Extend GIN

Hi! I am building a database with mathematical expressions. For example
something like '1+x/y'. I want to try to create an index to quickly find
records that match a pattern like '?a + ?b' ('1+x/y' is an example of
this). Is this feasible? (the jsquery project is doing something a little
like this) I do not know much about complicated indexes. I looked at the
GIN index which is somehow able to index contains and contained by. For
example in some way 1+x/y contains ?a+?b. I thought about creating a
function in Lua to check this and create an operator class to make this
work with the GIN index. Is something like that possible? Could it actually
work?

Thanks,
Herman