Sylvester.AbstractAlgebra 0.2.5

.NET Standard 2.0 .NET Framework 4.5

dotnet add package Sylvester.AbstractAlgebra --version 0.2.5

NuGet\Install-Package Sylvester.AbstractAlgebra -Version 0.2.5

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="0.2.5" />

For projects that support PackageReference, copy this XML node into the project file to reference the package.

<PackageVersion Include="Sylvester.AbstractAlgebra" Version="0.2.5" />
                    

                            Directory.Packages.props

<PackageReference Include="Sylvester.AbstractAlgebra" />
                    

                            Project file

For projects that support Central Package Management (CPM), copy this XML node into the solution Directory.Packages.props file to version the package.

paket add Sylvester.AbstractAlgebra --version 0.2.5

The NuGet Team does not provide support for this client. Please contact its maintainers for support.

#r "nuget: Sylvester.AbstractAlgebra, 0.2.5"

#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package.

#addin nuget:?package=Sylvester.AbstractAlgebra&version=0.2.5
                    

                            Install Sylvester.AbstractAlgebra as a Cake Addin

#tool nuget:?package=Sylvester.AbstractAlgebra&version=0.2.5
                    

                            Install Sylvester.AbstractAlgebra as a Cake Tool

The NuGet Team does not provide support for this client. Please contact its maintainers for support.

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
#load "Paket.fsx"
Paket.Package["Sylvester.AbstractAlgebra"] 
#load "Paket.Generated.Refs.fsx"

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))
let pad = Pad.Map
pad a

S "               Nancy"

// Is pad a homomorphism?
pad a + pad b

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	Compatible and additional computed target framework versions.
.NET	net5.0 was computed. net5.0-windows was computed. net6.0 was computed. net6.0-android was computed. net6.0-ios was computed. net6.0-maccatalyst was computed. net6.0-macos was computed. net6.0-tvos was computed. net6.0-windows was computed. net7.0 was computed. net7.0-android was computed. net7.0-ios was computed. net7.0-maccatalyst was computed. net7.0-macos was computed. net7.0-tvos was computed. net7.0-windows was computed. net8.0 was computed. net8.0-android was computed. net8.0-browser was computed. net8.0-ios was computed. net8.0-maccatalyst was computed. net8.0-macos was computed. net8.0-tvos was computed. net8.0-windows was computed. net9.0 was computed. net9.0-android was computed. net9.0-browser was computed. net9.0-ios was computed. net9.0-maccatalyst was computed. net9.0-macos was computed. net9.0-tvos was computed. net9.0-windows was computed.
.NET Core	netcoreapp2.0 was computed. netcoreapp2.1 was computed. netcoreapp2.2 was computed. netcoreapp3.0 was computed. netcoreapp3.1 was computed.
.NET Standard	netstandard2.0 is compatible. netstandard2.1 was computed.
.NET Framework	net45 is compatible. net451 was computed. net452 was computed. net46 was computed. net461 was computed. net462 was computed. net463 was computed. net47 was computed. net471 was computed. net472 was computed. net48 was computed. net481 was computed.
MonoAndroid	monoandroid was computed.
MonoMac	monomac was computed.
MonoTouch	monotouch was computed.
Tizen	tizen40 was computed. tizen60 was computed.
Xamarin.iOS	xamarinios was computed.
Xamarin.Mac	xamarinmac was computed.
Xamarin.TVOS	xamarintvos was computed.
Xamarin.WatchOS	xamarinwatchos was computed.

Compatible target framework(s)

Included target framework(s) (in package)

Learn more about Target Frameworks and .NET Standard.

.NETFramework 4.5
- FSharp.Core (>= 4.3.4)
- FSharpPlus (>= 1.0.0)
- Sylph (>= 0.2.5.2)
- Sylvester.Collections (>= 0.2.3)
- System.ValueTuple (>= 4.4.0)
.NETStandard 2.0
- FSharp.Core (>= 4.3.4)
- FSharpPlus (>= 1.0.0)
- Sylph (>= 0.2.5.2)
- Sylvester.Collections (>= 0.2.3)

NuGet packages

This package is not used by any NuGet packages.

GitHub repositories

This package is not used by any popular GitHub repositories.

Version	Downloads	Last updated
0.2.5	646	5/3/2020
0.2.3.2	532	3/24/2020
0.2.3.1	510	3/24/2020
0.2.3	533	3/24/2020
0.2.1.2	577	1/29/2020
0.2.1.1	571	1/29/2020
0.2.1	579	1/29/2020

Update to latest Sylph version.