Common lisp: is there a less painful way to input math expressions?

Question

I enjoy common lisp, but sometimes it is really painful to input simple math expressions like

a(8b^2+1)+4bc(4b^2+1)

(Sure I can convert this, but it is kind of slow, I write (+ () ()) first, and then in each bracket I put (* () ())...)

I'm wondering if anyone here knows a better way to input this. I was thinking about writing a math macro, where

(math “a(8b^2+1)+4bc(4b^2+1)”) 

expands to

(+ (* a (1+ (* 8 b b))) (* 4 b c (1+ (* 4 b b))))

but parsing is a problem for variables whose names are long.

Anybody has better suggestions?

Answer 1

There are reader macros for this purpose.

See: http://www.cliki.net/infix

For example:

CL-USER 17 > '#I(a*(8*b^^2+1)+ 4*b*c*(4*b^^2+1) )
(+ (* A (+ (* 8 (EXPT B 2)) 1)) (* 4 B C (+ (* 4 (EXPT B 2)) 1)))

' is the usual quote. #I( some-infix-expression ) is the reader macro.