Incorrect MathML is generated from LaTeX vmatrix

[abnerlee]

version 2.7.5

TeX input:

\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
1 &  2 & 3 \\
1 &  2 & 3 \\
\end{vmatrix}

MathJax will generate following MathML from it

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mo>|</mo>
    <mtable rowspacing="4pt" columnspacing="1em">
      <mtr>
        <mtd>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="bold">i</mi>
          </mrow>
        </mtd>
        <mtd>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="bold">j</mi>
          </mrow>
        </mtd>
        <mtd>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="bold">k</mi>
          </mrow>
        </mtd>
      </mtr>
      <mtr>
        <mtd>
          <mn>1</mn>
        </mtd>
        <mtd>
          <mn>2</mn>
        </mtd>
        <mtd>
          <mn>3</mn>
        </mtd>
      </mtr>
      <mtr>
        <mtd>
          <mn>1</mn>
        </mtd>
        <mtd>
          <mn>2</mn>
        </mtd>
        <mtd>
          <mn>3</mn>
        </mtd>
      </mtr>
    </mtable>
    <mo>|</mo>
  </mrow>
</math>

But if you copy the generated MathML code into http://www.wiris.com/editor/demo/en/developers#mathml-latex or MS Word, the actually rendered math equation is like:

So I think the generate MathML is incorrect for vmatrix, maybe

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mtable><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math>

is more correct.

[dpvc]

The MathML produced by MathJax is actually correct; but it seems that the WIRIS renderer does not implement the default attributes from the MathML Operator Dictionary, even for parentheses and other standard delimiters. WIRIS seems to require <mo stretchy="true">|</mo> in order to have the delimiters be stretchy, despite the entries in the operator dictionary for '|' in the prefix and postfix positions.

Although the Operator Dictionary given at the link above is non-normative, some form of default attributes for things like stretchy operators is essential to making MathML work as expected. If you add stretchy="true" to the <mo>|</mo> elements, WIRIS renders it as expected, but this attribute should be the default (according to the Operator Dictionary), so should not be needed explicitly. So it seems that WIRIS is at fault, here, not MathJax.

Note also that the MathML specification indicates that <mfenced> is equivalent to an expanded <mrow>-with-<mo> construction:

Thus, any mfenced element is completely equivalent to an expanded form described below.... A MathML renderer is required to render either of these forms in exactly the same way.

The fact that the WIRIS renderer treats <mfenced open="|" close="|">...</mfenced> differently from <mrow><mo>|</mo>...<mo>|</mo></mrow> (even if the fence="true" attribute is applied explicitly to the <mo> elements) indicate that WIRIS is not following the MathML specification.