 LIB "finvar.lib";
ring R=0,(a,b,c,d),dp;
matrix A[4][4]=
0,0,1,0,
0,0,0,1,
1,0,0,0,
0,1,0,0;
list L = group_reynolds(A);
matrix G = invariant_algebra_reynolds(L[1],1);
==> We have 4 relevant monomials in degree 1
==> We found generator number 1 in degree 1
==> We found generator number 2 in degree 1
==> Computing Groebner basis up to the new degree 2
==> We have 3 relevant monomials in degree 2
==> We found generator number 3 in degree 2
==> We found generator number 4 in degree 2
==> We found generator number 5 in degree 2
==> Computing Groebner basis up to the new degree 3
==> We found the degree bound 2
==> We went beyond the degree bound, so, we are done!
G;
==> G[1,1]=b+d
==> G[1,2]=a+c
==> G[1,3]=b2+d2
==> G[1,4]=ab+cd
==> G[1,5]=a2+c2
