Fix sphinx-doc#9864: mathjax: Failed to render equations via MathJax v2

MathJax library has been loaded via "defer" method since v4.3.0.  But
it prevents to work MathJax v2.  This rollbacks the change and use
"async" method as default again.

To support changing the loading method, this allows to specify it via
mathjax_options.

CHANGES

@@ -13,11 +13,16 @@ Deprecated
 Features added
 --------------
 
+* #9864: mathjax: Support chnaging the loading method of MathJax to "defer" via
+  :confval:`mathjax_options`
+
 Bugs fixed
 ----------
 
 * #9838: autodoc: AttributeError is raised on building document for functions
   decorated by functools.lru_cache
+* #9864: mathjax: Failed to render equations via MathJax v2.  The loading method
+  of MathJax is back to "async" method again
 
 Testing
 --------

doc/usage/extensions/math.rst

@@ -200,6 +200,11 @@ Sphinx but is set to automatically include it from a third-party site.
 
    .. versionadded:: 1.8
 
+   .. versionchanged:: 4.4.1
+
+      Allow to change the loading method (async or defer) of MathJax if "async"
+      or "defer" key is set.
+
 .. confval:: mathjax3_config
 
    The configuration options for MathJax v3 (which is used by default).

sphinx/ext/mathjax.py

@@ -81,10 +81,18 @@ def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: Dict
     domain = cast(MathDomain, app.env.get_domain('math'))
     if app.registry.html_assets_policy == 'always' or domain.has_equations(pagename):
         # Enable mathjax only if equations exists
-        options = {'defer': 'defer'}
+        options = {}
         if app.config.mathjax_options:
             options.update(app.config.mathjax_options)
-        app.add_js_file(app.config.mathjax_path, **options)  # type: ignore
+        if 'async' not in options and 'defer' not in options:
+            print(options, app.config.mathjax3_config)
+            if app.config.mathjax3_config:
+                # Load MathJax v3 via "defer" method
+                options['defer'] = 'defer'
+            else:
+                # Load other MathJax via "async" method
+                options['async'] = 'async'
+        app.add_js_file(app.config.mathjax_path, **options)
 
         if app.config.mathjax2_config:
             if app.config.mathjax_path == MATHJAX_URL:

tests/test_ext_math.py

@@ -71,7 +71,7 @@ def test_mathjax_options(app, status, warning):
     app.builder.build_all()
 
     content = (app.outdir / 'index.html').read_text()
-    assert ('<script defer="defer" integrity="sha384-0123456789" '
+    assert ('<script async="async" integrity="sha384-0123456789" '
             'src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">'
             '</script>' in content)
 
@@ -221,6 +221,7 @@ def test_mathjax3_config(app, status, warning):
 
     content = (app.outdir / 'index.html').read_text()
     assert MATHJAX_URL in content
+    assert ('<script defer="defer" src="%s">' % MATHJAX_URL in content)
     assert ('<script>window.MathJax = {"extensions": ["tex2jax.js"]}</script>' in content)
 
 
@@ -231,12 +232,35 @@ def test_mathjax2_config(app, status, warning):
     app.builder.build_all()
 
     content = (app.outdir / 'index.html').read_text()
-    assert MATHJAX_URL in content
+    assert ('<script async="async" src="%s">' % MATHJAX_URL in content)
     assert ('<script type="text/x-mathjax-config">'
             'MathJax.Hub.Config({"extensions": ["tex2jax.js"]})'
             '</script>' in content)
 
 
+@pytest.mark.sphinx('html', testroot='ext-math',
+                    confoverrides={'extensions': ['sphinx.ext.mathjax'],
+                                   'mathjax_options': {'async': 'async'},
+                                   'mathjax3_config': {'extensions': ['tex2jax.js']}})
+def test_mathjax_options_async_for_mathjax3(app, status, warning):
+    app.builder.build_all()
+
+    content = (app.outdir / 'index.html').read_text()
+    assert MATHJAX_URL in content
+    assert ('<script async="async" src="%s">' % MATHJAX_URL in content)
+
+
+@pytest.mark.sphinx('html', testroot='ext-math',
+                    confoverrides={'extensions': ['sphinx.ext.mathjax'],
+                                   'mathjax_options': {'defer': 'defer'},
+                                   'mathjax2_config': {'extensions': ['tex2jax.js']}})
+def test_mathjax_options_defer_for_mathjax2(app, status, warning):
+    app.builder.build_all()
+
+    content = (app.outdir / 'index.html').read_text()
+    assert ('<script defer="defer" src="%s">' % MATHJAX_URL in content)
+
+
 @pytest.mark.sphinx('html', testroot='ext-math',
                     confoverrides={'extensions': ['sphinx.ext.mathjax']})
 def test_mathjax_is_installed_only_if_document_having_math(app, status, warning):