Singular

LIB "central.lib";
ring A = 0,(e(1..4)),dp;
matrix D[4][4]=0;
D[2,4] = -e(1);
D[3,4] = -e(2);
// This is A_4_1 - the first real Lie algebra of dimension 4.
def A_4_1 = nc_algebra(1,D); setring A_4_1;
ideal F = variablesSorted(); F;
==> F[1]=e(1)
==> F[2]=e(4)
==> F[3]=e(3)
==> F[4]=e(2)
// the center of A_4_1 is generated by
// e(1) and -1/2*e(2)^2+e(1)*e(3)
// therefore one may consider computing it in the following way:
// 1. Compute a PBW basis consisting of
//    monomials with exponent <= (1,2,1,0)
ideal V = PBW_maxMonom( e(1) * e(2)^ 2 * e(3) );
// 2. Compute the centralizer of F within the vector space
//    spanned by these monomials:
ideal C = centralizeSet( F, V ); C;
==> C[1]=e(1)
==> C[2]=e(2)^2-2*e(1)*e(3)
inCenter(C); // check the result
==> 1