\documentclass[12pt]{amsart}
\usepackage{texdraw}
\setlength{\topmargin}{30mm}
\addtolength{\topmargin}{-1in}
\addtolength{\topmargin}{-\headsep}
\addtolength{\topmargin}{-\headheight}
\addtolength{\topmargin}{-\topskip}
\setlength{\textheight}{267mm}
\addtolength{\textheight}{\topskip}
\addtolength{\textheight}{-\footskip}
\addtolength{\textheight}{-30pt}
\setlength{\oddsidemargin}{-1in}
\addtolength{\oddsidemargin}{20mm}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\textwidth}{170mm}

\begin{document}
   \parindent0cm
   \begin{center}
      \large\bf The Tropicalisation of

      \bigskip

      \begin{math}
          f=-x^{5}+(-1-2\cdot t^{2}+241\cdot t^{4}+119\cdot t^{6}+25\cdot t^{8})\cdot x^{4}+(242\cdot t^{4}+603\cdot t^{6}-14136\cdot t^{8}-15319\cdot t^{10}-3990\cdot t^{12}-225\cdot t^{14})\cdot x^{3}+(-14641\cdot t^{8}-44770\cdot t^{10}-49632\cdot t^{12}+108026\cdot t^{14}+115325\cdot t^{16}+27000\cdot t^{18})\cdot x^{2}+y^{2}+(131769\cdot t^{14}+383328\cdot t^{16}+398574\cdot t^{18}+174240\cdot t^{20}+27225\cdot t^{22})\cdot x
      \end{math}
   \end{center}
   \vspace*{0.5cm}
   The vertices of the tropical curve are:
   \begin{center}
      \begin{math}
         (0,0),\;\; (-4,-8),\;\; (-6,-10)
      \end{math}
   \end{center}
   \vspace*{0.5cm}

   \begin{center}

    \begin{texdraw}
       \drawdim cm  \relunitscale 0.7 \arrowheadtype t:V
       %\linewd 0.05 \lpatt (0.1 0.4)
       %\move (-4 0) \avec (9 0) \move (0 -4) \avec (0 9)
       \linewd 0.1  \lpatt (1 0)
       

       \setgray 0.6

       
       \relunitscale 1.6
       \move (3 5) \fcir f:0 r:0.12
       \move (3 5) \lvec (-1 -3)
       \htext (-0.5 -1.5){$2$}
       \move (3 5) \rlvec (0 -1.87)
       \move (3 5) \rlvec (1.00053361792956243329775880469583778014941302027748 2.5)
       \move (-1 -3) \fcir f:0 r:0.12
       \move (-1 -3) \lvec (-3 -5)
       \htext (-3.5 -6.5){$2$}
       \move (-1 -3) \rlvec (0 -1.87)
       \htext (-1 -3.62){$2$}
       \move (-3 -5) \fcir f:0 r:0.12
       \move (-3 -5) \rlvec (0 -1.87)
       \move (-3 -5) \rlvec (-2.5 -1.24666666666666666666666666666666666666666666666667)

   %% HERE STARTS THE CODE FOR THE LATTICE
        \move (-4 -6) \fcir f:0.8 r:0.06
        \move (-4 -5) \fcir f:0.8 r:0.06
        \move (-4 -4) \fcir f:0.8 r:0.06
        \move (-4 -3) \fcir f:0.8 r:0.06
        \move (-4 -2) \fcir f:0.8 r:0.06
        \move (-4 -1) \fcir f:0.8 r:0.06
        \move (-4 0) \fcir f:0.8 r:0.06
        \move (-4 1) \fcir f:0.8 r:0.06
        \move (-4 2) \fcir f:0.8 r:0.06
        \move (-4 3) \fcir f:0.8 r:0.06
        \move (-4 4) \fcir f:0.8 r:0.06
        \move (-4 5) \fcir f:0.8 r:0.06
        \move (-4 6) \fcir f:0.8 r:0.06
        \move (-3 -6) \fcir f:0.8 r:0.06
        \move (-3 -5) \fcir f:0.8 r:0.06
        \move (-3 -4) \fcir f:0.8 r:0.06
        \move (-3 -3) \fcir f:0.8 r:0.06
        \move (-3 -2) \fcir f:0.8 r:0.06
        \move (-3 -1) \fcir f:0.8 r:0.06
        \move (-3 0) \fcir f:0.8 r:0.06
        \move (-3 1) \fcir f:0.8 r:0.06
        \move (-3 2) \fcir f:0.8 r:0.06
        \move (-3 3) \fcir f:0.8 r:0.06
        \move (-3 4) \fcir f:0.8 r:0.06
        \move (-3 5) \fcir f:0.8 r:0.06
        \move (-3 6) \fcir f:0.8 r:0.06
        \move (-2 -6) \fcir f:0.8 r:0.06
        \move (-2 -5) \fcir f:0.8 r:0.06
        \move (-2 -4) \fcir f:0.8 r:0.06
        \move (-2 -3) \fcir f:0.8 r:0.06
        \move (-2 -2) \fcir f:0.8 r:0.06
        \move (-2 -1) \fcir f:0.8 r:0.06
        \move (-2 0) \fcir f:0.8 r:0.06
        \move (-2 1) \fcir f:0.8 r:0.06
        \move (-2 2) \fcir f:0.8 r:0.06
        \move (-2 3) \fcir f:0.8 r:0.06
        \move (-2 4) \fcir f:0.8 r:0.06
        \move (-2 5) \fcir f:0.8 r:0.06
        \move (-2 6) \fcir f:0.8 r:0.06
        \move (-1 -6) \fcir f:0.8 r:0.06
        \move (-1 -5) \fcir f:0.8 r:0.06
        \move (-1 -4) \fcir f:0.8 r:0.06
        \move (-1 -3) \fcir f:0.8 r:0.06
        \move (-1 -2) \fcir f:0.8 r:0.06
        \move (-1 -1) \fcir f:0.8 r:0.06
        \move (-1 0) \fcir f:0.8 r:0.06
        \move (-1 1) \fcir f:0.8 r:0.06
        \move (-1 2) \fcir f:0.8 r:0.06
        \move (-1 3) \fcir f:0.8 r:0.06
        \move (-1 4) \fcir f:0.8 r:0.06
        \move (-1 5) \fcir f:0.8 r:0.06
        \move (-1 6) \fcir f:0.8 r:0.06
        \move (0 -6) \fcir f:0.8 r:0.06
        \move (0 -5) \fcir f:0.8 r:0.06
        \move (0 -4) \fcir f:0.8 r:0.06
        \move (0 -3) \fcir f:0.8 r:0.06
        \move (0 -2) \fcir f:0.8 r:0.06
        \move (0 -1) \fcir f:0.8 r:0.06
        \move (0 0) \fcir f:0.8 r:0.06
        \move (0 1) \fcir f:0.8 r:0.06
        \move (0 2) \fcir f:0.8 r:0.06
        \move (0 3) \fcir f:0.8 r:0.06
        \move (0 4) \fcir f:0.8 r:0.06
        \move (0 5) \fcir f:0.8 r:0.06
        \move (0 6) \fcir f:0.8 r:0.06
        \move (1 -6) \fcir f:0.8 r:0.06
        \move (1 -5) \fcir f:0.8 r:0.06
        \move (1 -4) \fcir f:0.8 r:0.06
        \move (1 -3) \fcir f:0.8 r:0.06
        \move (1 -2) \fcir f:0.8 r:0.06
        \move (1 -1) \fcir f:0.8 r:0.06
        \move (1 0) \fcir f:0.8 r:0.06
        \move (1 1) \fcir f:0.8 r:0.06
        \move (1 2) \fcir f:0.8 r:0.06
        \move (1 3) \fcir f:0.8 r:0.06
        \move (1 4) \fcir f:0.8 r:0.06
        \move (1 5) \fcir f:0.8 r:0.06
        \move (1 6) \fcir f:0.8 r:0.06
        \move (2 -6) \fcir f:0.8 r:0.06
        \move (2 -5) \fcir f:0.8 r:0.06
        \move (2 -4) \fcir f:0.8 r:0.06
        \move (2 -3) \fcir f:0.8 r:0.06
        \move (2 -2) \fcir f:0.8 r:0.06
        \move (2 -1) \fcir f:0.8 r:0.06
        \move (2 0) \fcir f:0.8 r:0.06
        \move (2 1) \fcir f:0.8 r:0.06
        \move (2 2) \fcir f:0.8 r:0.06
        \move (2 3) \fcir f:0.8 r:0.06
        \move (2 4) \fcir f:0.8 r:0.06
        \move (2 5) \fcir f:0.8 r:0.06
        \move (2 6) \fcir f:0.8 r:0.06
        \move (3 -6) \fcir f:0.8 r:0.06
        \move (3 -5) \fcir f:0.8 r:0.06
        \move (3 -4) \fcir f:0.8 r:0.06
        \move (3 -3) \fcir f:0.8 r:0.06
        \move (3 -2) \fcir f:0.8 r:0.06
        \move (3 -1) \fcir f:0.8 r:0.06
        \move (3 0) \fcir f:0.8 r:0.06
        \move (3 1) \fcir f:0.8 r:0.06
        \move (3 2) \fcir f:0.8 r:0.06
        \move (3 3) \fcir f:0.8 r:0.06
        \move (3 4) \fcir f:0.8 r:0.06
        \move (3 5) \fcir f:0.8 r:0.06
        \move (3 6) \fcir f:0.8 r:0.06
        \move (4 -6) \fcir f:0.8 r:0.06
        \move (4 -5) \fcir f:0.8 r:0.06
        \move (4 -4) \fcir f:0.8 r:0.06
        \move (4 -3) \fcir f:0.8 r:0.06
        \move (4 -2) \fcir f:0.8 r:0.06
        \move (4 -1) \fcir f:0.8 r:0.06
        \move (4 0) \fcir f:0.8 r:0.06
        \move (4 1) \fcir f:0.8 r:0.06
        \move (4 2) \fcir f:0.8 r:0.06
        \move (4 3) \fcir f:0.8 r:0.06
        \move (4 4) \fcir f:0.8 r:0.06
        \move (4 5) \fcir f:0.8 r:0.06
        \move (4 6) \fcir f:0.8 r:0.06
   %% HERE ENDS THE CODE FOR THE LATTICE
                          
    \end{texdraw}\end{center}

   \vspace*{0.5cm}
   The Newton subdivision of the tropical curve is:
   \vspace*{0.5cm}

   \begin{center}
       
    \begin{texdraw}
       \drawdim cm  \relunitscale 1
       \linewd 0.05
        \move (5 0)
        \lvec (1 0)
        \move (1 0)
        \lvec (0 2)
        \move (0 2)
        \lvec (5 0)

    
        \move (4 0)
        \lvec (0 2)
        \move (2 0)
        \lvec (0 2)
        \move (0 0) \fcir f:0.6 r:0.08
        \move (0 1) \fcir f:0.6 r:0.08
        \move (0 2) \fcir f:0.6 r:0.08
        \move (1 0) \fcir f:0.6 r:0.08
        \move (1 1) \fcir f:0.6 r:0.08
        \move (1 2) \fcir f:0.6 r:0.08
        \move (2 0) \fcir f:0.6 r:0.08
        \move (2 1) \fcir f:0.6 r:0.08
        \move (2 2) \fcir f:0.6 r:0.08
        \move (3 0) \fcir f:0.6 r:0.08
        \move (3 1) \fcir f:0.6 r:0.08
        \move (3 2) \fcir f:0.6 r:0.08
        \move (4 0) \fcir f:0.6 r:0.08
        \move (4 1) \fcir f:0.6 r:0.08
        \move (4 2) \fcir f:0.6 r:0.08
        \move (5 0) \fcir f:0.6 r:0.08
        \move (5 1) \fcir f:0.6 r:0.08
        \move (5 2) \fcir f:0.6 r:0.08
       \move (5 0)
       \fcir f:0 r:0.10
       \move (4 0)
       \fcir f:0 r:0.10
       \move (0 2)
       \fcir f:0 r:0.10
       \move (3 0)
       \fcir f:0 r:0.10
       \move (2 0)
       \fcir f:0 r:0.10
       \move (1 0)
       \fcir f:0 r:0.10
   \end{texdraw}
    
   \end{center}
\end{document}
