asc-community / Angourimath

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));

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("x2 + 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(
    "x2 + 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);

Find derivatives:

Entity func = "x2 + ln(cos(x) + 3) + 4x";
Entity derivative = func.Differentiate("x");
Console.WriteLine(derivative.Simplify());

Find limits:

WriteLine("(a x2 + b x) / (e x - h x2 - 3)".Limit("x", "+oo").InnerSimplified);

Find integrals:

WriteLine("x2 + a x".Integrate("x").InnerSimplified);

There are four types of sets:

WriteLine("{ 1, 2 }".Latexise());
WriteLine("[3; +oo)".Latexise());
WriteLine("RR".Latexise());
WriteLine("{ x : x8 + a x < 0 }".Latexise());

And there operators:

WriteLine(@"A \/ B".Latexise());
WriteLine(@"A /\ B".Latexise());
WriteLine(@"A \ B".Latexise());

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 * (...)

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

Download

Not everything is supported directly from F#, so if something missing, you will need to address that functional from AngouriMath.

open Functions
open Operators
open FromToString


solve "x" "x + 2 = 0"

simplify (solve "x" "x2 + 2 a x + a2 = 0")

differentiate "x" "x2 + a x"

integrate "x" "x2 + e"

limit "x" "0" "sin(a x) / x"

"sin(a x) / x" &&& "x" --> 0

latex "x / e + alpha + sqrt(x) + integral(y + 3, y, 1)"

If you already installed Jupyter and Interactive for it, install package by copying this to your first cell:

#r "nuget:AngouriMath.Interactive, *-*"
Interactive.magic();

Now any ILatexiseable will be displayed as LaTeX:

Check the F# and C# samples.

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<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";
}