[AUCTeX] How to implement the function? Identify state of input method.

[xiaopeng hu]

I use Ctrol to switch my input method between chinese and english.
When I input $, coming in math mode,I need to automatically switch to english input method (push "Ctrl" key).

First, I simulate a keystrike "t"+<space>, I will get a chinese character (not equal "t ")if my input method is chinese. Now I need Emacs automatically simulate a "Ctrl" key to switch to english input method.
All of these is just after when I input $.

How to implement the function?

Thanks