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[mlir] Fix MathJax rendering in Affine doc 

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.

{F14942131}

Reviewed By: ftynse

Differential Revision: https://reviews.llvm.org/D94004
This commit is contained in:
lewuathe 2021-01-06 01:59:45 +00:00 committed by Mehdi Amini
parent 74f93bc373
commit 4ae7952e2b
1 changed files with 8 additions and 8 deletions
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16
mlir/docs/Dialects/Affine.md
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@ -124,19 +124,19 @@ 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