Minimizing M2 calls in parser

[sommars]

Suppose we wanted to retrieve two rings R and S from M2, as could happen during m2_parse(). What if we called M2 once with the input of (R,S)? Would this improve speed?

[coneill-math]

This is unlikely to be easy to implement, as it requires the parser to peek ahead and grab several rings at once. After a recent update to m2(), subsequent calls are much faster.

[sommars]

No, peaking ahead isn't necessary. Instead of getting them on the fly, wait til you finish parsing, then grab all of them at once.

[coneill-math]

But the value returned by m2() determines how they are parsed, and thus how subsequent parsing occurs. For instance, R^2 becomes a module if R is a ring, and an expression if R is a variable.

It is possible this can be done in a lazier fashion than it is right now, but I don't see a way to do so without significantly modifying the parser (both physically and philosophically). Perhaps we can reopen if it becomes a bottleneck in the future?

[sommars]

Ohhhh, right. Yeah, that's true

[coneill-math]

It is certainly worth looking into ways of minimizing the calls to m2() when parsing. Some ideas:

1. Keep a list of known function/class names that will not need to be looked up.
2. Check the format of the name (e.g. m2rintring0000000000001) and only look up those that don't fit.

Both of these can be subverted by a malitious user, but at some point we need to trust them. I will reopen so that we can (potentially) add this in a future version.

[coneill-math]

Excess calls to m2() in the parser are more evident in the cloud version.

We should bump the priority on this.