[AUCTeX] Filling paragraphs with display math

[Yevgeniy Makarov]

Hello,

I have the following problem. When I fill paragraphs (using M-q) which
contain display math between $$, Emacs moves dollar signs as well. For
example,

Define a partial function $\eval$ as follows.
$$
\eval(t)=v\text{ iff }t\to_{\beta c}^* v
$$
Let $\eval(t)\simeq\eval(t')$ mean that $\eval(t)$ and $\eval(t')$ are
defined simultaneously and if they are
both defined then they are
equal. A natural question is
to decide, for terms $t,t'$ of an
observable type, whether $t\eq t'$ implies $\eval(t)\simeq\eval(t')$.

becomes

Define a partial function $\eval$ as follows. $$
\eval(t)=v\text{ iff
}t\to_{\beta c}^* v $$
Let $\eval(t)\simeq\eval(t')$ mean that
$\eval(t)$ and $\eval(t')$ are defined simultaneously and if they are
both defined then they are equal. A natural question is to decide,
for terms $t,t'$ of an observable type, whether $t\eq t'$ implies
$\eval(t)\simeq\eval(t')$.

I like $$ to be on the line by itself, as in the first fragment.

I read in the documentation that this may be related to the variable
LaTeX-fill-break-at-separators. But when I say, for example,

(setq LaTeX-fill-break-at-separators '($$))

Emacs' behavior does not change.

I would appreciate your advice about how leave $$ alone on the line
but to fill everyhing else (including $).

Thank you,
Yevgeniy