\def\ssan{4}
\def\ssak{2}
\def\ssau{s_3s_2}
\def\ssauk{\{1,4\}}
\def\ssax{\smat{
1 &   &   &   \\
x_{1} & x_{2} & -1 &   \\
x_{3} & x_{4} &   & -1 \\
  & 1 &   &  
}}
\def\ssaGRx{\smat{
1 &   \\
x_{1} & x_{2} \\
x_{3} & x_{4} \\
  & 1
}}
\def\ssaGRgjAu{\smat{
1 &   \\
  & x_{2} \\
  & x_{4} \\
  & 1
}}
\def\ssaGRgjBu{\smat{
1 &   \\
x_{1} &   \\
x_{3} &   \\
  & 1
}}
\def\ssagjA{\smat{
1 &   &   &   \\
  & 1 &   & x_{2} \\
  &   & 1 & x_{4} \\
  &   &   & 1
}}
\def\ssagjB{\smat{
1 &   &   &   \\
x_{1} & 1 &   &   \\
x_{3} &   & 1 &   \\
  &   &   & 1
}}
\def\ssadtul{\smat{
\frac{1}{z} &   &   &   \\
  & 1 &   &   \\
  &   & 1 &   \\
  &   &   & \frac{1}{z}
}}
\def\ssagjBi{\smat{
1 &   &   &   \\
-x_{1} & 1 &   &   \\
-x_{3} &   & 1 &   \\
  &   &   & 1
}}
\def\ssabageom{\smat{
\frac{1}{z} &   &   &   \\
-x_{1} & 1 &   & \frac{x_{2}}{z} \\
-x_{3} &   & 1 & \frac{x_{4}}{z} \\
  &   &   & \frac{1}{z}
}}
\def\ssaBm{\smat{
1 &   & \frac{x_{2}}{{\left(x_{1} x_{4} - x_{2} x_{3}\right)} z} & \frac{x_{4}}{x_{3} z} \\
  & 1 &   &   \\
  & \frac{x_{4}}{x_{2}} & 1 &   \\
  & \frac{1}{x_{2}} & \frac{x_{1}}{x_{1} x_{4} - x_{2} x_{3}} & 1
}}
\def\ssatauk{\smat{
  &   & \frac{1}{z} &   \\
  &   &   & \frac{1}{z} \\
1 &   &   &   \\
  & 1 &   &  
}}
\def\ssaBp{\smat{
\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{2}} & -\frac{x_{4}}{x_{2}} & 1 &   \\
  & \frac{x_{3}}{x_{1} x_{4} - x_{2} x_{3}} & -\frac{x_{1}}{x_{1} x_{4} - x_{2} x_{3}} &   \\
  &   & \frac{1}{x_{3}} &   \\
-x_{1} z & z &   & x_{2}
}}
\def\ssaBmx{\smat{
1 & -\frac{1}{x_{1} z} &   & \frac{x_{4}}{x_{3} z} \\
  & 1 &   &   \\
  &   & 1 &   \\
  & -\frac{x_{3}}{x_{1} x_{4}} & \frac{1}{x_{4}} & 1
}}
\def\ssahx{\smat{
  &   & \frac{1}{z} &   \\
1 &   &   &   \\
  &   &   & \frac{1}{z} \\
  & 1 &   &  
}}
\def\ssaBpx{\smat{
-x_{1} & 1 &   &   \\
  & \frac{x_{3}}{x_{1} x_{4}} & -\frac{1}{x_{4}} &   \\
  &   & \frac{1}{x_{3}} &   \\
-x_{3} z &   & z & x_{4}
}}
\def\ssaBmxx{\smat{
1 & -\frac{1}{x_{1} z} & -\frac{1}{x_{3} z} &   \\
  & 1 &   &   \\
  & \frac{x_{3}}{x_{1}} & 1 &   \\
  &   &   & 1
}}
\def\ssahxx{\smat{
  &   & \frac{1}{z} &   \\
1 &   &   &   \\
  & 1 &   &   \\
  &   &   & \frac{1}{z}
}}
\def\ssaBpxx{\smat{
-x_{1} & 1 &   &   \\
  & -\frac{x_{3}}{x_{1}} & 1 &   \\
  &   & \frac{1}{x_{3}} &   \\
  &   &   & 1
}}
\def\ssagy{\smat{
-x_{1} & 1 &   & \frac{x_{2}}{z} \\
  &   &   & \frac{1}{z} \\
1 &   &   &   \\
-x_{3} z &   & z & x_{4}
}}
\def\ssaBmg{\smat{
1 &   &   & \frac{x_{2}}{x_{4} z} \\
-\frac{x_{3}}{x_{1} x_{4} - x_{2} x_{3}} & 1 &   & \frac{1}{x_{4} z} \\
-\frac{x_{4}}{x_{1} x_{4} - x_{2} x_{3}} & \frac{x_{4}}{x_{3}} & 1 &   \\
  &   &   & 1
}}
\def\ssahg{\smat{
1 &   &   &   \\
  & 1 &   &   \\
  &   & 1 &   \\
  &   &   & 1
}}
\def\ssaBpg{\smat{
-\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{4}} & 1 & -\frac{x_{2}}{x_{4}} &   \\
  & \frac{x_{3}}{x_{1} x_{4} - x_{2} x_{3}} & -\frac{x_{1}}{x_{1} x_{4} - x_{2} x_{3}} &   \\
  &   & \frac{1}{x_{3}} &   \\
-x_{3} z &   & z & x_{4}
}}
\def\ssatrMA{\smat{
1 &   \\
  & x_{2} \\
  & x_{4} \\
  & 1
}}
\def\ssatrMB{\smat{
x_{1} & x_{2} \\
x_{3} & x_{4} \\
  & 1 \\
-1 &  
}}
\def\ssatrMC{\smat{
x_{3} & x_{4} \\
  & 1 \\
-1 &   \\
  &  
}}
\def\ssatrMD{\smat{
  & 1 \\
-1 &   \\
  &   \\
  &  
}}
\def\ssatrminA{x_{4}}
\def\ssatrminB{x_{1} x_{4} - x_{2} x_{3}}
\def\ssatrminC{x_{3}}
\def\ssatrminD{1}

\def\ssagUigi{\smat{
1 & -\frac{x_{4}}{{\left(x_{1} x_{4} - x_{2} x_{3}\right)} z} &   & \frac{x_{4}}{x_{3} z} \\
  & 1 & \frac{x_{2}}{x_{4}} &   \\
  &   & 1 &   \\
  & -\frac{x_{3}}{x_{1} x_{4} - x_{2} x_{3}} & \frac{1}{x_{4}} & 1
}}
\def\ssayA{\smat{
1 &   &   &   \\
  & 1 & -\frac{x_{2}}{x_{4}} &   \\
  &   & 1 &   \\
  &   &   & 1
}}
\def\ssayAi{\smat{
1 &   &   &   \\
  & 1 & \frac{x_{2}}{x_{4}} &   \\
  &   & 1 &   \\
  &   &   & 1
}}
\def\ssaxB{\smat{
1 & -\frac{x_{4}}{{\left(x_{1} x_{4} - x_{2} x_{3}\right)} z} &   & \frac{x_{4}}{x_{3} z} \\
  & 1 &   &   \\
  &   & 1 &   \\
  & -\frac{x_{3}}{x_{1} x_{4} - x_{2} x_{3}} & \frac{1}{x_{4}} & 1
}}

\def\ssayAbageom{\smat{
\frac{1}{z} &   &   &   \\
-\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{4}} & 1 & -\frac{x_{2}}{x_{4}} &   \\
-x_{3} &   & 1 & \frac{x_{4}}{z} \\
  &   &   & \frac{1}{z}
}}
\def\ssayAbageomB{\smat{
\frac{1}{z} &   &   &   \\
-\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{4}} & 1 &   &   \\
-x_{3} &   & 1 & \frac{x_{4}}{z} \\
  &   &   & \frac{1}{z}
}}
\def\ssapigx{\smat{
1 &   \\
\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{4}} &   \\
x_{3} & x_{4} \\
  & 1
}}


\def\ssavikappax{\smat{
1 &   &   &   \\
  & x_{4} &   & -1 \\
  & -x_{2} & 1 &   \\
  & 1 &   &  
}}
\def\ssaetaL{\smat{
1 &   &   &   \\
  & 1 &   &   \\
  & -\frac{x_{2}}{x_{4}} & 1 &   \\
  & \frac{1}{x_{4}} &   & 1
}}
\def\ssaeta{\smat{
1 &   &   &   \\
  & x_{4} &   &   \\
  &   & 1 & -\frac{x_{2}}{x_{4}} \\
  &   &   & \frac{1}{x_{4}}
}}
\def\ssaetaR{\smat{
1 &   &   &   \\
  & 1 &   & -\frac{1}{x_{4}} \\
  &   & 1 &   \\
  &   &   & 1
}}

\def\ssazeta{\smat{
1 &   &   &   \\
x_{1} & \frac{x_{2}}{x_{4}} & -1 & -x_{2} \\
x_{3} & 1 &   & -x_{4} \\
  & \frac{1}{x_{4}} &   &  
}}

\def\ssazetaw{\smat{
  &   & 1 &   \\
-1 & -x_{2} & x_{1} & \frac{x_{2}}{x_{4}} \\
  & -x_{4} & x_{3} & 1 \\
  &   &   & \frac{1}{x_{4}}
}}


\def\ssazetawA{\frac{1}{x_{4}}}
\def\ssazetawB{\frac{x_{3}}{x_{4}}}
\def\ssazetawC{\frac{x_{1} x_{4} - x_{2} x_{3}}{x_{4}}}

\def\ssayBbageomA{\smat{
1 &   &   &   \\
  & 1 & \frac{x_{2}}{x_{4}} &   \\
  &   & 1 &   \\
  &   &   & 1
}}
\def\ssayBbageomAt{\smat{
1 &   &   &   \\
  & 1 & \frac{t x_{2}}{x_{4}} &   \\
  &   & 1 &   \\
  &   &   & 1
}}





\def\ssaGRxt{\smat{
1 &   \\
x_{1}+(t-1)\frac{x_2x_3}{x_4} & tx_{2} \\
x_{3} & x_{4} \\
  & 1
}}












%%%%%%%%%%%%%%%%%%%%%ssb


\def\ssbn{5}
\def\ssbk{2}
\def\ssbu{s_2}
\def\ssbuk{\{1,3\}}
\def\ssbwp{s_2s_1s_4s_3s_2}
\def\ssbvp{s_1}
\def\ssbwpk{\{3,5\}}
\def\ssbw{s_2s_1s_4s_3s_2}
\def\ssbv{s_2s_1}
\def\ssbwk{\{3,5\}}
\def\ssbx{\smat{
  & -1 &   &   &   \\
1 &   &   &   &   \\
t_{1} & t_{5} & 1 &   &   \\
  & t_{4} t_{5} & t_{4} & 1 &   \\
  & t_{3} t_{4} t_{5} & t_{3} t_{4} & t_{3} & 1
}}
\def\ssbdeovpwp{y_2(t_{1})\ds_{1}y_4(t_{3})y_3(t_{4})y_2(t_{5})}
\def\ssbGRx{\smat{
  & -1 \\
1 &   \\
t_{1} & t_{5} \\
  & t_{4} t_{5} \\
  & t_{3} t_{4} t_{5}
}}
\def\ssbgju{\smat{
1 &   &   &   &   \\
\frac{t_{5}}{t_{1}} & \frac{1}{t_{1}} & -1 &   &   \\
  & 1 &   &   &   \\
-t_{4} t_{5} &   &   & 1 &   \\
-t_{3} t_{4} t_{5} &   &   &   & 1
}}
\def\ssbGRgju{\smat{
1 &   \\
\frac{t_{5}}{t_{1}} & \frac{1}{t_{1}} \\
  & 1 \\
-t_{4} t_{5} &   \\
-t_{3} t_{4} t_{5} &  
}}
\def\ssbhjx{\smat{
1 &   &   &   &   \\
-\frac{t_{5}}{t_{1}} & 1 &   &   &   \\
  &   & 1 &   &   \\
t_{4} t_{5} &   &   & 1 &   \\
t_{3} t_{4} t_{5} &   &   &   & 1
}}
\def\ssbhjxx{\smat{
  & -1 &   &   &   \\
1 & \frac{t_{5}}{t_{1}} &   &   &   \\
t_{1} & t_{5} & 1 &   &   \\
  &   & t_{4} & 1 &   \\
  &   & t_{3} t_{4} & t_{3} & 1
}}
\def\ssbg{[2, 4, 8, 5, 6]}
\def\ssbh{[3, 4, 7, 5, 6]}
\def\ssbgneck{[\{1,3\},\{2,3\},\{3,4\},\{4,8\},\{5,8\}]}
\def\ssbhneck{[\{1,2\},\{2,3\},\{3,4\},\{4,7\},\{5,7\}]}
\def\ssbpidup{\smat{
  & -1 &   &   &   \\
1 &   & -\frac{1}{t_{1}} &   &   \\
t_{1} & t_{5} &   &   &   \\
  & t_{4} t_{5} & t_{4} & 1 &   \\
  & t_{3} t_{4} t_{5} & t_{3} t_{4} & t_{3} & 1
}}
\def\ssbeta{\smat{
t_{1} & t_{5} &   &   &   \\
  & 1 &   &   &   \\
  &   & \frac{1}{t_{1}} &   &   \\
  &   & t_{4} & 1 &   \\
  &   & t_{3} t_{4} & t_{3} & 1
}}
\def\ssbzeta{\smat{
  & -1 &   &   &   \\
\frac{1}{t_{1}} & -\frac{t_{5}}{t_{1}} & -1 &   &   \\
1 &   &   &   &   \\
  & t_{4} t_{5} &   & 1 &   \\
  & t_{3} t_{4} t_{5} &   &   & 1
}}
\def\ssbetaB{\smat{
  & 1 &   &   &   \\
-1 &   &   &   &   \\
  &   & 1 &   &   \\
  &   &   & 1 &   \\
  &   &   &   & 1
}}
\def\ssbetaBi{\smat{
  & -1 &   &   &   \\
1 &   &   &   &   \\
  &   & 1 &   &   \\
  &   &   & 1 &   \\
  &   &   &   & 1
}}
\def\ssbzetaB{\smat{
  & -1 &   &   &   \\
\frac{1}{t_{1}} & -\frac{t_{5}}{t_{1}} & -1 &   &   \\
1 &   &   &   &   \\
  & t_{4} t_{5} &   & 1 &   \\
  & t_{3} t_{4} t_{5} &   &   & 1
}}
\def\ssbzetaw{\smat{
  &   &   &   & -1 \\
-1 &   & \frac{1}{t_{1}} &   & -\frac{t_{5}}{t_{1}} \\
  &   & 1 &   &   \\
  & 1 &   &   & t_{4} t_{5} \\
  &   &   & -1 & t_{3} t_{4} t_{5}
}}
\def\ssbzetawA{ t_{3} t_{4} t_{5} }
\def\ssbzetawB{ t_{4} t_{5} }
\def\ssbzetawC{ t_{4} t_{5} }
\def\ssbzetawD{ \frac{t_{5}}{t_{1}} }
\def\ssbzetawE{ 1 }


\def\ssbgAneck{13}
\def\ssbtrminA{ 1 }
\def\ssbgBneck{23}
\def\ssbtrminB{ \frac{t_{5}}{t_{1}} }
\def\ssbgCneck{34}
\def\ssbtrminC{ t_{4} t_{5} }
\def\ssbgDneck{48}
\def\ssbtrminD{ t_{4} t_{5} }
\def\ssbgEneck{58}
\def\ssbtrminE{ t_{3} t_{4} t_{5} }

