Bug 66200

For example Math currently parses expressions like this:

"a + 2 b" => "{a +  2} b" instead of "a + {2 b}"
"x + 3 y^2" => "{x +  3} y^2" instead of "x + 3 y^2"

I tried to fix that in bug 66081, but I suspect it would be a bit more complicated than what I initially thought, so I'm moving it as a separate bug. Currently, the grammar used by starmath/source/parse.cxx is (approximately) as follows:

Expression = Relation ([relation token] Relation)+
Relation = Sum ([sum token] Sum) +
Sum = Product ([product token] Product)+
Product = Power ([power token] Power)+
Power = Term ([sub/sup script tokens] Term)+
Term = ['{' token] Expression ['}' token] | [text token] | [symbol token] | Matrix | Binom | ... other terms ...
Binom = ['binom' token] Sum Sum
Matrix = ...
... = other rules

The parsing can be done linearly and stops when an unexpected token is read. What we'd like in order to fix this bug is to define

Product = Power (([power token] Power)+ | Power+)

so that an explicit [power token] like "*" is not needed to write a product i.e. we can write "a b" instead of "a * b". Unfortunately, after some attempts this breaks some unit tests. For example the naive parsing of "binom a b" could become

Term
=> binom Sum Sum
=> binom Product Sum        
=> binom (Power)+ Sum
=> binom (Term)+ Sum
=> binom a b Sum
=> binom a b Product
=> binom a b (Power)+
=> binom a b (Term)+
=> failure!

rather than the expected

Term
=> binom Sum Sum
=> binom Term Term
=> binom a b

The grammar can probably be modified to avoid some of the issues but I suspect a general solution will require to use techniques like those of parsers generated by GNU bison (https://en.wikipedia.org/wiki/GNU_bison).