MaximaSharp

MaximaSharp is a simple library that uses Maxima to perform symbolic algebra, plot functions, and do basic operations with C#'s lambda functions, expressions, and strings. Both examples and Maxima are included.

What is Maxima?

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions.

Using MaximaSharp

Given the following lambda expressions declared in C#:

Expression<Func<double, double>> f = x => 3 * Math.Pow(x, 2) + 2 * x 
			+ Math.Pow(Math.Cos(x), 2) + Math.Pow(Math.Sin(x), 2);
Expression<Func<double, double>> g = x => 2 * x + 5 * 2;
Expression<Func<double, double, double>> h = (y, z) => 3 * y + z;

Simplifying

Simplifying functions is easy:

Console.WriteLine(f.Simplify());
Console.WriteLine(g.Simplify());
Console.WriteLine(h.Simplify());
// Output:
// x => (((3 * (x ^ 2)) + (2 * x)) + 1)
// x => (2 * (x + 5))
// (y, z) => (z + (3 * y))

Differentiating

It's also possible to take the derivative of functions:

Console.WriteLine(f.Differentiate());
Console.WriteLine(g.Differentiate());
Console.WriteLine(h.Differentiate("y"));
// Output:
// x => ((6 * x) + 2)
// x => 2
// (y, z) => 3

Integrating

Definite and indefinite integrals can also be found:

Console.WriteLine(f.Integrate().Simplify());
Console.WriteLine(f.Integrate(0, 2));
Console.WriteLine(g.Integrate());
Console.WriteLine(h.Integrate("y"));
// Output:
// x => (x * (((x ^ 2) + x) + 1))
// x => 14
// x => ((x ^ 2) + (10 * x))
// (y, z) => ((y * z) + ((3 * (y ^ 2)) / 2))

Plotting

Plot functions easily with gnuplot:

Maxima.GnuPlot(@"plot x+5*cos(x)");
Maxima.GnuPlot(@"
	set parametric 
	set pm3d depthorder hidden3d
	set isosamples 30, 20
	splot [-pi:pi][-pi:pi] cos(u)*(cos(v)+3), sin(u)*(cos(v)+3), sin(v) w pm
");
Console.ReadLine();

Produces the following graphs:

More stuff

Evaluate functions:

Console.WriteLine(f.At(5));
Console.WriteLine(g.At(10));
// Output:
// 86
// 30

Perform basic operations on functions:

Console.WriteLine(g.Plus(h));
Console.WriteLine(g.Minus(h));
Console.WriteLine(f.Times(g).Simplify());
Console.WriteLine(f.Over(g).Simplify());
// Output:
// (x, y, z) => (((2 * x) + 10) + ((3 * y) + z))
// (x, y, z) => (((2 * x) + 10) - ((3 * y) + z))
// x => ((2 * (x + 5)) * (((3 * (x ^ 2)) + (2 * x)) + 1))
// x => ((((3 * (x ^ 2)) + (2 * x)) + 1) / (2 * (x + 5)))

Note: evaluating functions and basic operations are performed without the use of Maxima.

Convert strings back into expressions:

var expr = Maxima.ToExpression("double, double", "x", "10 * x + 5 * cos(x)");
Console.WriteLine(expr);
Console.WriteLine(expr.Differentiate().Simplify().At(0));
// Output:
// x => ((10 * x) + (5 * Cos(x)))
// 10

Example: converting user input to an expression that can be differentiated, integrated, plotted, or evaluated.