From 4ce64185c019fe0363152d46b695b6e6d1005909 Mon Sep 17 00:00:00 2001
From: Yuto Horikawa <hyrodium@gmail.com>
Date: Mon, 5 Sep 2022 20:39:35 +0900
Subject: [PATCH] Fix documentation around LaTeX commands (#583)

* fix latex commands

* fix Some terminology/conventions section
---
 docs/src/maths/nondiff_points.md |  4 ++--
 docs/src/maths/propagators.md    | 12 ++++++------
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/docs/src/maths/nondiff_points.md b/docs/src/maths/nondiff_points.md
index b48002886..d072d4fff 100644
--- a/docs/src/maths/nondiff_points.md
+++ b/docs/src/maths/nondiff_points.md
@@ -42,8 +42,8 @@ plot(abs)
 
 `abs` is the classic example of a function where the derivative is not defines as the limit from above is not equal to the limit from below
 
-$$\mathrm{abs}'(0) = \lim_{h->0^-} \dfrac{\mathrm{abs}(0)-\mathrm{abs}(0-h)}{0-h} = -1$$
-$$\mathrm{abs}'(0) = \lim_{h->0^+} \dfrac{abs(0)-\mathrm{abs}(0-h)}{0-h} = 1$$
+$$\operatorname{abs}'(0) = \lim_{h \to 0^-} \dfrac{\operatorname{abs}(0)-\operatorname{abs}(0-h)}{0-h} = -1$$
+$$\operatorname{abs}'(0) = \lim_{h \to 0^+} \dfrac{\operatorname{abs}(0)-\operatorname{abs}(0-h)}{0-h} = 1$$
 
 Now, as discussed in the introduction the AD system would on it's own choose either 1 or -1, depending on implementation.
 
diff --git a/docs/src/maths/propagators.md b/docs/src/maths/propagators.md
index 2f91cffc1..aba531f55 100644
--- a/docs/src/maths/propagators.md
+++ b/docs/src/maths/propagators.md
@@ -47,12 +47,12 @@ This document will explain this point of view in some detail.
 
 ##### Some terminology/conventions
 
-Let ``p`` be an element of type M, which is defined by some assignment of numbers ``x_1,...,x_m``,
-say ``(x_1,...,x_m) = (a_1,...,1_m)``
+Let ``p`` be an element of type ``M``, which is defined by some assignment of numbers ``x_1, \dots, x_m``,
+say ``(x_1, \dots, x_m) = (a_1, \dots, a_m)``
 
-A _function_ ``f:M \to K`` on ``M`` is (for simplicity) a polynomial ``K[x_1, ... x_m]``
+A _function_ ``f:M \to K`` on ``M`` is (for simplicity) a polynomial ``K[x_1, \dots, x_m]``
 
-The tangent space ``T_pM`` of ``T`` at point ``p`` is the ``K``-vector space spanned by derivations ``d/dx``.
+The tangent space ``T_pM`` of ``M`` at point ``p`` is the ``K``-vector space spanned by derivations ``d/dx``.
 The tangent space acts linearly on the space of functions. They act as usual on functions. Our starting point is
 that we know how to write down ``d/dx(f) = df/dx``.
 
@@ -60,8 +60,8 @@ The collection of tangent spaces ``{T_pM}`` for ``p\in M`` is called the _tangen
 
 Let ``df`` denote the first order information of ``f`` at each point. This is called the differential of ``f``.
 If the derivatives of ``f`` and ``g`` agree at ``p``, we say that ``df`` and ``dg`` represent the same cotangent at ``p``.
-The covectors ``dx_1, ..., dx_m`` form the basis of the cotangent space ``T^*_pM`` at ``p``. Notice that this vector space is
-dual to ``T_p``
+The covectors ``dx_1, \dots, dx_m`` form the basis of the cotangent space ``T^*_pM`` at ``p``. Notice that this vector space is
+dual to ``T_pM``.
 
 The collection of cotangent spaces ``{T^*_pM}`` for ``p\in M`` is called the _cotangent bundle_ of ``M``.