{"id":142,"date":"2020-10-25T21:44:19","date_gmt":"2020-10-26T04:44:19","guid":{"rendered":"https:\/\/devblogs.microsoft.com\/math-in-office\/?p=142"},"modified":"2020-11-25T12:04:06","modified_gmt":"2020-11-25T20:04:06","slug":"mathml-element-deprecated-on-web","status":"publish","type":"post","link":"https:\/\/devblogs.microsoft.com\/math-in-office\/mathml-element-deprecated-on-web\/","title":{"rendered":"MathML mfenced element deprecated on web"},"content":{"rendered":"

The MathML working group is planning to deprecate the <mfenced> element<\/a> as well as the <mo> fence and separator attributes for use on the web. The justification is to simplify web implementations by deprecating MathML features that are redundant. This post explains how <mfenced> and the fence and separator attributes can be handled in other ways and it discusses the implications for OfficeMath<\/a>.<\/p>\n

Emulating <mfenced> with <mrow><\/h2>\n

The MathML <mfenced> element is handy for representing a variety of delimited expressions, such as parenthesized, braced, and bracketed expressions. The expressions can contain separators. Examples are (\ud835\udc4e + \ud835\udc4f), (\ud835\udc4e + \ud835\udc4f], and the quantum mechanical expectation value \u27e8\ud835\udf13|\u210b|\ud835\udf13\u27e9, in which the \u2018|\u2019 is a separator. The <mfenced> element corresponds quite closely to the OMML<\/a> delimiters element <d> used in Office app files, which is why the OfficeMath MathML writers use it.<\/p>\n

To show how <mfenced> can be emulated by an <mrow>, consider (\ud835\udc4e + \ud835\udc4f]. Using <mfenced>, it is represented by<\/p>\n

\u00a0 \u00a0<mfenced close=\"]\">\r\n<\/code> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <mi>a<\/mi><mo>+<\/mo><mi>b<\/mi>\r\n<\/code>\u00a0\u00a0 <\/mfenced><\/code><\/pre>\n
Since left parenthesis is the default start delimiter, the <mfenced> doesn\u2019t need the attribute open=”(“, although it could have it. The equivalent <mrow> representation is<\/p>\n
\u00a0\u00a0 <mrow>\r\n<\/code>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <mo>(<\/mo>\r\n<\/code> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 < mi>a<\/mi><mo>+<\/mo><mi>b<\/mi>\r\n<\/code> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <mo>]<\/mo>\r\n<\/code>  \u00a0<\/mrow><\/code><\/pre>\n
Here the <mo> fence=”true” attribute isn\u2019t needed since the MathML operator dictionary assigns fence=”true” to parentheses, brackets, braces and other Unicode characters that are fences by default. You need the attribute fence=”false” or stretchy=”false” if you don\u2019t want the delimiters to grow to fit their content.<\/p>\n
Comparing these representations, we see that <mfenced> is more compact. On the other hand, the <mrow> emulation is more general in that you can include attributes like different math colors on the individual delimiters and you can embellish the delimiters with accents. If you want a delimited expression with just the open delimiter, e.g., {\ud835\udc4e + \ud835\udc4f, you omit the <mo> for the close delimiter. Similarly, a delimited expression with no open delimiter, e.g., \ud835\udc4e + \ud835\udc4f}, omits the open delimiter. For more discussion of <mfenced> and <mrow>, see the MathML 3.0 spec<\/a>.<\/p>\n
Parsing <mrow> emulation of <mfenced><\/h2>\n
The <mfenced> element is an example of Polish prefix notation: you know up front what kind of math object is involved. In contrast, you must parse an <mrow> emulation of <mfenced> to figure out what it represents. The parsing is a little tricky, but it\u2019s not that hard since the delimiter roles are implied by the order in which the delimiters appear inside the <mrow>.<\/p>\n
The basic principle is that the start and end delimiters are fences, and any delimiters in between are separators. The main OfficeMath MathML reader uses a SAX parser<\/a>, which cannot look ahead. But the reader can store information for looking behind. The algorithm is: the first delimiter of an <mrow> is a start delimiter <mo> and other delimiters are marked as separators. When the parser comes to the end of the delimiter expression (<\/mrow>), it remarks the last delimiter as an end delimiter. If there are only two delimiters, there are no separators. If there\u2019s only one delimiter, it\u2019s a start delimiter unless it comes at the end. This algorithm converts <mrow> delimiter elements into the OfficeMath <d> equivalent. It will be used soon in Office apps since FireFox removed support of <mfenced> (OneNote counted on it in FireFox!) and the Chromium code base won\u2019t support it either. Yes, Chromium will support \u201ccore\u201d Presentation MathML. Many browsers are based on Chromium<\/a>, e.g., Chrome and Edge.<\/p>\n
Some MathML elements are \u201cinferred mrow\u2019s\u201d in that they treat multiple children as a single argument and the algorithm works with them as well. Such elements include <math>, <msqrt>, <menclose>, <mphantom>, <mpadded> and <mtd>.<\/p>\n
Poorly formed <mrow> expressions<\/h2>\n
Best practice <mrow> delimiter emulation restricts the contents of the <mrow> to the contents of the delimited expression. But what if there are other things inside an <mrow> such as in (note: <math> is an inferred <mrow>)<\/p>\n
<math >\r\n   <mo>(<\/mo>\r\n   <mi>a<\/mi>\r\n   <mo>+<\/mo>\r\n   <mi>b<\/mi>\r\n   <mo>)<\/mo>\r\n   <mo>+<\/mo>\r\n   <mo>|<\/mo>\r\n   <mi>a<\/mi>\r\n   <mo>+<\/mo>\r\n   <mi>b<\/mi>\r\n   <mo>|<\/mo>\r\n<\/math>\r\n<\/pre>\n
Two tricks are useful: with no form-disambiguating attribute like \u201cform\u201d=\u201dprefix\u201d on the delimiter <mo>\u2019s (as in this example), use the default form value given in the MathML operator dictionary<\/a>. This works for all default delimiter pairs, but not for \u2018|\u2019 which can be used as a separator (infix), open delimiter (prefix), or close delimiter (postfix). For \u2018|\u2019 use the algorithm above with a small twist: when there is an active \u2018|\u2019 start delimiter, treat a \u2018|\u2019 as an end delimiter. When finished processing any delimiter expression, reset the state to \u201cno delimiters\u201d. As such \u2018|\u2019 is alternately a start delimiter and end delimiter. This algorithm cannot produce nested absolute-value expressions. To nest an absolute value, use appropriate form attributes, or, best practice, put the absolute value in its own <mrow>.<\/p>\n","protected":false},"excerpt":{"rendered":"
The MathML working group is planning to deprecate the <mfenced> element as well as the <mo> fence and separator attributes for use on the web. The justification is to simplify web implementations by deprecating MathML features that are redundant. This post explains how <mfenced> and the fence and separator attributes can be handled in other […]<\/p>\n","protected":false},"author":40611,"featured_media":55,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-142","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-in-office"],"acf":[],"blog_post_summary":"
The MathML working group is planning to deprecate the <mfenced> element as well as the <mo> fence and separator attributes for use on the web. The justification is to simplify web implementations by deprecating MathML features that are redundant. This post explains how <mfenced> and the fence and separator attributes can be handled in other […]<\/p>\n","_links":{"self":[{"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/posts\/142","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/users\/40611"}],"replies":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/comments?post=142"}],"version-history":[{"count":0,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/posts\/142\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/media\/55"}],"wp:attachment":[{"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/media?parent=142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/categories?post=142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/math-in-office\/wp-json\/wp\/v2\/tags?post=142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}