Paul commented "TeX doesn't specify its rendering in detail either except via the code itself. In other words, the only proper rendering of TeX is that done by TeX itself."
Actually Appendix G of The TeXbook describes how TeX lays out math. The Office math layout program<https://blogs.msdn.microsoft.com/murrays/2006/11/14/lineservices/> uses the algorithms therein, which is why the results look so much like TeX. The actual code is completely different from TeX’s, but the layout principles are generally the same. It’s good to have this discussion. Clearly Presentation MathML is used a lot for interchanging math zones between programs. Also I haven’t given up on the idea of the browsers rendering MathML well natively. If IE ever succeeds, it’ll likely look like TeX, since both IE and Edge use LineServices<https://blogs.msdn.microsoft.com/murrays/2006/11/14/lineservices/>. And it should be way faster than Java script code. My main complaints about Presentation MathML are 1) lack of an explicit n-ary element (for integrals, summations, products, etc.) and 2) lack of document level math properties<https://blogs.msdn.microsoft.com/murrays/2008/10/27/default-document-math-properties/>, like default math font. Also Presentation MathML depends too much on proper use of <mrow>, which wouldn’t even be needed if the elements were all “prefix” elements like <mfrac> and <mfenced>. But infix notation can be translated to prefix notation, a good example being conversion of the linear format<http://www.unicode.org/notes/tn28/UTN28-PlainTextMath-v3.pdf> to the OMML<https://blogs.msdn.microsoft.com/murrays/2006/10/06/mathml-and-ecma-math-omml/>-like internal format for LineServices. Similarly RichEdit’s MathML reader converts using the rich-text string stack<https://msdn.microsoft.com/en-us/library/windows/desktop/hh768736(v=vs.85).aspx> originally developed for the linear format. The bottom line is that MathML isn’t perfect, but it’s a widely used standard and gets the job done. As such, it’s hardly a failure. And it’s nicely supported on the web thanks to MathJax. Murray
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