More changes

main.tex

@@ -192,18 +192,18 @@ function:
 \begin{align*}
   R: \mathbb R^{s.shape} \to \mathbb R^{d.shape},
 \end{align*}
-its gradient at the position \texttt{s=position} is a linear map of the following shape:
-\footnote{There are various ways to think about derivatives and gradients of
-  multi-dimensional functions. A different view on gradients would be that at a
-  given point $s=s_0$ the gradient is a matrix with \texttt{s.size} columns and
-  \texttt{d.size} rows. Obviously, it is not feasible to store such a matrix on a
-  computer due to its size. There we think of this matrix in terms of a linear
-  map which maps an array of shape \texttt{s.shape} to an array of shape
-  \texttt{d.shape}. This linear map shall be implemented on the computer in terms
-  of a function. Think of this map as a linear approximation to \texttt{R} based
-  at \texttt{s\_0}.}
+its gradient at the position \texttt{s=position} is a linear map of the
+following shape: \footnote{There are various ways to think about derivatives and
+  gradients of multi-dimensional functions. A different view on gradients would
+  be that at a given point $s=\text{position}$ the gradient is a matrix with
+  \texttt{s.size} columns and \texttt{d.size} rows. Obviously, it is not
+  feasible to store such a matrix on a computer due to its size. There we think
+  of this matrix in terms of a linear map which maps an array of shape
+  \texttt{s.shape} to an array of shape \texttt{d.shape}. This linear map shall
+  be implemented on the computer in terms of a function. Think of this map as a
+  linear approximation to \texttt{R} based at \texttt{position}.}
 \begin{align*}
-  \left. \frac{dR}{ds}\right|_{s=position} = R': \mathbb R^{s.shape} \to \mathbb R^{d.shape}
+  \left. \frac{dR}{ds}\right|_{s=\text{position}} = R': \mathbb R^{s.shape} \to \mathbb R^{d.shape}
 \end{align*}
 What needs to be implemented is a function \texttt{R\_prime(position, s0)} which
 takes the arguments \texttt{position} (which is an array of shape \texttt{s.shape}
@@ -315,8 +315,4 @@ Why is this already sufficient?
   R^\dagger$. All in all, we need an implementation for $R$ and $R^\dagger$.
 \end{itemize}
 
-% \section*{Bibliography test}
-% RESOLVE was first presented in \cite{Resolve2016}.
-% \printbibliography
-
 \end{document}