Steiner

Fs1:=[2*x1-1, 4*x2^2-3, -2*x3+u1-2*u2*x2, -2*u2*x4-2*u1*x3+u2^2+u1^2, -2*x5+u1+1-2*u2*x2, -2*u2*x6-2*u1*x5+2*x5+u1^2+u2^2-1];

Fs2:=[2*x1-1, 4*x2^2-3, -2*x3+u1-2*u2*x2, -2*u2*x4-2*u1*x3+u2^2+u1^2, -2*x5+u1+1+2*u2*x2, -2*u2*x6-2*u1*x5+2*x5+u1^2+u2^2-1];

Fs3:=[2*x1-1, 4*x2^2-3, -2*x3+u1+2*u2*x2, -2*u2*x4-2*u1*x3+u2^2+u1^2, -2*x5+u1+1-2*u2*x2, -2*u2*x6-2*u1*x5+2*x5+u1^2+u2^2-1];

Fs4:=[2*x1-1, 4*x2^2-3, -2*x3+u1+2*u2*x2, -2*u2*x4-2*u1*x3+u2^2+u1^2, -2*x5+u1+1+2*u2*x2, -2*u2*x6-2*u1*x5+2*x5+u1^2+u2^2-1];

T:=[Fs1,Fs2,Fs3,Fs4];

Fs:=[2*x1-1,x2^2+x1^2-1,x4^2+x3^2-u2^2-u1^2,2*u2*x4+2*u1*x3-u2^2-u1^2,x6^2+x5^2-2*x5-u2^2-u1^2+2*u1,2*u2*x6+2*u1*x5-2*x5-u1^2-u2^2+1];
Gs:=[-x5*u2^2-x6*u2+x6*u1*u2+u2^2<0,x3*u2^2-x4*u2*u1<0,u2*x2<0];
fvar:=[u1,u2];
ord:=[x1,x2,x3,x4,x5,x6];

Apollonius
Fa:=[x1*x2-x1+u1,-x2^2+2*u1*x1-2*x1-u1^2+1,-x3^2+2*u2*x1-2*x1-u2^2+1,-x1*x4+u2*x4+x1*x3-u3*x3];
Ga:=[t1>0,t1<1,t1*x1=1,t2>0,t2<1,t2*x1=u1,-t2+1=x2,t3>0,t3<1,(1-t3)*x4=x3,t3*x1+(1-t3)*u3=u2];
fvar := [u1,u2,u3];
ord := [x1,x2,x3,x4];

Paterson
Fp :=[x1^2-(x1-1)^2,x2*u1*u3+u1+u1*u2*x3-u2*u1-u1*x3+x1*x3*u3-x1*u3-x1*x2*u2+x1*x2,(x3-1)^2+x2^2-(x3-u2)^2-(x2-u3)^2,-u1*u3*x4+u3^2*u1-u1*u2*x5+u1*u2^2-x1*x5*u3+x1*u2*x4,x5^2+x4^2-(x5-u2)^2-(x4-u3)^2];
Gp:=[0 < -u3^2*x3+u3^2-x2*u3+x2*u3*u2,0<u3*(u3*x5-u2*x4),0<u3*u1];
fvar:=[u1,u2,u3];
ord:=[x1,x2,x3,x4,x5];

SquareSteiner
F:=[x1^2+x2^2-u2^2-u3^2,-x1*u2-x2*u3,2*x3-u1-u2,2*x4-u3,x5*x1^2+x5*x2^2-2*x5*u2*x1-2*x5*u3*x2+x5*u2^2+x5*u3^2+2*u3*x1*x2-2*x1*u3^2-2*u2*x2^2+2*u3*u2*x2,x6*x1^2+x6*x2^2-2*x6*u2*x1-2*x6*u3*x2+x6*u2^2+x6*u3^2+2*u2*x2*x1-2*x2*u2^2-2*u3*x1^2+2*u3*u2*x1];
G:=[u3*u1^3 < 0,u1*x1*u3^2-u1*x2*u3*u2 < 0];
fvar:=[u1,u2,u3];
ord:=[x1,x2,x3,x4,x5,x6];

Feuerbach




