MathML 4 extensions for alignment and possible deprecation of <maligngroup/> and <malignmark/> #181
Description
Having just implemented a polyfill for elementary math, that got me thinking about some related ideas:
- The most obvious concept related to long division is synthetic division. It is basically the same idea as long division except that you are dividing polynomials. With synthetic division, the columns contain numbers (the coefficients of the polynomial), not just digits. As a refresher, see this page and the example taken from it below):
| Polynomial Division | Synthetic Division |
|---|---|
 |
 |
- Synthetic division is a shorthand for long division of polynomials (left example above). Long division of polynomials is basically the same idea as long division of numbers except that instead of digits, you have monomials that need to go into their own column. Doing that automatically requires knowing the variable you want to "sort" on so that each monomial goes into the proper column.
- A very similar property is needed when displaying systems of equations -- each monomial wants to be in it's own column (in this case, the top level element would not be
mlongdiv, butmstack).
There are a few complications such as decimal alignment of the coefficients:
8.44x + 55 y = 0
3.1 x - 0.7y = -1.1
Note that alignment requires knowing what characters/operators act as column separators (e.g., +and -, along with = and a few other relational operators). These would be inside of mo elements, so potentially any mo element could be a separator, or maybe an attribute specifies what the separators are (something to think about/discuss).
The above example is taken from the MathML 3 spec formaligngroup and malignmark. I think only MathPlayer ever implemented those elements and I suspect that you can count on your fingers the number of times they have been used. It is a very complicated feature to implement and to use. In contrast, I think the above features are an incremental extension to elementary math layout, so implementation (especially via an extension to the polyfill I wrote), means that supporting these features would be universal (assuming I or someone else extended the polyfill). Just as important, using this extension would be simple as it is a declarative notation that doesn't require modifying the generated layout other than at a high level (wrapping with mstack or mlongdiv). It would be less powerful though.
I suspect that this proposed extension to elementary math handles the large majority of cases where people play games with tables to achieve alignment, both in MathML and in TeX. @davidcarlisle: do you have any estimate of how many uses of table for alignment in TeX would be covered by this proposed extension? What are some of the cases that are missed by it?
