# [Mlir-commits] [mlir] 4ae7952 - [mlir] Fix MathJax rendering in Affine doc

Mehdi Amini llvmlistbot at llvm.org
Tue Jan 5 18:11:50 PST 2021

Author: lewuathe
Date: 2021-01-06T02:11:36Z
New Revision: 4ae7952e2b3566d373c55c8e9740051ca37ed738

URL: https://github.com/llvm/llvm-project/commit/4ae7952e2b3566d373c55c8e9740051ca37ed738
DIFF: https://github.com/llvm/llvm-project/commit/4ae7952e2b3566d373c55c8e9740051ca37ed738.diff

LOG: [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

Modified:
mlir/docs/Dialects/Affine.md

Removed:

################################################################################
diff  --git a/mlir/docs/Dialects/Affine.md b/mlir/docs/Dialects/Affine.md
index cedbb0106c30..1ce535a0c9b7 100644
--- a/mlir/docs/Dialects/Affine.md
+++ b/mlir/docs/Dialects/Affine.md
@@ -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