Here is the patch, finally done with git since in hg I cannot fix the
commit message to Emacs/auctex standard when rebasing.

>From 4bbb2980366078c29b174a65ce39ce911e13330e Mon Sep 17 00:00:00 2001
From: Uwe Brauer <o...@mat.ucm.es>
Date: Sun, 18 Sep 2016 15:41:29 +0000
Subject: [PATCH] Add informations about prettify and semi WYSIWYG

* doc/auctex.texi (Display): Repair some markup
questions. Add sentences about
prettify-symbols-unprettify-at-point. Add paragaph about Semi WYSIWYG.
---
 doc/auctex.texi | 30 ++++++++++++++++++++++++------
 1 file changed, 24 insertions(+), 6 deletions(-)

diff --git a/doc/auctex.texi b/doc/auctex.texi
index 673b6ad..627df9d 100644
--- a/doc/auctex.texi
+++ b/doc/auctex.texi
@@ -102,7 +102,7 @@ navigation and a few other things.  (@pxref{Installation,,,reftex,The
 Ref@TeX{} manual})
 
 For detailed information about the @previewlatex{} subsystem of
-@AUCTeX{}, see @ref{Top,,Introduction,preview-latex,The @previewlatex{}
+@AUCTeX{}, see @xref{Top,,Introduction,preview-latex,The @previewlatex{}
 Manual}.
 
 There is a mailing list for general discussion about @AUCTeX{}: write a
@@ -1811,8 +1811,19 @@ Moreover, you can focus in a specific portion of the code by narrowing
 the buffer to the desired region.  @AUCTeX{} provides also functions to
 narrow the buffer to the current group and to @LaTeX{} environments.
 
-Lastly, @AUCTeX{} with Emacs 25 or later can display certain math macros
-using Unicode characters.  That's called prettification.
+Another tool to obtain more WYSIWYG feeling is to set
+@code{font-latex-fontify-script} to @code{invisible} so that the
+@code{^} and @code{_} in sub and superscripts are not displayed.
+
+Lastly, @AUCTeX{} with GNU Emacs 25 or later can display certain math
+macros using Unicode characters.  That's called prettification and is
+pretty lightweight and reasonable robust, however it only provides a
+limited WYSIWYG feature compared to @previewlatex{} a subsystem of
+@AUCTeX{}, see @xref{Top,,Introduction,preview-latex,The @previewlatex{}
+Manual} which let LaTeX generate images that are displayed in your
+buffer.  It is extremely accurate but sometimes fragile with some
+packages.  Please note that you can use prettification and preview-latex
+together.
 
 @menu
 * Font Locking::                Font Locking
@@ -2174,6 +2185,10 @@ variables @code{font-latex-fontify-script} and
 @defopt font-latex-fontify-script
 If non-nil, fontify subscript and superscript strings.
 
+In addition you can configure Emacs so that the @code{^} and @code{_} in
+sub and superscripts are not displayed.  To enable that feature you have
+to set the variable @code{font-latex-fontify-script} to @code{invisible}.
+
 Note that this feature is not available on XEmacs, for which it is
 disabled per default.  In GNU Emacs raising and lowering is not enabled
 for versions 21.3 and before due to it working not properly.
@@ -2183,7 +2198,7 @@ for versions 21.3 and before due to it working not properly.
 Display specification for subscript and superscript content.  The car is
 used for subscript, the cdr is used for superscript.  The feature is
 implemented using so-called display properties.  For information on what
-exactly to specify for the values, see @ref{Other Display Specs, , Other
+exactly to specify for the values, see @xref{Other Display Specs, , Other
 Display Specifications, elisp, GNU Emacs Lisp Reference Manual}.
 @end defopt
 
@@ -2587,7 +2602,7 @@ will no longer be required for them.
 @section Prettifying
 
 Emacs 25 is able to prettify symbols in programming language buffers,
-@pxref{Misc for Programs,,,emacs,GNU Emacs Manual}.  The canonical
+@pxref{Misc for Programs,,,emacs,GNU Emacs Manual}. The canonical
 example is to display @code{(lambda () ...)} as @code{(λ () ...)} in
 Lisp buffers.
 
@@ -2595,7 +2610,10 @@ Lisp buffers.
 and greek letters using their Unicode representation, too.  For example,
 the @TeX{} code @code{\alpha \times \beta} will be displayed as @code{α
 × β}.  When point is on one of the characters, it'll be unprettified
-automatically, meaning you see the verbatim text again.
+automatically, meaning you see the verbatim text again.  For this
+behaviour however you need to set
+@code{prettify-symbols-unprettify-at-point} to t or @code{right-edge}
+which will unprettify the symbol when point moves into or near it.
 
 To enable prettification in @AUCTeX{}, simply add
 @code{prettify-symbols-mode} to @code{TeX-mode-hook}.  If you enabled
-- 
1.9.1

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