The angourimath's intro from scarlet-dev

AngouriMath

AngouriMath is an open-source library that enables to work with non-linear multi-variable expressions. Its functionality includes derivation, variable substitution, equation solving, equation system solving, definite integration, formula-to-latex formatting, working with mathematical sets, and some more.

If you are new to AM, we suggest you checking out some samples instead of reading boring documentation. If you prefer full manual to AM, see Wiki. If you want to contribute, we surely appreciate it, but so far do not have documentation for you. It will appear soon!

Examples

Build an expression

var x = MathS.Var("x");
var y = MathS.Var("y");
var c = x * y + x / y;
Console.WriteLine(MathS.Sqr(c));
>>> (x * y + x / y) ^ 2

Use as a simple calculator

var inp = "1 + 2 * log(3, 9)";
var expr = MathS.FromString(inp);
Console.WriteLine(expr.Eval());
>>> 5

Substitute variables

var x = MathS.Var("x");
var expr = x * 2 + MathS.Sin(x) / MathS.Sin(MathS.Pow(2, x));
var subs = expr.Substitute(x, 0.3);
Console.WriteLine(subs.Eval());
>>> 0,9134260185941638995386706112

Find derivatives

var x = MathS.Var("x");
var func = MathS.Sqr(x) + MathS.Ln(MathS.Cos(x) + 3) + 4 * x;
var derivative = func.Derive(x);
Console.WriteLine(derivative.Simplify());
>>> 4 + (-1) * sin(x) / (cos(x) + 3) + 2 * x

Build expressions faster

Entity expr = "sqr(x + y)";
Console.WriteLine(expr.Expand().Simplify());
>>> x ^ 2 + 2 * x * y + y ^ 2

Simplify

var x = MathS.Var("x");
var a = MathS.Var("a");
var b = MathS.Var("b");
var expr = MathS.Sqrt(x) / x + a * b + b * a + (b - x) * (x + b) + 
    MathS.Arcsin(x + a) + MathS.Arccos(a + x);
Console.WriteLine(expr.Simplify());
>>> 2 * a * b + b ^ 2 + pi / 2 + x ^ (-1 / 2) - x ^ 2

Render latex

var x = MathS.Var("x");
var y = MathS.Var("y");
var expr = x.Pow(y) + MathS.Sqrt(x + y / 4) * (6 / x);
Console.WriteLine(expr.Latexise());
>>> {x}^{y}+\sqrt{x+\frac{y}{4}}\times \frac{6}{x}

Play with complex numbers

var expr = MathS.Pow(MathS.e, MathS.pi * MathS.i);
Console.WriteLine(expr);
Console.WriteLine(expr.Eval());
>>> e ^ (pi * i)
>>> -1

Solve equations analytically

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)";
foreach (var root in expr.Solve("x"))
    Console.WriteLine(root);
>>> arcsin((1 - sqrt(1 + (-4) * a)) / 2) - (-2) * n * pi
>>> 2 * n * pi + pi - arcsin((1 - sqrt(1 + (-4) * a)) / 2)
>>> arcsin(0.5 * (1 + sqrt(1 + (-4) * a))) - (-2) * n * pi
>>> 2 * n * pi + pi - arcsin((1 + sqrt(1 + (-4) * a)) / 2)
>>> b
>>> -i
>>> i
>>> 1
>>> 2

Solve systems of non-linear equations

Under developing now and forever (always available)

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.PrintOut());

Integrate

Only definite integral over single variable is supported yet :(

var x = MathS.Var("x");
var expr = MathS.Sin(x) + MathS.Sqrt(x) / (MathS.Sqrt(x) + MathS.Cos(x)) + MathS.Pow(x, 3);
Console.WriteLine(expr.DefiniteIntegral(x, -3, 3));
var expr2 = MathS.Sin(x);
Console.WriteLine(expr2.DefiniteIntegral(x, 0, MathS.DecimalConst.pi));
>>> 5.56669223384056 + 0.0889406793629381i
>>> 1.98003515236381

Compile functions

Compiled functions work 15x+ faster

var x = MathS.Var("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));

Try new syntax

Entity expr = "3x3 + 2 2 2 - x(3 0.5)";
Console.WriteLine(expr);
>>> 3 * x ^ 3 + 2 ^ 2 ^ 2 - x * sqrt(3)

Work with sets

var A = new Set(3, 4, (5, 6)); // {3, 4} | [5; 6]
var B = new Set((x, MathS.Sqrt(x)), 4);
var C = (A | B) & A;

Try SymPy syntax

var x = SySyn.Symbol("x");
var expr = SySyn.Exp(x) + x;
Console.WriteLine(SySyn.Diff(expr));
Console.WriteLine(SySyn.Diff(expr, x));
Console.WriteLine(SySyn.Diff(expr, x, x));

Work with numbers

var rat1 = Number.CreateRational(3, 4);
var rat2 = Number.CreateRational(5, 6);
Console.WriteLine((rat1 + rat2).ToString());
>>> 19 / 12

Translate number systems

string x = MathS.ToBaseN(-32.25, 4);
Console.WriteLine("-32.25(10) = " + x + "(4)");
double y = MathS.FromBaseN("AB.3", 16);
Console.WriteLine("AB.3(16) = " + y + "(1)");
>>> -32.25(10) = -200.1(4)
>>> AB.3(16) = 171,1875(1)

Performance

Performane improved a lot. Testing on i7-7700HQ and expr = MathS.Sin(x) we get the following report:

Function	Time per iteration
Substitute(x, 3).Eval() from 1.0.13	12000 ns
Substitute(x, 3).Eval() from 1.0.15	2500 ns
Call(3) from 1.0.15	54 ns
Complex.Sin(3)	27 ns

If we take expr = MathS.Sin(MathS.Sqr(x)) + MathS.Cos(MathS.Sqr(x)) + MathS.Sqr(x) + MathS.Sin(MathS.Sqr(x)), AM Compiled is faster than any other methods:

Method	Time per iteration
AM Compiled	310.0 ns
In-code expression	424.2 ns
LinqCompiled	435.9 ns
Substitute(x, 3).Eval()	6777.3 ns

It is true since release of 1.0.17.1 Beta, when cache instructions in compiled functions were added.

Finally, if we take expr = (MathS.Log(x, 3) + MathS.Sqr(x)) * MathS.Sin(x + MathS.Cosec(x)), we get the following performance

Method	Time per iteration
AM Compiled	380.8 ns
In-code expression	211.5 ns
Substitute(x, 3).Eval()	5656.3 ns

So, for most cases compilation will save you enough time even though built-in functions are still faster sometimes.

More information

More info about methods see on Wiki.

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