# Question:Error when I generate the normal set (Gröbner basis)

## Question:Error when I generate the normal set (Gröbner basis)

Maple 2016

Hi all,

I am using Maple 2016.

I have defined 5 polynomials: f1, f2, f3, f4 and f5 with 5 unknowns q1,q2 ,q3, q4 and lamda.

After this, I generated the Gröbner basis. But when I try to find the normal set I got an error.

with(Groebner);

f1 := lamda*q1-(3380075947548081*q1*(1/140737488355328)-259050600068343*q2*(1/140737488355328)-1826834460600733*q3*(1/1125899906842624)+4414049272733425*q4*(1/9007199254740992))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f2 := lamda*q2+(259050600068343*q1*(1/140737488355328)+3380075947548081*q2*(1/140737488355328)-4414049272733425*q3*(1/9007199254740992)-1826834460600733*q4*(1/1125899906842624))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f3 := (1826834460600733*q1*(1/1125899906842624)-4414049272733425*q2*(1/9007199254740992)+843667886835955*q3*(1/35184372088832)-862655592804515*q4*(1/18014398509481984))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)))+lamda*q3;
f4 := lamda*q4-(4414049272733425*q1*(1/9007199254740992)+1826834460600733*q2*(1/1125899906842624)+862655592804515*q3*(1/18014398509481984)+843667886835955*q4*(1/35184372088832))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f5 := q1^2+q2^2+q3^2+q4^2-1;
ord := tdeg(q1, q2, q3, q4, lamda);
tdeg(q1, q2, q3, q4, lamda)
G := Basis([f1, f2, f3, f4, f5], ord);

IsZeroDimensional(G);
false
ns, rv := NormalSet(G, ord);
Error, (in Groebner:-NormalSet) The case of non-zero-dimensional varieties is not handled.