5; 6|]; Seq [|1; 3; 5; 6|]; Seq [|2; 3; 5; 6|];
Seq [|1; 2; 3; 5; 6|]; Seq [|4; 5; 6|]; Seq [|1; 4; 5; 6|];
Seq [|2; 4; 5; 6|]; Seq [|1; 2; 4; 5; 6|]; Seq [|3; 4; 5; 6|];
Seq [|1; 3; 4; 5; 6|]; Seq [|2; 3; 4; 5; 6|]; Seq [|1; 2; 3; 4; 5; 6|]|]
``````

### Lattices

``````
let lat = Lattice(s, (|+|), (|*|))
lat
``````
``````Sylvester.Lattice`1[Sylvester.Set`1[System.Int32]]
``````
``````
``````
Product Versions
.NET net5.0 net5.0-windows net6.0 net6.0-android net6.0-ios net6.0-maccatalyst net6.0-macos net6.0-tvos net6.0-windows net7.0 net7.0-android net7.0-ios net7.0-maccatalyst net7.0-macos net7.0-tvos net7.0-windows
.NET Core netcoreapp2.0 netcoreapp2.1 netcoreapp2.2 netcoreapp3.0 netcoreapp3.1
.NET Standard netstandard2.0 netstandard2.1
.NET Framework net45 net451 net452 net46 net461 net462 net463 net47 net471 net472 net48
MonoAndroid monoandroid
MonoMac monomac
MonoTouch monotouch
Tizen tizen40 tizen60
Xamarin.iOS xamarinios
Xamarin.Mac xamarinmac
Xamarin.TVOS xamarintvos
Xamarin.WatchOS xamarinwatchos
Compatible target framework(s)

### NuGet packages

This package is not used by any NuGet packages.

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