How to simplify formula with MathNet.Symbolics?

Question

I'm using the MathNet.Symbolics library to simplify an algebraic formulas like

string f = Infix.Print(Infix.ParseOrThrow("L+H+L+H"))

And I correctly get f="2*L+2*H"

My problem arise when I need to subtract two of these formulas:

string f = Infix.Print(Infix.ParseOrThrow("L+H+L+H - (L+H)"))

And here I get f="2*L+2*H - (L+H)" instead of (L+H)

What should I do to get the correct simplification?

Answer 1

Math.NET Symbolics always applies auto-simplification when constructing an expression, such that a denormalized form cannot even exist. This is essential to keep the algebraic algorithm complexity low, but is intentionally very limited. This is really more a term normalization, not a simplification.

The expression 2*H + 2*L - (H + L) is technically indeed in normalized/auto-simplified form, but this may be more obvious when using Infix.PrintStrict which is much less readable but shows exactly how the expression is represented internally: 2*H + 2*L + (-1)*(H + L).

There are quite a few algebraic routines that you can use to manipulate and simplify such expressions, in this case a simple algebraic expansions will do the trick:

var e1 = Infix.ParseOrThrow("L+H+L+H");
var e2 = Infix.ParseOrThrow("L+H");
var e3 = e1 - e2;
// or: var e3 = Infix.ParseOrThrow("L+H+L+H - (L+H)");

var expanded = Algebraic.Expand(e3);
Infix.Print(expanded); // prints "H + L"