MathFlow 1.0.0

MathFlow

C# math expression library with symbolic computation support.

Install

dotnet add package MathFlow

Basic usage

using MathFlow.Core;

var engine = new MathEngine();

// basic stuff
var result = engine.Calculate("2 + 3 * 4"); // returns 14
Console.WriteLine(engine.Calculate("sin(pi/2)")); // 1

// with variables
var vars = new Dictionary<string, double> { ["x"] = 3, ["y"] = 4 };
var answer = engine.Calculate("x^2 + y^2", vars); // 25

Features

Expressions

• Parse mathematical expressions from strings
• Evaluate with variables
• Works with standard math notation

Operations

Basic: +, -, *, /, ^, %

Trig: sin, cos, tan, asin, acos, atan (also sinh, cosh, tanh)

Other: exp, ln, log10, sqrt, abs, floor, ceil, round, sign, min, max, factorial

Constants: pi, e, tau (2*pi), phi (golden ratio)

Advanced stuff

Derivatives

var derivative = engine.Differentiate("x^3 + 2*x^2 - 5*x + 3", "x");
// gives you: 3*x^2 + 4*x - 5

Simplification

var simplified = engine.Simplify("x + 2*x + 3*x");
Console.WriteLine(simplified); // 6*x

Equation solving

// find root near initial guess
double root = engine.FindRoot("x^2 - 4", 3); // returns 2

// find all roots in range
double[] roots = engine.FindRoots("x^3 - 6*x^2 + 11*x - 6", 0, 4);
// gives [1, 2, 3]

Integration (numerical)

double integral = engine.Integrate("x^2", "x", 0, 1); 
// returns ~0.333333

Working with expressions

You can also build expressions programmatically:

var expr1 = engine.Parse("x + 2");
var expr2 = engine.Parse("y - 1");
var combined = expr1 * expr2; // creates (x + 2) * (y - 1)

Substitute variables:

var substituted = engine.Substitute("x^2 + y", "x", "sin(t)");
// gives: sin(t)^2 + y

Output formats

LaTeX

string latex = engine.ToLatex("sqrt(x^2 + y^2)");
// \sqrt{x^{2} + y^{2}}

MathML

string mathml = engine.ToMathML("x/2");
// outputs MathML format

Custom functions

You can register your own:

engine.RegisterFunction("double", args => args[0] * 2);
var result = engine.Calculate("double(5)"); // 10

More examples

Check the Examples folder for more usage examples including:

• Complex numbers
• Vector operations
• Statistical functions
• Linear regression

API

Main methods:

• Calculate(expression, variables?) - evaluate expression
• Parse(expression) - parse to AST
• Simplify(expression) - simplify expression
• Differentiate(expression, variable) - take derivative
• Integrate(expression, variable, a, b) - numerical integration
• FindRoot(expression, guess) - find root using Newton's method
• FindRoots(expression, start, end) - find all roots in range
• Expand(expression) - expand expression
• Factor(expression) - factor expression (limited support)
• Substitute(expression, var, replacement) - replace variable
• ToLatex(expression) - convert to LaTeX
• ToMathML(expression) - convert to MathML

Requirements

.NET 8.0 or later

Tests

Run tests with:

dotnet test

Known issues

• Factor() method is not fully implemented
• Some edge cases in complex expressions might not simplify optimally
• Performance could be better for very large expressions

Contributing

PRs welcome. Please add tests for new features.

License

MIT

Credits

Inspired by various math expression parsers and CAS systems.