C# library for algebra simplification and solving

Question

There are quite a few algebra solvers and simplifiers on the web (for example, the decent one at algebra.com). However, I'm looking for something I can plug into C# as part of a larger project (I'm making my own calculator, but obviously I'd ask permission etc.).

Ideally, I'd use code like:

String s = MathLib.Simplify("5x*(500/x^2*(sqrt(3)/4)+1)+2x^2+(sqrt(3)/2)*x^2");

And 's' would simplify down to: "1082.532/x+5*x+2.866*x^2"

(3dp accuracy there, but one could change that if need be).

Solving for a particular variable would be nice too. I need something lightweight, and fast too (calculations such as the above would preferably be under 5ms or so including the startup latency).

After some research, programs like Sage, Octave or Mathematica are probably overkill (my app will only be a small <200k exe probably). Dotnumerics.com or Mathdotnet.com may be suitable, but the former doesn't seem to mention algebraic simplification, and the lack of documentation and examples in the latter is a turn off. I'm wondering if there are any appropriate alternatives as well. A large list can be found here: http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

Answer 1

I've managed to successfully call into SymPy to get this done from C#. SymPy provides a relatively robust simplify function that I've had good success with. Now I'm not entirely sure how to package this nicely yet (not having to install ironpython), or even how hard a direct port of the code might be.

1. Install IronPython
2. Get SymPy
3. Add these resources to your project
   • IronPython.dll
   • IronPython.Modules.dll
   • Microsoft.Dynamic.dll
   • Microsoft.Scripting.dll

4. C# code as follows:

   var engine = Python.CreateEngine();
   var paths = engine.GetSearchPaths();
   paths.Add(@"c:\program files (x86)\ironpython 2.7\lib");
   paths.Add(@"c:\Development\sympy");
   engine.SetSearchPaths(paths);
   
   // expression to simplify
   var expr = "0 + 1 * 1 * (x - 2) / (1 - 2) * (x - 3) / (1 - 3) * (x - 4) / (1 - 4) + 8 * 1 * (x - 1) / (2 - 1) * (x - 3) / (2 - 3) * (x - 4) / (2 - 4) + 27 * 1 * (x - 1) / (3 - 1) * (x - 2) / (3 - 2) * (x - 4) / (3 - 4) + 64 * 1 * (x - 1) / (4 - 1) * (x - 2) / (4 - 2) * (x - 3) / (4 - 3)";
   
   var scope = engine.CreateScope();
   var script = engine.CreateScriptSourceFromString(@"
   from sympy import *
   import clr
   from System import String
   
   expr = simplify('" + expr + @"')
   result = clr.Convert(expr, String)
   ");
   
   script.Execute(scope);
   
   // prints "x**3"
   Console.WriteLine(scope.GetVariable("result"));
   

Answer 2

Symbolism is a C# library which implements automatic simplification of algebraic expressions.

Going with your example expression, the following program:

var x = new Symbol("x");

(5 * x * (500 / (x ^ 2) * (sqrt(3.0) / 4) + 1) + 2 * (x ^ 2) + (sqrt(3.0) / 2) * (x ^ 2))
    .AlgebraicExpand()
    .Disp();

displays this at the console:

1082.5317547305483 / x + 5 * x + 2.8660254037844384 * (x ^ 2)

Answer 3

There is a flurry of answers to be found in a related SO question. Though none, other that mathdotnet, fall at the intersection of symbolics (the kind of simplificaiton you are asking for above), lightweight-ishness, and accessibility on .Net.

I see you have already found the mathdotnet forum. Note a couple of its developers are SO users:

• Christoph Rüegg
• Joannes Vermorel (though ohloh tells me he's more attached to the numerics section)

That might supplement the support you ask for.

Answer 4

Have you tried creating a few simple classes implementing the Shunting Yard Algorithm(Reverse Polish Notation) than process the postfix notation using stack processingstack processing?