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Based on the "Mathematics" category.
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README
AngouriMath
New opensource crossplatform symbolic algebra library for C# 路 F# 路 Jupyter 路 C++ (WIP) Get started 路 Examples 路 Contributions 路 What's new 路 Website
Status board
Builds and tests
Kernel/C#  F#  Interactive  C++  

Build  
Test 
Note, that all tests and builds are tested for the following three operating systems: Windows, Ubuntu, Mac OS.
Coverage
Kernel/C#  F#  C++ 

???  ??? 
Versions
Prerelease  Stable  Downloads  

Kernel/C#  
F#  
Interactive  
Experimental  
Terminal  
C++  WIP  WIP 
There are also latestmaster versions (updated on every push to master) on MyGet:  MyGet  Downloads              
Source to install from MyGet:
https://www.myget.org/F/angourimath/api/v3/index.json
Other info
Website  Stars  License 

If you want, you can add a badge to your repo:
[![Powered by AngouriMath](https://img.shields.io/badge/Powered%20byAngouriMathpurple?style=flatsquare&labelColor=646)](https://am.angouri.org)
What is it about?
AngouriMath is an open source symbolic algebra library. That is, via AngouriMath, you can automatically solve equations, systems of equations, differentiate, parse from string, compile expressions, work with matrices, find limits, convert an expression to LaTeX, and many other things.
Where can be used?
The two areas of use:
馃И Research / Data Science [click 馃柋锔廬
AngouriMath for research
As F#, great firstfunctional language, skyrocketing in the area of data analysis and interactive research, AngouriMath offers a few ways to conveniently work with symbolic expressions.
Notebooks
[gif](./.github/additional/readme/vscnotebook.gif)
Notebooks provide amazing experience working with function visualization, for functions over one and two variables. With dotnet/interactive, it can be used in Visual Studio Code notebooks as well as Jupyter notebooks. To install the package, simply run this in the notebook:
#r "nuget:AngouriMath.Interactive,**"
Terminal
[[gif](./Sources/Terminal/terminal.gif)](./Sources/Terminal)
As both a demonstration sample and a convenient tool, this repository includes tool called AngouriMath.Terminal. It is a CLIbased program to interact with AngouriMath (as opposed to APIbased interaction, that is, consuming it as a lib).
Or build from sources:
git clone https://github.com/asccommunity/AngouriMath
cd AngouriMath/Sources/Terminal/AngouriMath.Terminal
dotnet run c release
See the online Jupyter notebook on
how to use the F# API of AngouriMath. Note, that the C# API is still available
via open AngouriMath
command, then you can call the main library's methods.
See its [source folder](./Sources/Terminal).
More
Read more about using AngouriMath for research on the website.
馃捇 Software Development [click 馃柋锔廬
It is installed from nuget for both C# and F# and can be used by Web/Desktop/Mobile development.
Installing the library
 Install AngouriMath from NuGet.
 Write the following code:
cs using AngouriMath; using System; Entity expr = "x + sin(y)"; Console.WriteLine(expr);
 Run.
More detailed Quick Start.
If you are new to AM, we suggest you checking out some samples instead of reading boring documentation. If you want to contribute, we would be happy to welcome you in our community.
For any questions, feel free to contact us via Discord.
Official website: am.angouri.org.
Examples
Expand any section to see. Examples with live shell are on the website.
Computations
Use as a simple calculator:
Entity expr = "1 + 2 * log(3, 9)";
Console.WriteLine(expr.EvalNumerical());
Console.WriteLine("2 / 3 + sqrt(16)".EvalNumerical());
>>> 2 / 3 + 4i
Console.WriteLine("(2) ^ 3".EvalNumerical());
Build expressions with variables and substitute them:
Entity expr = "2x + sin(x) / sin(2 ^ x)";
var subs = expr.Substitute("x", 0.3m);
Console.WriteLine(subs);
Simplify complicated expressions:
Console.WriteLine("2x + x + 3 + (4 a * a^6) / a^3 / 5".Simplify());
var expr = "1/2 + sin(pi / 4) + (sin(3x)2 + cos(3x)2)";
Console.WriteLine(expr.Simplify());
Compiled functions work 15x+ faster
var x = MathS.Variable("x");
var expr = MathS.Sin(x) + MathS.Sqrt(x) / (MathS.Sqrt(x) + MathS.Cos(x)) + MathS.Pow(x, 3);
var func = expr.Compile(x);
Console.WriteLine(func.Substitute(3));
var expr = "sin(x) + sqrt(x) / (sqrt(x) + cos(x)) + x3";
var compiled = expr.Compile("x");
Console.WriteLine(compiled.Substitute(4));
Algebra
Start with boolean algebra:
Entity expr1 = "a and b or c";
// Those are the same
Entity expr3 = "a > b";
Entity expr3 = "a implies b";
Entity expr = "a > true";
Console.WriteLine(MathS.SolveBooleanTable(expr, "a"));
>>> Matrix[2 x 1]
>>> False
>>> True
Next, solve some equations:
Console.WriteLine("x^2 + x + a".SolveEquation("x"));
Under developing now and forever (always available)
Entity expr = "(sin(x)^2  sin(x) + a)(b  x)((3) * x + 2 + 3 * x ^ 2 + (x + (3)) * x ^ 3)";
Console.WriteLine(expr.SolveEquation("x").Latexise());
Try some inequalities:
Console.WriteLine("(x  6)(x + 9) >= 0".Solve("x"));
Systems of equations:
var system = MathS.Equations(
"x^2 + y + a",
"y  0.1x + b"
);
Console.WriteLine(system);
var solutions = system.Solve("x", "y");
Console.WriteLine(solutions);
System:
Result:
var system = MathS.Equations(
"cos(x2 + 1)^2 + 3y",
"y * (1) + 4cos(x2 + 1)"
);
Console.WriteLine(system.Latexise());
var solutions = system.Solve("x", "y");
Console.WriteLine(solutions);
(solution matrix is too complicated to show)
Calculus
Find derivatives:
Entity func = "x^2 + ln(cos(x) + 3) + 4x";
Entity derivative = func.Differentiate("x");
Console.WriteLine(derivative.Simplify());
Find limits:
WriteLine("(a x^2 + b x) / (e x  h x^2  3)".Limit("x", "+oo").InnerSimplified);
Find integrals:
WriteLine("x^2 + a x".Integrate("x").InnerSimplified);
Sets
There are four types of sets:
WriteLine("{ 1, 2 }".Latexise());
WriteLine("[3; +oo)".Latexise());
WriteLine("RR".Latexise());
WriteLine("{ x : x^8 + a x < 0 }".Latexise());
And there operators:
WriteLine(@"A \/ B".Latexise());
WriteLine(@"A /\ B".Latexise());
WriteLine(@"A \ B".Latexise());
Syntax
You can build LaTeX with AngouriMath:
var expr = "x ^ y + sqrt(x) + integral(sqrt(x) / a, x, 1) + derive(sqrt(x) / a, x, 1) + limit(sqrt(x) / a, x, +oo)";
Console.WriteLine(expr.Latexise());
>>> {x}^{y}+\sqrt{x}+\int \left[\frac{\sqrt{x}}{a}\right] dx+\frac{d\left[\frac{\sqrt{x}}{a}\right]}{dx}+\lim_{x\to \infty } \left[\frac{\sqrt{x}}{a}\right]
You can parse Entity
from string with
var expr = MathS.FromString("x + 2 + sqrt(x)");
Entity expr = "x + 2 + sqrt(x)";
A few convenient features: x2
=> x^2
, a x
=> a * x
, (...)2
=> (...)^2
, 2(...)
=> 2 * (...)
Compilation
Now you can compile expressions with pritimives into native lambdas. They will be at least as fast as if you wrote them in line in code, or faster if you have same subexpressions in your expression.
Entity expr = "a and x > 3";
var func = expr.Compile<bool, double, bool>("a", "x");
WriteLine(func(true, 6));
WriteLine(func(false, 6));
WriteLine(func(true, 2));
WriteLine(func(false, 2));
Output:
True
False
False
False
Multithreading
You are guaranteed that all functions in AM run in one thread. It is also guaranteed that you can safely run multiple functions from AM in different threads, that is, all static variables and lazy properties are threadsafe.
There is also support of cancellation a task. However, to avoid injecting the cancellation token argument into all methods,
we use AsyncLocal<T>
instead. That is why instead of passing your token to all methods what you need is to pass it once
to the MathS.Multithreading.SetLocalCancellationToken(CancellationToken)
method.
There is a sample code demonstrating cancellation:
var cancellationTokenSource = new CancellationTokenSource();
// That goes instead of passing your token to methods
MathS.Multithreading.SetLocalCancellationToken(cancellationTokenSource.Token);
// Then you normally run your task
var currTask = Task.Run(() => InputText.Text.Solve("x"), cancellationTokenSource.Token);
try
{
await currTask;
LabelState.Text = currTask.Result.ToString();
}
catch (OperationCanceledException)
{
LabelState.Text = "Operation canceled";
}
F#
Download
Not everything is supported directly from F#, so if something missing, you will need to call the necessary methods from AngouriMath.
open Functions
open Operators
open Shortcuts
printfn "%O" (solutions "x" "x + 2 = 0")
printfn "%O" (simplified (solutions "x" "x^2 + 2 a x + a^2 = 0"))
printfn "%O" (``dy/dx`` "x^2 + a x")
printfn "%O" (integral "x" "x2 + e")
printfn "%O" (``lim x>0`` "sin(a x) / x")
printfn "%O" (latex "x / e + alpha + sqrt(x) + integral(y + 3, y, 1)")
C++ (Experimental)
At the moment, AngouriMath.CPP is in the experimental phase. See how to get AngouriMath for C++.
#include <AngouriMath.h>
int main()
{
AngouriMath::Entity expr = "x y + 2";
std::cout << expr.Differentiate("x");
}
Contribution
AngouriMath is a free opensource project, there is no big company backing us. That is why we warmly welcome any contributors to the project. Aside from volunteer donations, you can help developing the project: check the [guide for developers](./CONTRIBUTING.md).
License & citation
The project is open source, but can be used in closed commercial projects. There is no restriction on it with the only requirement to keep the MIT license with all distributives of AngouriMath.
*Note that all licence references and agreements mentioned in the AngouriMath README section above
are relevant to that project's source code only.