[!WARNING] AngouriMath is deprecated. You can still use it, but it's unlikely it will go forward. Full story at wbg.gg

AngouriMath

New open-source cross-platform symbolic algebra library for C# · F# · Jupyter · C++ (WIP)
Get started · Examples · Contributions · What's new · Website

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 #### 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 latest-master versions (updated on every push to master) on [MyGet](https://www.myget.org/feed/Packages/angourimath): | MyGet | Downloads | |-------|-----------| | [](https://www.myget.org/feed/angourimath/package/nuget/AngouriMath) |  | | [](https://www.myget.org/feed/angourimath/package/nuget/AngouriMath.FSharp) |  | | [](https://www.myget.org/feed/angourimath/package/nuget/AngouriMath.Interactive) |  | | [](https://www.myget.org/feed/angourimath/package/nuget/AngouriMath.Experimental) |  | 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: ``` [](https://am.angouri.org) ``` [](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:

💻 Software Development _{[click 🖱️]}

It is installed from [nuget](https://am.angouri.org/quickstart/#dotnet) for both C# and F# and can be used by Web/Desktop/Mobile development. ## Installing the library 1. Install AngouriMath from [NuGet](https://www.nuget.org/packages/AngouriMath). 2. Write the following code: ```cs using AngouriMath; using System; Entity expr = "x + sin(y)"; Console.WriteLine(expr); ``` 3. 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](https://am.angouri.org/). ## Examples Expand any section to see. Examples with live shell are on the [website](https://am.angouri.org/).

Computations

Use as a simple calculator: ```cs Entity expr = "1 + 2 * log(3, 9)"; Console.WriteLine(expr.EvalNumerical()); ``` ```cs Console.WriteLine("2 / 3 + sqrt(-16)".EvalNumerical()); >>> 2 / 3 + 4i ``` ```cs Console.WriteLine("(-2) ^ 3".EvalNumerical()); ``` Build expressions with variables and substitute them: ```cs Entity expr = "2x + sin(x) / sin(2 ^ x)"; var subs = expr.Substitute("x", 0.3m); Console.WriteLine(subs); ``` Simplify complicated expressions: ```cs Console.WriteLine("2x + x + 3 + (4 a * a^6) / a^3 / 5".Simplify()); ``` ```cs var expr = "1/2 + sin(pi / 4) + (sin(3x)2 + cos(3x)2)"; Console.WriteLine(expr.Simplify()); ``` Compiled functions work 15x+ faster ```cs 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)); ``` ```cs 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: ```cs Entity expr1 = "a and b or c"; // Those are the same Entity expr3 = "a -> b"; Entity expr3 = "a implies b"; ``` ```cs Entity expr = "a -> true"; Console.WriteLine(MathS.SolveBooleanTable(expr, "a")); ``` ``` >>> Matrix[2 x 1] >>> False >>> True ``` Next, solve some equations: ```cs Console.WriteLine("x^2 + x + a".SolveEquation("x")); ``` Under developing now and forever (always available) ```cs 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: ```cs Console.WriteLine("(x - 6)(x + 9) >= 0".Solve("x")); ``` Systems of equations: ```cs 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: ```cs 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: ```cs Entity func = "x^2 + ln(cos(x) + 3) + 4x"; Entity derivative = func.Differentiate("x"); Console.WriteLine(derivative.Simplify()); ``` Find limits: ```cs WriteLine("(a x^2 + b x) / (e x - h x^2 - 3)".Limit("x", "+oo").InnerSimplified); ``` Find integrals: ```cs WriteLine("x^2 + a x".Integrate("x").InnerSimplified); ```

Sets

There are four types of sets: ```cs WriteLine("{ 1, 2 }".Latexise()); WriteLine("[3; +oo)".Latexise()); WriteLine("RR".Latexise()); WriteLine("{ x : x^8 + a x < 0 }".Latexise()); ``` And there operators: ```cs WriteLine(@"A \/ B".Latexise()); WriteLine(@"A /\ B".Latexise()); WriteLine(@"A \ B".Latexise()); ```

Syntax

You can build LaTeX with AngouriMath: ```cs 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 ```cs 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. ```cs Entity expr = "a and x > 3"; var func = expr.Compile("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 thread-safe. There is also support of cancellation a task. However, to avoid injecting the cancellation token argument into all methods, we use `AsyncLocal` 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: ```cs 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. ```fs 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++. ```cpp #include int main() { AngouriMath::Entity expr = "x y + 2"; std::cout << expr.Differentiate("x"); } ```

Contribution

AngouriMath is a free open-source 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.

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.