**Parsing mathematical expressions**

[AM] Mathematical expressions like those parsed by the [[expr]] command are not easily manipulated via Tcl commands. What I mean is,
if I want to use complex numbers or add support for array expressions (see TIP 363 ([http://www.tcl.tk/cgi-bin/tct/tip/363]), I can 
do that via Tcl's prefix notation:

   set sum [+ $op1 $op2]

or 

   set dotp [inprod $vector1 $vector2]

That is okay for simple expressions, but when things get more complicated, like:

   set diffusion [expr {$diff*(2.0*$conck - $conckm1 - $conckp1)/$deltx**2}]

the prefix notation is cumbersome:

   set diffusion [vecmult $diff [vecdiv [vecsub [vecmult 2.0 $conck] $conckm1 $conckp1] [expr {$deltx**2}]]]

My idea is to make a small extension to convert expression from the mathematical infix notation to Tcl's prefix automatically.
I currently have something that almost does the job, but it is still a fair amount of work to make it practical. You could even
add extra functionality here, like the introduction of custom operations.

Benefits for the student: learn about parsing.

Benefits for Tcl: more flexibility in mathematical/physical applications.

[Lars H]: This is not so far from what the [infix] package does already, but I suppose you might want the extra speed of a C-coded parser (and a slightly nicer calling convention). One thing I've thought about is relation to these things is that one could make it possible to stash parsed/translated/compiled forms of expressions within the intRep of the [Tcl_Obj] of the expression, like Tcl does with its [expr]essions. Or rather, I've though about whether it would be possible to expose such functionality at the ''script level''. Currently [infix] stashes its "compiled code" in an [array] instead, which is a major reason why the calling convention is unintuitive…

[AM] Ah! I had forgotten about [infix]. Now, this is beginning to take the form of a not entirely trivial project, I'd say.

[Lars H]: How so? Having an existing codebase to make fully practical (perhaps even for a delimited field) seems less ambitious than getting something to work in the first place. Oh, you mean my idea about stashing things in Tcl_Objs? Yes, that's probably a separate project, and perhaps not one suited for GSOC. (Actually, I don't think it would be that much coding, but it would require a thorough understanding of the concepts.)

[Sarnold]: Did you check [xsource]? It is worth checking out, even if it has bugs remaining.
[AM] Interesting, but at a first glance not quite what I am after. Lars's [infix] package comes closer, as it allows you to define what an operation actually means. But I will have a closer look ;).