Use of letters for doing matrix math in Javascript

Question

I'm doing a course in Quantum Computation. In it, we represent possible actions, or operators, by matrices. I've been looking into creating a webpage for solving these maths problems. It is also a small challenge for myself in order to freshen up my JS.

I've been looking at various options, like Sylvester, MathJax and MathML.

Problem: However, none of the above appear to give functionality for using letters throughout my computation.

For instance, in Quantum Computation we often use multiply a matrix containing unknowns alpha and beta, with other matrices.

This is the sort of math I need to do:

http://i.stack.imgur.com/vH9Dk.gif

Ideally, I'd write this in the style of:

M=[[a],[b]], which of course, I cannot. Further, I'd be able to multiply to get "2*a" etc.

Any suggestions?

Answer 1

As suggested in the comments on the question, you could use strings. Then you just have to write your own matrix-matrix multiplication routine which will understand the difference between an entry containing a string and an entry containing a number.

However, as soon as you do more than one of these, you'll end up with expressions as well as variables and numbers. So we can generalise this to make every element be an expression. This is the beginnings of a symbolic algebra system as @High Performance Mark pointed out.

In javascript, I would guess that you want a set of expression objects, each implementing an interface including a method that returns whether the expression is determined or not yet. The gnarly bit is simplifying the resulting expressions to resolve the values of the variables.

Alternatively, do a bit more maths beforehand; move the variables out of the equations, and then let the code do the calculation.