fix: minor corrections

Makefile

@@ -4,3 +4,4 @@ thesis: main.tex
 	lualatex -shell-escape main.tex
 	biber main
 	lualatex -shell-escape main.tex
+	lualatex -shell-escape main.tex

contents/basic_iterative_methods.tex

@@ -54,7 +54,7 @@ \subsection{Jacobi and Gauss-Seidel}
 	\label{eq:general-preconditioned-system-of-linear-equations}
 \end{equation}
 which represents a modified version of Equation~\eqref{eq:general-system-of-linear-equations}, that is obtained by multiplying each side of the equation by the inverse of a matrix $M$.
-By the rules of linear algebra, Equation~\ref{eq:general-preconditioned-system-of-linear-equations} is equivalent to the original system and, therefore, has the same solution.
+By the rules of linear algebra, Equation~\eqref{eq:general-preconditioned-system-of-linear-equations} is equivalent to the original system and, therefore, has the same solution.
 However, it can also be considered as a left-preconditioned version of Equation~\eqref{eq:general-system-of-linear-equations}, with $M$ as a preconditioner.
 Considering again the fixed point of Equation~\eqref{eq:general-preconditioned-system-of-linear-equations} yields the iteration
 \begin{equation}

contents/discretization_of_pdes.tex

@@ -254,7 +254,7 @@ \subsection{Stencil Codes}
 		\{(\bm{a} + \bm{\hat{a}}, b \cdot \hat{b} ) \} \; + & \text{if} \; A = \{(\bm{a}, b ) \} \cup \tilde{A} \\
 		\{(\bm{a}, b ) \} \cdot \tilde{B} + \tilde{A} \cdot B & 
 		\text{and} \; B = \{(\bm{\hat{a}}, \hat{b} ) \} \cup \tilde{B} \\ & \\
-		\emptyset & \text{if} \; A = \emptyset \vee B = \emptyset
+		\emptyset & \text{else} %\text{if} \; A = \emptyset \vee B = \emptyset
 	\end{cases}
 \label{eq:stencil-mult}
 \end{equation}

scripts/stencils.py

@@ -44,6 +44,7 @@ def mult(s1: set, s2: set):
 
 s1 = {(0, 2), (1, -1), (-1, -1)}
 s2 = {(0, 2), (1, -1), (-1, -1)}
+# s2 = {(0, 4), (1, -1), (-1, -1), (2, -1), (-2, -1)}
 s1_ = s1.copy()
 s2_ = s2.copy()
 tmp0 = add(s1_, s2_)