This example shows how to process a complete HTML page containing MathJax version 2 styled <script> tags (that store the math content in the page). In version 2, these <script> tags are generated automatically by the tex2jax or other pre-processors, but they could also be created by other software that generates the page so as to avoid the need for the pre-processing step.
MathJax version 3 does not look for such <script> tags itself, but you can implement it yourself, as in this example.
The key lines are
<script>
MathJax = {
options: {
renderActions: {
find: [10, function (doc) {
for (const node of document.querySelectorAll('script[type^="text/tex"]')) {
const display = !!node.type.match(/; *mode=display/);
const math = new doc.options.MathItem(node.textContent, doc.inputJax[0], display);
const text = document.createTextNode('');
node.parentNode.replaceChild(text, node);
math.start = {node: text, delim: '', n: 0};
math.end = {node: text, delim: '', n: 0};
doc.math.push(math);
}
}, '']
}
}
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
which set up a renderAction that replaces the usual page-search action (the find action at priority 10) with one that searches for <script> tags with type="math/tex" (or type="math/tex; mode=display"), and creates the needed MathItem instances for them. The <script> tags are replaced by empty text nodes, and the math item refers to these for its starting and ending locations.