monitor(":w ResultGHB.txt","o");
ring r=5,(u223,u222,u12,u23,u1,u2,delta2v,deltav1,deltav2,deltav3,v11,v12,v13,v22,v23,v33,v1,v2,v3,v),wp(1024,1024,256,256,64,64,4,3,3,3,2,2,2,2,2,2,1,1,1,0);

//i to je chto j//

//Simplifying assumptions://
number u111=1;
number u112=0;
number u113=0;
number u123=0;

//extra//
//number u222=1;
number u122=-1;
number u11=1;
number u13=0;
number u22=-1;
//number u23=-1;
//number u1=1;
number u3=1;


poly Rv=v-u1^2-u2^2-u3^2;
poly Rv1=v1-2*(u11*u1+u12*u2+u13*u3);
poly Rv2=v2-2*(u12*u1+u22*u2+u23*u3);
poly Rv3=v3-2*(u13*u1+u23*u2+(-u11-u22)*u3);
poly Rv11=v11-2*(u111*u1+u112*u2+u113*u3+u11*u11+u12*u12+u13*u13);
poly Rv12=v12-2*(u112*u1+u122*u2+u123*u3+u11*u12+u12*u22+u13*u23);
poly Rv13=v13-2*(u113*u1+u123*u2+(-u111-u122)*u3+u11*u13+u12*u23+u13*(-u11-u22));
poly Rv22=v22-2*(u122*u1+u222*u2+u223*u3+u12*u12+u22*u22+u23*u23);
poly Rv23=v23-2*(u123*u1+u223*u2+(-u112-u222)*u3+u12*u13+u22*u23+u23*(-u11-u22));
poly Rv33=v33-2*((-u111-u122)*u1+(-u112-u222)*u2+(-u113-u223)*u3+u13*u13+u23*u23+(-u11-u22)*(-u11-u22));

poly Rdeltav1=deltav1-4*(u11*u111+2*u12*u112+2*u13*u113+u22*u122+2*u23*u123+(-u11-u22)*(-u111-u122));
poly Rdeltav2=deltav2-4*(u11*u112+2*u12*u122+2*u13*u123+u22*u222+2*u23*u223+(-u11-u22)*(-u112-u222));
poly Rdeltav3=deltav3-4*(u11*u113+2*u12*u123+2*u13*(-u111-u122)+u22*u223+2*u23*(-u112-u222)+(-u11-u22)*(-u113-u223));

//poly Rgradv2=gradv2-(v1^2+v2^2+v3^2);
//poly Rdeltav=deltav-(v11+v22+v33);

//poly RD2vgradvgradv=D2vgradvgradv-(v11*v1*v1+2*v12*v1*v2+2*v13*v1*v3+v22*v2*v2+2*v23*v2*v3+v33*v3*v3);

//poly RD2vgradvgraddeltav=D2vgradvgraddeltav-(v11*v1*deltav1+v12*v1*deltav2+v12*v2*deltav1+v13*v1*deltav3+v13*v3*deltav1+v22*v2*deltav2+v23*v2*deltav3+v23*v3*deltav2+v33*v3*deltav3);

//poly RdetD2v=detD2v-(v11*v22*v33+2*v12*v23*v13-v13*v22*v13-v12*v12*v13-v11*v23*v23);

//poly RD2vHS=D2vHS-(v11^2+2*v12^2+2*v13^2+v22^2+2*v23^2+v33^2);

//poly Rgradvgraddeltav=v1*deltav1+v2*deltav2+v3*deltav3;

//poly Rgraddeltav2=graddeltav2-(deltav1^2+deltav2^2+deltav3^2);

poly Rdelta2v=delta2v-4*(u111^2+3*u112^2+3*u113^2+3*u122^2+6*u123^2+3*(-u111-u122)^2+u222^2+3*u223^2+3*(-u112-u222)^2+(-u113-u223)^2);

ideal I=Rdelta2v,Rdeltav1,Rdeltav2,Rdeltav3,Rv11,Rv12,Rv13,Rv22,Rv23,Rv33,Rv1,Rv2,Rv3,Rv;


option(prot);
groebner(I);
monitor("");