You can just turn on auto-complete with M-x auto-complete-mode. The default ac-sources has ac-source-words-in-same-mode-buffers, which will start working pretty well once you have some content in a Maxima buffer. To always enable auto-complete-mode, just add it to the mode hook (see below). It looks like there are other related modes like imaxima, so you may need to add it to several hooks.
For proper completion, you could create your own auto-complete source. Simple examples include words-in-same-mode-buffers in auto-complete.el, and the ac-math package. Once you define your source, you can add it in the hooks.
(ac-define-source maxima
...
)
(defun jpk/maxima-mode-hook ()
(add-to-list 'ac-sources 'ac-source-maxima)
(auto-complete-mode 1))
(add-hook 'maxima-mode-hook #'jpk/maxima-mode-hook)
(add-hook 'inferior-maxima-mode-hook #'jpk/maxima-mode-hook)
As noted by @lawlist, Maxima has some built-in completion functions. You can probably build your own ac source pretty easily by reusing code from that (e.g. maxima-symbols).
share/builtins-list.txtwhich is included in the Maxima installation; maybe you can somehow tell a text editor that's the list of words to be completed. Incidentally,rmaximais a script which launchesmaximaviarlwrapwhich handles autocompletion and some other line-editing functionality;rmaximausesshare/builtins-list.txtfor the list of words. - Robert Dodier