## 10 Reputation

`> f1 := (1-x[1])^6*mul(x[1]-omega*x[j], j = 2 .. 5)-(1-omega*x[1])^6*mul(omega*x[1]-x[j], j = 2 .. 5);> f2 := (1-x[2])^6*(x[2]-omega*x[1])*mul(x[2]-omega*x[j], j = 3 .. 5)-(1-omega*x[2])^6*(omega*x[2]           -x[1])*mul(omega*x[2]-x[j], j = 3 .. 5);> f3 := (1-x[3])^6*mul(x[3]-omega*x[j], j = 1 .. 2)*mul(x[3]-omega*x[j], j = 4 .. 5)           -(1-omega*x[3])^6*mul(omega*x[3]-x[j], j = 1 .. 2)*mul(omega*x[3]-x[j], j = 4 .. 5);> f4 := (1-x[4])^6*mul(x[4]-omega*x[j], j = 1 .. 3)*(x[4]-omega*x[5])           -(1-omega*x[4])^6*mul(omega*x[4]-x[j], j = 1 .. 3)*(omega*x[4]-x[5]);> f5 := (1-x[5])^6*mul(x[5]-omega*x[j], j = 1 .. 4)-(1-omega*x[5])^6*mul(omega*x[5]-x[j], j = 1 .. 4);> omega := exp((1/3)*(2*Pi*I));#To make equations with real and integer coefficients                        > for j to 5 do x[j] := omega*z[j] end do;#One can make all five equations linear in z[5], by replace the fifth equation by six equations>o:= exp((1/6)*(2*Pi*I)); >for j from 1 to 6 do  g||j:=mul(1-omega*z[n], n = 1 .. 5)-o^j*mul(1-omega^2*z[n], n = 1 .. 5):od;`