I'm searching a solution to write equations other than (but compatible with) latex. While latex is excellent for math rendering, it is not suited to describe the structure or meaning of the equations.
I'm thinking about this since the beginning of my thesis (both in chemistry and physics with a lot of maths). I experienced a lot of frustration using latex with which I have to rewrite again and again the same equation that I cannot manipulate programmatically. I do not find a satisfactory framework that would have the following properties:
- Easy to write and read
- Encode the mathematical content (is that thing a function, variable, vector, operator?)
- Can be used programmatically (through sympy or lualatex for example)
- Self consistent (1 formula contain all you have to know about it)
- Can be labeled with many contextual tags
My final goals are to:
- Quickly write equations while writing working notes
- Store them for later reuse
- Classify and store well known formulas (in math and physics)
- Classify and index equations according to their structure, the type of equation they solve, the kind of problem people
- tag equation according to the purpose I am using them punctually (approximation, relation, equation of motion, description of the hamiltonian, ...)
- Render (through latex) equations according to the mathematical conventions (e.g. different type setting for constant, function, real, vector, etc.)
- Select a mathematical structure then choose only the symbols.
I guess these issues are shared (at least partly) by many people. I know, this is a quite complex question... But I think mathematical software already have this kind of features. I do not expect definitive answers, but I'm seeking informations about:
- Others experiences on that topics
- Beginning of solutions (or the way you would personally approach the problem)
- Markdown language well suited for math typing (as more information is injected in each equation, the typing synthax seem to be very important)
- Promising (openSource) projects on that topic and pitfall I should try to avoid while working on that (quite broad) problem.
I think what you want is too ambitious and results from a somewhat naive view of mathematical formulae as self-contained structures. In fact almost all mathematical formulae have a lot of implicit dependence on each other, on context and on conventions. If one were to make all those dependencies explicit, the resulting structure would be quite complicated indeed, which would almost certainly go against your desire to be able to quickly write formulae. In fact I think one might compare the situation with that of (open source) software packages which have to establish dependences very carefully to make sure that one component will always have the proper functioning (meaning) while still being able manipulate many components fairly easily.
This being said, take a look at OpenMath, which is a long standing project with some ambitions common to what you describe.