Die Gleichungen in SINGULAR

ring r=(real,15),(d(1),x(8..21),E(1..6),a(1..7),y(1),s(1)),lp;
ideal i=
0.001*s(1) - 0.001*a(1) + x(21),
-0.001*s(1) + x(11) + x(12) + 0.001*a(1),
-d(1)+ x(13) + x(14) + 0.001*a(2), 
-0.5e-7*d(1)+1000*x(11) - a(3) + x(8),
-1000*x(13) + a(4) - x(8),
-x(12) - x(14) - x(15),
x(15) + x(16) + x(18) + 0.00005*a(6) - 0.00005*x(8),
x(19) - 0.0001*a(3) - 0.0001*a(4) - 0.00005*a(6) + 0.00025*x(8),
-x(16) - x(18) + x(20),
y(1) - a(3) + a(4),
2.353906762967828e-15 - 1.669390676296782*E(1) + 1.433999999999999*E(2) +x(11),
5.60375146541599e-17 + 1.433999999999999*E(1) - 1.439603751465415* E(2) + x(12),
2.353906762967828e-15 - 1.669390676296782*E(3) + 1.433999999999999* E(4) + x(13),
5.60375146541599e-17 + 1.433999999999999*E(3) - 1.439603751465415*E(4) + x(14),
2.353906762967828e-15 - 1.669390676296782*E(5) + 1.433999999999999*E(6) + x(15),
5.60375146541599e-17 + 1.433999999999999*E(5) - 1.439603751465415*E(6) + x(16),
-1.433999999999999e-14 + 1.433999999999999*E(6) + x(17),
1.439603751465415e-14 - 1.439603751465415*E(6) + x(18),
-11.99999999999999 + x(8),
11.99999999999999 + a(7);

ideal ei=
38.46153846153845*(a(1) - a(3)-0.364),
38.46153846153845*(a(1) - a(5)-0.364),
38.46153846153845*(a(2) - a(4)-0.364),
38.46153846153845*(a(2) - a(5)-0.364),
38.46153846153845*(a(6) - a(5)-0.364),
38.46153846153845*(a(6) - a(7)-0.364);