Clarify further doc/README.md following Jim's comments.

Relative links. Cf. #7800.

1 files changed, 31 insertions, 32 deletions

diff --git a/doc/README.md b/doc/README.md
index 416726e1b..6c6e1f01f 100644
--- a/doc/README.md
+++ b/doc/README.md
@@ -13,58 +13,56 @@ Additionnally, you can view the documentation for the current master version at
 <https://gitlab.com/coq/coq/-/jobs/artifacts/master/file/_install_ci/share/doc/coq/sphinx/html/index.html?job=documentation>.
 
 The reference manual is written is reStructuredText and compiled
-using Sphinx (see [`sphinx/README.rst`](/doc/sphinx/README.rst))
+using Sphinx. See [`sphinx/README.rst`](sphinx/README.rst)
 to learn more about the format that is used.
 
 The documentation for the standard library is generated from
 the `.v` source files using coqdoc.
 
-Prerequisite
+Dependencies
 ------------
 
-To produce the complete documentation in HTML, the following tools are required:
+### HTML documentation
 
-  - Python 3
-  - Sphinx 1.6.5 (http://www.sphinx-doc.org/en/stable/)
-  - sphinx_rtd_theme
-  - pexpect
-  - beautifulsoup4
-  - Antlr4 runtime for Python 3
+To produce the complete documentation in HTML, you will need Coq dependencies
+listed in [`INSTALL`](../INSTALL). Additionally, the Sphinx-based
+reference manual requires Python 3, and the following Python packages:
 
-To produce the documentation in PDF and PostScript formats the following
-additional tools are required:
+    sphinx sphinx_rtd_theme beautifulsoup4 antlr4-python3-runtime pexpect sphinxcontrib-bibtex
 
-  - latex (latex2e)
-  - pdflatex
-  - dvips
-  - makeindex
-
-Under recent Debian based operating systems (Debian 10 "Buster",
-Ubuntu 18.04, ...) a working set of packages for compiling the
-documentation for Coq is:
+You can install them using `pip3 install` or using your distribution's package
+manager. E.g. under recent Debian-based operating systems (Debian 10 "Buster",
+Ubuntu 18.04, ...) you can use:
 
-    texlive-latex-extra texlive-fonts-recommended
-    python3-sphinx python3-pexpect python3-sphinx-rtd-theme
-    python3-bs4 python3-sphinxcontrib.bibtex python3-pip
+    apt install python3-sphinx python3-pexpect python3-sphinx-rtd-theme \
+                python3-bs4 python3-sphinxcontrib.bibtex python3-pip
 
-Then, install the Python3 Antlr4 package:
+Then, install the missing Python3 Antlr4 package:
 
     pip3 install antlr4-python3-runtime
 
 Nix users should get the correct development environment to build the
-HTML documentation from Coq's [`default.nix`](/default.nix) (note this
+HTML documentation from Coq's [`default.nix`](../default.nix) (note this
 doesn't include the LaTeX packages needed to build the full documentation).
 
-If you are in an older / different distribution / operating system, you can
-install the Python packages required to build the reference manual using
-python3-pip:
+### Other formats
+
+To produce the documentation in PDF and PostScript formats, the following
+additional tools are required:
+
+  - latex (latex2e)
+  - pdflatex
+  - dvips
+  - makeindex
+
+Install them using your package manager. E.g. on Debian / Ubuntu:
 
-    pip3 install sphinx sphinx_rtd_theme beautifulsoup4 antlr4-python3-runtime pexpect sphinxcontrib-bibtex
+    apt install texlive-latex-extra texlive-fonts-recommended
 
 Compilation
 -----------
 
-To produce all documentation about Coq, just run:
+To produce all documentation about Coq in all formats, just run:
 
     ./configure           # (if you hadn't already)
     make doc
@@ -97,7 +95,8 @@ Installation
 
 To install all produced documents, do:
 
-    make DOCDIR=/some/directory/for/documentation install-doc
+    make install-doc
 
-`DOCDIR` defaults to `/usr/share/doc/coq` or whatever value was specificied
-through the `-docdir` option of `./configure`.
+This will install the documentation in `/usr/share/doc/coq` unless you
+specify another value through the `-docdir` option of `./configure` or the
+`DOCDIR` environment variable.