move figures to separate folder

kolosovpetro · kolosovpetro · commit fc918598f112 · 2024-10-19T01:21:21.000+02:00
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -12,6 +12,7 @@ and this project adheres to [Semantic Versioning v2.0.0](https://semver.org/spec
 - Add build scripts
 - Add mathematica program
 - Add table for seventh powers
+- Move figures to separate folder
 
 ## [1.0.2] - 2024-09-25
 
diff --git a/out/PolynomialIdentityInvolvingBTandFaulhaber.pdf b/out/PolynomialIdentityInvolvingBTandFaulhaber.pdf
diff --git a/src/auxiliary/oeis_row_sums_cubes.tex b/src/auxiliary/oeis_row_sums_cubes.tex
diff --git a/src/figures/01_fig_finite_differences_cubes.tex b/src/figures/01_fig_finite_differences_cubes.tex
@@ -14,5 +14,5 @@
             7   & 343   &               &                 &
         \end{tabular}
     \end{center}
-    \caption{Table of finite differences of the polynomial $n^3$.} \label{tab:table}
-\end{table}
+    \caption{Table of finite differences of the polynomial $n^3$.} \label{tab:differneces-of-cubes}
+\end{table}
diff --git a/src/figures/02_fig_triangle_row_sums_give_cubes.tex b/src/figures/02_fig_triangle_row_sums_give_cubes.tex
@@ -0,0 +1,18 @@
+\begin{table}[H]
+    \setlength\extrarowheight{-6pt}
+    \begin{tabular}{c|cccccccc}
+        $n/k$ & 0 & 1  & 2  & 3  & 4  & 5  & 6  & 7 \\
+        \hline
+        0     & 1 &    &    &    &    &    &    &   \\
+        1     & 1 & 1  &    &    &    &    &    &   \\
+        2     & 1 & 7  & 1  &    &    &    &    &   \\
+        3     & 1 & 13 & 13 & 1  &    &    &    &   \\
+        4     & 1 & 19 & 25 & 19 & 1  &    &    &   \\
+        5     & 1 & 25 & 37 & 37 & 25 & 1  &    &   \\
+        6     & 1 & 31 & 49 & 55 & 49 & 31 & 1  &   \\
+        7     & 1 & 37 & 61 & 73 & 73 & 61 & 37 & 1
+    \end{tabular}
+    \caption{Values of $6k(n-k) + 1$.
+    See the OEIS entry: \href{https://oeis.org/A287326}{\texttt{A287326}}~\cite{kolosov2017third}.}
+    \label{tab:triangle_row_sums_give_cubes}
+\end{table}
diff --git a/src/figures/03_fig_triangle_row_sums_give_fifth_power.tex b/src/figures/03_fig_triangle_row_sums_give_fifth_power.tex
@@ -0,0 +1,18 @@
+\begin{table}[H]
+    \setlength\extrarowheight{-6pt}
+    \begin{tabular}{c|cccccccc}
+        $n/k$ & 0 & 1    & 2    & 3    & 4    & 5    & 6    & 7 \\
+        \hline
+        0     & 1 &      &      &      &      &      &      &   \\
+        1     & 1 & 1    &      &      &      &      &      &   \\
+        2     & 1 & 31   & 1    &      &      &      &      &   \\
+        3     & 1 & 121  & 121  & 1    &      &      &      &   \\
+        4     & 1 & 271  & 481  & 271  & 1    &      &      &   \\
+        5     & 1 & 481  & 1081 & 1081 & 481  & 1    &      &   \\
+        6     & 1 & 751  & 1921 & 2431 & 1921 & 751  & 1    &   \\
+        7     & 1 & 1081 & 3001 & 4321 & 4321 & 3001 & 1081 & 1
+    \end{tabular}
+    \caption{Values of $30k^2(n-k)^2 + 1$.
+    See the OEIS entry \href{https://oeis.org/A300656}{\texttt{A300656}}~\cite{kolosov2018fifth}.}
+    \label{tab:row-sums-gives-fifth-power}
+\end{table}
diff --git a/src/figures/04_fig_triangle_row_sums_give_seventh_power.tex b/src/figures/04_fig_triangle_row_sums_give_seventh_power.tex
diff --git a/src/figures/05_fig_coefficients_a.tex b/src/figures/05_fig_coefficients_a.tex
@@ -14,6 +14,6 @@
             7     & 1 & -450054 & 491400 & -60060 & 0   & 0    & 0     & 51480
         \end{tabular}
     \end{center}
-    \caption{Coefficients $\coeffA{m}{r}$. See the OEIS entries (two links to references).}
+    \caption{Coefficients $\coeffA{m}{r}$. See OEIS sequences~\cite{kolosov2018numerator,kolosov2018denominator}.}
     \label{tab:table_of_coefficients_a}
-\end{table}
+\end{table}
diff --git a/src/sections/01_introduction/introduction.tex b/src/sections/01_introduction/introduction.tex
@@ -1,22 +1,23 @@
 Considering the table of forward finite differences of the polynomial $n^3$
-\begin{table}[H]
-    \begin{center}
-        \setlength\extrarowheight{-6pt}
-        \begin{tabular}{c|cccc}
-            $n$ & $n^3$ & $\Delta(n^3)$ & $\Delta^2(n^3)$ & $\Delta^3(n^3)$ \\
-            \hline
-            0   & 0     & 1             & 6               & 6               \\
-            1   & 1     & 7             & 12              & 6               \\
-            2   & 8     & 19            & 18              & 6               \\
-            3   & 27    & 37            & 24              & 6               \\
-            4   & 64    & 61            & 30              & 6               \\
-            5   & 125   & 91            & 36              &                 \\
-            6   & 216   & 127           &                 &                 \\
-            7   & 343   &               &                 &
-        \end{tabular}
-    \end{center}
-    \caption{Table of finite differences of the polynomial $n^3$.} \label{tab:table}
-\end{table}
+%\begin{table}[H]
+%    \begin{center}
+%        \setlength\extrarowheight{-6pt}
+%        \begin{tabular}{c|cccc}
+%            $n$ & $n^3$ & $\Delta(n^3)$ & $\Delta^2(n^3)$ & $\Delta^3(n^3)$ \\
+%            \hline
+%            0   & 0     & 1             & 6               & 6               \\
+%            1   & 1     & 7             & 12              & 6               \\
+%            2   & 8     & 19            & 18              & 6               \\
+%            3   & 27    & 37            & 24              & 6               \\
+%            4   & 64    & 61            & 30              & 6               \\
+%            5   & 125   & 91            & 36              &                 \\
+%            6   & 216   & 127           &                 &                 \\
+%            7   & 343   &               &                 &
+%        \end{tabular}
+%    \end{center}
+%    \caption{Table of finite differences of the polynomial $n^3$.} \label{tab:table}
+%\end{table}
+\input{figures/01_fig_finite_differences_cubes}
 We can easily observe that finite differences
 \footnote{\input{sections/01_introduction/footnote}}
 of the polynomial $n^3$ may be expressed according
diff --git a/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example1.tex b/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example1.tex
@@ -35,22 +35,5 @@
     \end{equation*}
     It is also clearly seen why the above identity is true evaluating the terms $6k(n-k) + 1$ over $0 \leq k \leq n$ as
     the following table shows
-    \begin{table}[H]
-        \setlength\extrarowheight{-6pt}
-        \begin{tabular}{c|cccccccc}
-            $n/k$ & 0 & 1  & 2  & 3  & 4  & 5  & 6  & 7 \\
-            \hline
-            0     & 1 &    &    &    &    &    &    &   \\
-            1     & 1 & 1  &    &    &    &    &    &   \\
-            2     & 1 & 7  & 1  &    &    &    &    &   \\
-            3     & 1 & 13 & 13 & 1  &    &    &    &   \\
-            4     & 1 & 19 & 25 & 19 & 1  &    &    &   \\
-            5     & 1 & 25 & 37 & 37 & 25 & 1  &    &   \\
-            6     & 1 & 31 & 49 & 55 & 49 & 31 & 1  &   \\
-            7     & 1 & 37 & 61 & 73 & 73 & 61 & 37 & 1
-        \end{tabular}
-        \caption{Values of $6k(n-k) + 1$.
-        See the OEIS entry: \href{https://oeis.org/A287326}{\texttt{A287326}}~\cite{kolosov2017third}.}
-        \label{tab:table-row-sums-gives-cubes}
-    \end{table}
+    \input{figures/02_fig_triangle_row_sums_give_cubes}
 \end{examp}
diff --git a/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example2.tex b/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example2.tex
@@ -40,22 +40,5 @@
     It is also clearly seen
     why the above identity is true evaluating the terms $30k^2(n-k)^2 + 1$ over $0 \leq k \leq n$ as
     the following table shows
-    \begin{table}[H]
-        \setlength\extrarowheight{-6pt}
-        \begin{tabular}{c|cccccccc}
-            $n/k$ & 0 & 1    & 2    & 3    & 4    & 5    & 6    & 7 \\
-            \hline
-            0     & 1 &      &      &      &      &      &      &   \\
-            1     & 1 & 1    &      &      &      &      &      &   \\
-            2     & 1 & 31   & 1    &      &      &      &      &   \\
-            3     & 1 & 121  & 121  & 1    &      &      &      &   \\
-            4     & 1 & 271  & 481  & 271  & 1    &      &      &   \\
-            5     & 1 & 481  & 1081 & 1081 & 481  & 1    &      &   \\
-            6     & 1 & 751  & 1921 & 2431 & 1921 & 751  & 1    &   \\
-            7     & 1 & 1081 & 3001 & 4321 & 4321 & 3001 & 1081 & 1
-        \end{tabular}
-        \caption{Values of $30k^2(n-k)^2 + 1$.
-        See the OEIS entry \href{https://oeis.org/A300656}{\texttt{A300656}}~\cite{kolosov2018fifth}}
-        \label{tab:row-sums-gives-fifth-power}
-    \end{table}
+    \input{figures/03_fig_triangle_row_sums_give_fifth_power}
 \end{examp}
diff --git a/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example3.tex b/src/sections/02_coefficients_via_system_of_equations/coefficients_via_system_of_equations_example3.tex
@@ -53,5 +53,5 @@
     It is also clearly seen
     why the above identity is true evaluating the terms $140 k^3 (n-k)^3 - 14k(n-k) + 1$ over $0 \leq k \leq n$ as
     the OEIS sequence \href{https://oeis.org/A300785}{\textit{A300785}}~\cite{kolosov2018seventh} shows
-    \input{auxiliary/04_fig_triangle_row_sums_give_seventh_power}
+    \input{figures/04_fig_triangle_row_sums_give_seventh_power}
 \end{examp}
diff --git a/src/sections/03_finding_a_recurrence_relation/finding_a_recurrence_relation.tex b/src/sections/03_finding_a_recurrence_relation/finding_a_recurrence_relation.tex
@@ -124,25 +124,7 @@
 where $\bernoulli{t}$ are Bernoulli numbers~\cite{bateman1953higher}.
 It is assumed that $\bernoulli{1}=\frac{1}{2}$.
 For example,
-\begin{table}[H]
-    \begin{center}
-        \setlength\extrarowheight{-6pt}
-        \begin{tabular}{c|cccccccc}
-            $m/r$ & 0 & 1       & 2      & 3      & 4   & 5    & 6     & 7 \\ [3px]
-            \hline
-            0     & 1 &         &        &        &     &      &       &       \\
-            1     & 1 & 6       &        &        &     &      &       &       \\
-            2     & 1 & 0       & 30     &        &     &      &       &       \\
-            3     & 1 & -14     & 0      & 140    &     &      &       &       \\
-            4     & 1 & -120    & 0      & 0      & 630 &      &       &       \\
-            5     & 1 & -1386   & 660    & 0      & 0   & 2772 &       &       \\
-            6     & 1 & -21840  & 18018  & 0      & 0   & 0    & 12012 &       \\
-            7     & 1 & -450054 & 491400 & -60060 & 0   & 0    & 0     & 51480
-        \end{tabular}
-    \end{center}
-    \caption{Coefficients $\coeffA{m}{r}$.}
-    \label{tab:table_of_coefficients_a}
-\end{table}
+\input{figures/05_fig_coefficients_a}
 The coefficients $\coeffA{m}{r}$ are also registered in the OEIS~\cite{kolosov2018numerator,kolosov2018denominator}.
 It is as well interesting to notice that row sums of the $\coeffA{m}{r}$ give powers of $2$
 \begin{equation*}
