mmm-mode sage-shell:sage-mode integration in specific latex environments

[Poetastrophe]

I was looking into how I could get sage-shell:sage-mode to work in sageblock and sagesilent environments. I found this post about getting python-mode to work in specific environments. https://emacs.stackexchange.com/questions/20136/pythontex-and-auctex#20150
But I honestly do not know how to implement this correctly for sage-shell:sage-mode. But I thought it would be neat for working with math-documents.

[stakemori]

I am not familiar with mmm-mode but the following code seems to work to some extent:

(require 'mmm-auto)
(setq mmm-global-mode 'maybe)

(let ((envs '("sageblock" "sagesilent")))
  (mmm-add-classes
   `((latex-sage
      :submode sage-shell:sage-mode
      :face mmm-default-submode-face
      :front ,(rx-to-string
               `(and "\\begin{" (or ,@envs) "}" eol))
      :back ,(rx-to-string
              `(and "\\end{" (or ,@envs) "}" eol))))))

(mmm-add-mode-ext-class 'latex-mode nil 'latex-sage)

Unfortunately syntax highlighting in example.tex is broken with this configuration. I guess the method used by org-mode better than mmm-mode. Perhaps I should examine how org-mode highlights source blocks.