
	columns/m1/.style={column type=c,column name= $m_1$},
	columns/m2/.style={column type=c,column name= $m_2{=}n_1$},
	columns/n2/.style={column type=c,column name= $n_2$},
	columns/res/.style={column type=c,column name= res},
	columns/nbsol_qr/.style={column type=c,column name= $\delta_{\textup{alg}}$},
	columns/nbsol_phc/.style={column type=c,column name= $\delta_{\textup{phc}}$},
	columns/nbsol_brt/.style={column type=c,column name= $\delta_{\textup{brt}}$},
	]
	{T31.txt}
	\caption{Numerical results for PHCpack, Bertini and our method for dense systems in $n=3$ variables of increasing degree $d$. The table shows matrix sizes, accuracy and number of solutions.}
	\label{t31}
\end{table}

\begin{table}[h!]
	\centering
	\footnotesize
	\pgfplotstabletypeset[
	every head row/.style={before row=\toprule,after row=\midrule},
	every last row/.style={after row=\bottomrule},
	columns = {Var1,time_mac,time_ker,time_basis,time_EV,time_qr,time_phc,time_brt},
	columns/Var1/.style={int detect,column type=c|,column name=$d$},
	columns/time_mac/.style={column type=c,column name= $t_M$},
	columns/time_ker/.style={column type=c,column name= $t_N$},
	columns/time_basis/.style={column type=c,column name= $t_B$},
	columns/time_EV/.style={column type=c,column name= $t_S$},
	columns/time_qr/.style={column type=c,column name= $t_{\textup{alg}}$},
	columns/time_phc/.style={column type=c,column name= $t_{\textup{phc}}$},
	columns/time_brt/.style={column type=c,column name= $t_{\textup{brt}}$},
	]
	{T32.txt}
	\caption{Timing results for PHCpack, Bertini and our method for dense systems in $n=3$ variables of increasing degree $d$.}
	\label{t32}
\end{table}

\begin{table}[h!]
	\centering
	\footnotesize
	\pgfplotstabletypeset[
	every head row/.style={before row=\toprule,after row=\midrule},
	every last row/.style={after row=\bottomrule},
	columns = {Var1,nbsol,m1,m2,n2,res,nbsol_qr,nbsol_phc,nbsol_brt},
	columns/Var1/.style={int detect,column type=c|,column name=$d$},
	columns/nbsol/.style={int detect,column type=c,column name= $\delta$},
	columns/m1/.style={column type=c,column name= $m_1$},
	columns/m2/.style={column type=c,column name= $m_2{=}n_1$},
	columns/n2/.style={column type=c,column name= $n_2$},
	columns/res/.style={column type=c,column name= res},
	columns/nbsol_qr/.style={column type=c,column name= $\delta_{\textup{alg}}$},
	columns/nbsol_phc/.style={column type=c,column name= $\delta_{\textup{phc}}$},
	columns/nbsol_brt/.style={column type=c,column name= $\delta_{\textup{brt}}$},
	]
	{T41.txt}
	\caption{Numerical results for PHCpack, Bertini and our method for dense systems in $n=4$ variables of increasing degree $d$. The table shows matrix sizes, accuracy and number of solutions.}
	\label{t41}
\end{table}

\begin{table}[h!]
	\centering
	\footnotesize
	\pgfplotstabletypeset[
	every head row/.style={before row=\toprule,after row=\midrule},
	every last row/.style={after row=\bottomrule},
	columns = {Var1,time_mac,time_ker,time_basis,time_EV,time_qr,time_phc,time_brt},
	columns/Var1/.style={int detect,column type=c|,column name=$d$},
	columns/time_mac/.style={column type=c,column name= $t_M$},
	columns/time_ker/.style={column type=c,column name= $t_N$},
	columns/time_basis/.style={column type=c,column name= $t_B$},
	columns/time_EV/.style={column type=c,column name= $t_S$},
	columns/time_qr/.style={column type=c,column name= $t_{\textup{alg}}$},
	columns/time_phc/.style={column type=c,column name= $t_{\textup{phc}}$},
	columns/time_brt/.style={column type=c,column name= $t_{\textup{brt}}$},
	]
	{T42.txt}
	\caption{Timing results for PHCpack, Bertini and our method for dense systems in $n=4$ variables of increasing degree $d$.}
	\label{t42}
\end{table}

\begin{table}[h!]
	\centering
	\footnotesize
	\pgfplotstabletypeset[
	every head row/.style={before row=\toprule,after row=\midrule},
	every last row/.style={after row=\bottomrule},
	columns = {Var1,nbsol,m1,m2,n2,res,nbsol_qr,nbsol_phc,nbsol_brt},
	columns/Var1/.style={int detect,column type=c|,column name=$d$},
	columns/nbsol/.style={int detect,column type=c,column name= $\delta$},
	columns/m1/.style={column type=c,column name= $m_1$},
	columns/m2/.style={column type=c,column name= $m_2{=}n_1$},
	columns/n2/.style={column type=c,column name= $n_2$},
	columns/res/.style={column type=c,column name= res},
	columns/nbsol_qr/.style={column type=c,column name= $\delta_{\textup{alg}}$},
	columns/nbsol_phc/.style={column type=c,column name= $\delta_{\textup{phc}}$},
	columns/nbsol_brt/.style={column type=c,column name= $\delta_{\textup{brt}}$},
	]
	{T51.txt}
	\caption{Numerical results for PHCpack, Bertini and our method for dense systems in $n=5$ variables of increasing degree $d$. The table shows matrix sizes, accuracy and number of solutions.}
	\label{t51}
\end{table}

\begin{table}[h!]
	\centering
	\footnotesize
	\pgfplotstabletypeset[
	every head row/.style={before row=\toprule,after row=\midrule},
	every last row/.style={after row=\bottomrule},
	columns = {Var1,time_mac,time_ker,time_basis,time_EV,time_qr,time_phc,time_brt},
	columns/Var1/.style={int detect,column type=c|,column name=$d$},
	columns/time_mac/.style={column type=c,column name= $t_M$},
	columns/time_ker/.style={column type=c,column name= $t_N$},
	columns/time_basis/.style={column type=c,column name= $t_B$},
	columns/time_EV/.style={column type=c,column name= $t_S$},
	columns/time_qr/.style={column type=c,column name= $t_{\textup{alg}}$},