Although the SINGULAR language is C like, the indices of all objects which may have an index start at 1.

ring r; ideal i=1,x,z; i[2]; ==> x intvec v=1,2,3; v[1]; ==> 1 poly p=x+y+z; p[2]; ==> y vector h=[x+y,x,z]; h[1]; ==> x+y h[1][1]; ==> x