[mlir] Fix MathJax rendering in Affine doc

[Lewuathe]

Summary

MathJax is not properly imported in Affine doc. It causes the invalid rendering
of math formulas in the Affine doc page.

https://mlir.llvm.org/docs/Dialects/Affine/#affine-expressions

Importing MathJax code from CDN resolved the rendering issue as follows.

[jpienaar]

mlir/docs/Dialects/Affine.md

1

This might make more sense in the Hugo template directly (in mlir-www repo) rather than have it in the markdown for the dialect.

[Lewuathe]

mlir/docs/Dialects/Affine.md

1

Thanks. Okay, I'll send a PR to the repository mlir-www.

[Lewuathe]

Post review follow-up moving MathJax import to mlir-www

[Lewuathe]

I have created a PR in the mlir-www repository to add MathJax.
https://github.com/llvm/mlir-www/pull/53

[ftynse]

Thanks!

[Lewuathe]

@ftynse Thanks! Can I ask you to land this change in the repository on behalf of me? I do not have any write permission in the repository.

mlir/docs/Dialects/Affine.md

 # 'affine' Dialect
 
 This dialect provides a powerful abstraction for affine operations and analyses.
 
 [TOC]
 
 ## Polyhedral Structures
 
 MLIR uses techniques from polyhedral compilation to make dependence analysis and

 ceildiv, and (4) addition and subtraction. All of these operators associate from
 left to right.
 
 A _multidimensional affine expression_ is a comma separated list of
 one-dimensional affine expressions, with the entire list enclosed in
 parentheses.
 
 **Context:** An affine function, informally, is a linear function plus a
-constant. More formally, a function f defined on a vector $$\vec{v} \in
-\mathbb{Z}^n$$ is a multidimensional affine function of $$\vec{v}$$ if
-$$f(\vec{v})$$ can be expressed in the form $$M \vec{v} + \vec{c}$$ where $$M$$
-is a constant matrix from $$\mathbb{Z}^{m \times n}$$ and $$\vec{c}$$ is a
-constant vector from $$\mathbb{Z}$$. $$m$$ is the dimensionality of such an
+constant. More formally, a function f defined on a vector $\vec{v} \in
+\mathbb{Z}^n$ is a multidimensional affine function of $\vec{v}$ if
+$f(\vec{v})$ can be expressed in the form $M \vec{v} + \vec{c}$ where $M$
+is a constant matrix from $\mathbb{Z}^{m \times n}$ and $\vec{c}$ is a
+constant vector from $\mathbb{Z}$. $m$ is the dimensionality of such an
 affine function. MLIR further extends the definition of an affine function to
 allow 'floordiv', 'ceildiv', and 'mod' with respect to positive integer
 constants. Such extensions to affine functions have often been referred to as
 quasi-affine functions by the polyhedral compiler community. MLIR uses the term
 'affine map' to refer to these multidimensional quasi-affine functions. As
-examples, $$(i+j+1, j)$$, $$(i \mod 2, j+i)$$, $$(j, i/4, i \mod 4)$$, $$(2i+1,
-j)$$ are two-dimensional affine functions of $$(i, j)$$, but $$(i \cdot j,
-i^2)$$, $$(i \mod j, i/j)$$ are not affine functions of $$(i, j)$$.
+examples, $(i+j+1, j)$, $(i \mod 2, j+i)$, $(j, i/4, i \mod 4)$, $(2i+1,
+j)$ are two-dimensional affine functions of $(i, j)$, but $(i \cdot j,
+i^2)$, $(i \mod j, i/j)$ are not affine functions of $(i, j)$.
 
 ### Affine Maps
 
 Syntax:
 
 ```
 affine-map-inline
    ::= dim-and-symbol-id-lists `->` multi-dim-affine-expr