I'm checking the documentation in doc/info. I tried the examples from Affine.texi, but they fail.
(%i1) load (affine);
; compilation unit finished
; caught 32 WARNING conditions
; caught 101 STYLE-WARNING conditions
; printed 91 notes
(%i2) grobner_basis ([3*x^2+1, y*x]);
Maxima encountered a Lisp error:
Error during processing of --eval option "(cl-user::run)":
The function MUST-REPLACEP is undefined.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i3) polysimp (y^2*x + x^3*9 + 2);
I'm not sure what happens here.
You can also check other functions and examples.