R = QQ[a121,a122,a123,a124,a131,a132,a133,a134,a141,a142,a143,a144,a231,a232,a233,a234,a241,a242,a243,a244,a341,a342,a343,a344]; M = matrix { {a121,a131,a231,a141,a241,a341}, {a122,a132,a232,a142,a242,a342}, {a123,a133,a233,a143,a243,a343}, {a124,a134,a234,a144,a244,a344}}; secondDerived = M * exteriorPower(2,M); I = ideal(-a121*a133-a122*a233+a123*a131+a123*a232+a124*a343-a134*a243+a143*a234, -a121*a144-a122*a244-a123*a344+a124*a141+a124*a242+a134*a243-a143*a234, a121*a242-a122*a241-a123*a341+a131*a243+a141*a244-a143*a231-a144*a241, -a121*a142+a122*a141-a123*a342+a132*a243+a142*a244-a143*a232-a144*a242, -a121*a132+a122*a131+a124*a342+a132*a233-a133*a232-a134*a242+a142*a234, a121*a232-a122*a231+a124 *a341+a131*a233-a133*a231-a134*a241+a141*a234, a121*a342+a131*a343-a132*a241-a133*a341+a141*a344+a142*a231-a144*a341, -a122*a341+a132*a241-a142*a231+a232*a343-a233*a342+a242*a344-a244*a342, a123*a342-a131*a143-a132*a243+a133*a141+a142*a233+a143*a344-a144*a343, -a123*a341+a133*a241-a143*a231-a232*a243+a233*a242+a243*a344-a244*a343, a124*a342-a131*a144-a132*a244-a133*a344+a134*a141+a134*a343+a142*a234, -a124*a341+a134*a241-a144*a231-a232*a244-a233*a344+a234*a242+a234*a343, -a121*a143-a122*a243+a123*a141+a123*a242-a123*a343+a133*a243-a143*a233+a143*a244-a144*a243, -a121*a134-a122*a234+a124*a131+a124*a232+a124*a344-a133*a234+a134*a233-a134*a244+a144*a234, -a121*a341+a131*a241-a141*a231+a231*a242+a231*a343-a232*a241-a233*a341+a241*a344-a244*a341, a122*a342-a131*a142+a132*a141-a132*a242+a132*a343-a133*a342+a142*a232+a142*a344-a144*a342); C1 = ideal(a141+a242+a343, a131+a232-a344, a122+a133+a144, a121-a233-a244, a232*a241-a231*a242+a233*a341+a244*a341-a231*a343-a241*a344, a144*a234-a134*a244+a124*a344, a144*a233+a143*a234-a134*a243-a133*a244+a124*a343+a123*a344, a143*a233-a133*a243+a123*a343, a144*a232+a142*a234-a134*a242-a132*a244+a124*a342-a133*a344-a144*a344, a143*a232+a142*a233-a133*a242-a132*a243+a123*a342-a133*a343-a144*a343, a142*a232-a132*a242-a133*a342-a144*a342, a144*a231-a134*a241-a234*a242+a232*a244+a124*a341-a234*a343+a233*a344, a143*a231-a133*a241-a233*a242+a232*a243+a123*a341+a244*a343-a243*a344, a142*a231-a132*a241-a133*a341-a144*a341+a233*a342+a244*a342-a232*a343-a242*a344, a144*a243*a342-a143*a244*a342-a144*a242*a343+a142*a244*a343+a143*a242*a344-a142*a243*a344, a143*a234*a342-a134*a243*a342-a142*a234*a343+a134*a242*a343+a142*a233*a344-a133*a242*a344+a123*a342*a344, a134*a233*a342-a133*a234*a342-a134*a232*a343+a132*a234*a343+a133*a232*a344-a132*a233*a344, a144*a243*a341-a143*a244*a341-a144*a241*a343-a242*a244*a343-a244*a343^2+a143*a241*a344+a242*a243*a344+a243*a343*a344, a144*a242*a341-a142*a244*a341-a144*a241*a342-a242*a244*a342-a244*a342*a343+a142*a241*a344+a242^2*a344+a242*a343*a344, a143*a242*a341-a142*a243*a341-a143*a241*a342-a242*a243*a342+a142*a241*a343+a242^2*a343-a243*a342*a343+a242*a343^2, a143*a234*a341-a134*a243*a341+a134*a241*a343+a234*a242*a343+a234*a343^2-a133*a241*a344-a233*a242*a344+a123*a341*a344-a233*a343*a344, a142*a234*a341-a134*a242*a341+a134*a241*a342+a234*a242*a342+a234*a342*a343-a132*a241*a344-a232*a242*a344-a133*a341*a344-a144*a341*a344-a232*a343*a344, a134*a233*a341-a133*a234*a341-a134*a231*a343-a232*a234*a343+a133*a231*a344+a232*a233*a344+a234*a343*a344-a233*a344^2, a134*a232*a341-a132*a234*a341-a134*a231*a342-a232*a234*a342+a132*a231*a344+a232^2*a344+a234*a342*a344-a232*a344^2, a143*a234*a242-a142*a234*a243+a142*a233*a244-a133*a242*a244-a124*a243*a342+a123*a244*a342+a124*a242*a343, a134*a233*a242-a133*a234*a242-a134*a232*a243+a132*a234*a243+a133*a232*a244-a132*a233*a244+a124*a233*a342-a123*a234*a342-a124*a232*a343-a133*a234*a343-a134*a244*a343+a123*a232*a344+a133*a233*a344-a143*a234*a344+a134*a243*a344+a133*a244*a344-a123*a344^2, a124*a233*a242-a123*a234*a242-a124*a232*a243-a133*a234*a243+a123*a232*a244+a133*a233*a244-a143*a234*a244+a133*a244^2-a124*a244*a343+a124*a243*a344-a123*a244*a344, a134*a143*a242-a133*a144*a242-a134*a142*a243+a132*a144*a243+a133*a142*a244-a132*a143*a244-a124*a143*a342+a123*a144*a342+a124*a142*a343+a133*a144*a343+a144^2*a343-a123*a142*a344-a133*a143*a344-a143*a144*a344, a143*a234*a241+a234*a242*a243-a133*a241*a244-a233*a242*a244-a124*a243*a341+a123*a244*a341+a124*a241*a343+a234*a243*a343-a233*a244*a343, a133*a234*a241+a233*a234*a242-a133*a231*a244-a232*a233*a244-a124*a233*a341+a124*a231*a343-a234*a244*a343+a233*a244*a344, a124*a233*a241-a123*a234*a241-a124*a231*a243+a233*a234*a243+a123*a231*a244-a233^2*a244+a234*a243*a244-a233*a244^2, a134*a142*a233-a133*a142*a234+a132*a143*a234-a132*a134*a243-a133*a134*a343-a134*a144*a343+a123*a132*a344+a133^2*a344+a133*a144*a344, a124*a142*a233-a123*a142*a234-a133*a143*a234-a124*a132*a243+a123*a132*a244+a133^2*a244-a134*a143*a244+a133*a144*a244-a124*a133*a343-a124*a144*a343+a124*a143*a344, a124*a133*a142-a123*a134*a142-a124*a132*a143-a133*a134*a143+a123*a132*a144+a133^2*a144-a134*a143*a144+a133*a144^2); C2 = ideal(a122*a341+a133*a341+a144*a341-a121*a342+a233*a342+a244*a342-a131*a343-a232*a343-a141*a344-a242*a344, a122*a241+a133*a241+a144*a241-a121*a242+a233*a242-a131*a243-a232*a243-a141*a244-a244*a343+a243*a344, a144*a231-a134*a241-a234*a242+a232*a244+a124*a341-a234*a343+a233*a344, a143*a231-a133*a241-a233*a242+a232*a243+a123*a341+a244*a343-a243*a344, a142*a231-a132*a241-a133*a341-a144*a341+a121*a342+a131*a343+a141*a344, a141*a231-a131*a241+a232*a241-a231*a242+a121*a341+a233*a341+a244*a341-a231*a343-a241*a344, a122*a231+a133*a231-a121*a232-a131*a233-a141*a234+a134*a241-a124*a341, a134*a141-a131*a144+a142*a234-a132*a244+a124*a342+a134*a343-a133*a344, a133*a141-a131*a143+a142*a233-a132*a243+a123*a342-a144*a343+a143*a344, a132*a141-a131*a142+a142*a232-a132*a242+a122*a342-a133*a342-a144*a342+a132*a343+a142*a344, a124*a141-a121*a144-a143*a234+a124*a242+a134*a243-a122*a244-a123*a344, a123*a141-a121*a143-a143*a233+a123*a242-a122*a243+a133*a243-a144*a243+a143*a244-a123*a343, a122*a141-a121*a142-a143*a232-a144*a242+a132*a243+a142*a244-a123*a342, a124*a131-a121*a134+a124*a232+a134*a233-a122*a234-a133*a234+a144*a234-a134*a244+a124*a344, a123*a131-a121*a133+a123*a232-a122*a233+a143*a234-a134*a243+a124*a343, a122*a131-a121*a132-a133*a232+a132*a233+a142*a234-a134*a242+a124*a342, 2*a123*a232*a341+2*a133*a233*a341+a144*a233*a341+a143*a234*a341+2*a124*a242*a341+a134*a243*a341+a133*a244*a341+2*a144*a244*a341-2*a123*a231*a342+2*a233^2*a342-2*a124*a241*a342+2*a234*a243*a342+2*a233*a244*a342+2*a244^2*a342-2*a133*a231*a343-2*a232*a233*a343+a141*a234*a343-2*a134*a241*a343-a234*a242*a343-a131*a244*a343-a232*a244*a343+a124*a341*a343+a234*a343^2-a141*a233*a344-2*a133*a241*a344-2*a144*a241*a344-3*a233*a242*a344+a131*a243*a344+a232*a243*a344-2*a242*a244*a344+a123*a341*a344-a233*a343*a344+3*a244*a343*a344-3*a243*a344^2, 2*a123*a132*a341+2*a133^2*a341+2*a124*a142*a341+2*a134*a143*a341+2*a133*a144*a341+2*a144^2*a341-2*a121*a133*a342-2*a121*a144*a342+2*a123*a232*a342-2*a122*a233*a342+2*a133*a233*a342+a144*a233*a342+a143*a234*a342+2*a124*a242*a342+a134*a243*a342-2*a122*a244*a342+a133*a244*a342+2*a144*a244*a342-2*a131*a133*a343-2*a131*a144*a343-a144*a232*a343-2*a132*a233*a343-a142*a234*a343+a134*a242*a343-a132*a244*a343+2*a124*a342*a343+2*a134*a343^2-2*a131*a143*a344-2*a141*a144*a344+a143*a232*a344+a142*a233*a344-a133*a242*a344-3*a132*a243*a344-2*a142*a244*a344-2*a133*a343*a344, 2*a123*a132*a241+2*a133^2*a241+2*a124*a142*a241+4*a133*a144*a241+2*a144^2*a241-2*a121*a133*a242-2*a121*a144*a242+2*a123*a232*a242-2*a122*a233*a242+2*a133*a233*a242+3*a144*a233*a242-a143*a234*a242+2*a124*a242^2-2*a131*a133*a243-2*a131*a144*a243-3*a144*a232*a243-2*a132*a233*a243-a142*a234*a243+2*a134*a242*a243-2*a131*a143*a244-2*a141*a144*a244+3*a143*a232*a244+a142*a233*a244-2*a122*a242*a244+2*a144*a242*a244-4*a132*a243*a244-2*a142*a244^2+2*a124*a143*a341-2*a123*a144*a341+a124*a243*a342+a123*a244*a342-2*a143*a234*a343+a124*a242*a343+2*a134*a243*a343+a122*a244*a343-2*a133*a244*a343-4*a144*a244*a343+2*a143*a233*a344-a123*a242*a344-a122*a243*a344+4*a144*a243*a344, a121*a142*a234+a131*a143*a234+a141*a144*a234-a143*a232*a234+a142*a233*a234-2*a134*a233*a242+a122*a234*a242+a133*a234*a242-2*a144*a234*a242+2*a134*a232*a243-a121*a132*a244-a131*a133*a244-a131*a144*a244-a122*a232*a244+a144*a232*a244-a132*a233*a244+2*a142*a234*a244+a134*a242*a244-2*a132*a244^2+2*a124*a233*a342+3*a124*a244*a342-2*a124*a232*a343+a122*a234*a343+a133*a234*a343-2*a144*a234*a343+4*a134*a244*a343+a121*a122*a344+a121*a133*a344+a121*a144*a344-2*a123*a232*a344+a122*a233*a344-a133*a233*a344+a144*a233*a344+a143*a234*a344-4*a124*a242*a344-2*a134*a243*a344+2*a122*a244*a344-2*a133*a244*a344-2*a124*a343*a344+2*a123*a344^2, a141^2*a234+4*a142*a234*a241-2*a141*a234*a242+a234*a242^2-a131*a141*a244+a141*a232*a244-4*a132*a241*a244+a131*a242*a244-a232*a242*a244+4*a143*a234*a341-4*a124*a242*a341-4*a134*a243*a341-4*a133*a244*a341-4*a144*a244*a341+4*a124*a241*a342+2*a121*a244*a342-2*a233*a244*a342-2*a244^2*a342-2*a141*a234*a343+4*a134*a241*a343+2*a234*a242*a343+3*a131*a244*a343+a232*a244*a343+a234*a343^2+a121*a141*a344+a141*a233*a344-4*a133*a241*a344+a121*a242*a344-3*a233*a242*a344+2*a131*a243*a344+2*a232*a243*a344+4*a141*a244*a344+2*a242*a244*a344+4*a123*a341*a344-a121*a343*a344-a233*a343*a344+2*a244*a343*a344-2*a243*a344^2, a131*a141*a234-a141*a232*a234+4*a132*a234*a241-a131*a234*a242+a232*a234*a242-a131^2*a244-4*a132*a231*a244+2*a131*a232*a244-a232^2*a244-4*a124*a232*a341-4*a134*a233*a341+4*a133*a234*a341-4*a144*a234*a341+4*a134*a244*a341+4*a124*a231*a342-2*a121*a234*a342-2*a233*a234*a342-2*a234*a244*a342+4*a134*a231*a343-3*a131*a234*a343+3*a232*a234*a343+a121*a131*a344-4*a133*a231*a344+a121*a232*a344+3*a131*a233*a344-a232*a233*a344+a141*a234*a344+3*a234*a242*a344-a131*a244*a344-a232*a244*a344-4*a124*a341*a344+a234*a343*a344+a121*a344^2-a233*a344^2, a121*a141*a234+a141*a233*a234-2*a134*a233*a241-2*a133*a234*a241-4*a144*a234*a241+a121*a234*a242-3*a233*a234*a242+2*a134*a231*a243+2*a232*a234*a243-a121*a131*a244+2*a133*a231*a244-a121*a232*a244-a131*a233*a244+a232*a233*a244+a141*a234*a244+4*a134*a241*a244+a234*a242*a244-a131*a244^2-a232*a244^2+2*a124*a233*a341+2*a123*a234*a341-2*a124*a231*a343+a121*a234*a343-a233*a234*a343+3*a234*a244*a343+a121^2*a344-2*a123*a231*a344+a233^2*a344-4*a124*a241*a344-2*a234*a243*a344+a121*a244*a344-a233*a244*a344, a141*a144*a233-a141*a143*a234+a144*a233*a242-a143*a234*a242-a131*a144*a243-2*a144*a232*a243-a142*a234*a243+a134*a242*a243+a131*a143*a244+2*a143*a232*a244+a142*a233*a244-a133*a242*a244-a124*a243*a342+a123*a244*a342+a121*a144*a343-a144*a233*a343-2*a143*a234*a343+a134*a243*a343+a122*a244*a343+a133*a244*a343-a144*a244*a343-a124*a343^2-a121*a143*a344+3*a143*a233*a344-a122*a243*a344-2*a133*a243*a344+a144*a243*a344+a123*a343*a344, a131*a144*a233-a144*a232*a233-a131*a143*a234+a143*a232*a234+2*a134*a233*a242-2*a133*a234*a242-a131*a134*a243-a134*a232*a243-2*a132*a234*a243+a131*a133*a244+a133*a232*a244+2*a132*a233*a244-2*a124*a233*a342+2*a123*a234*a342+a121*a134*a343-a134*a233*a343+a122*a234*a343-a133*a234*a343+a144*a234*a343-3*a134*a244*a343-a121*a133*a344-a122*a233*a344+2*a133*a233*a344-a144*a233*a344+2*a134*a243*a344+a133*a244*a344+a124*a343*a344-a123*a344^2, a121*a144*a233+a144*a233^2-a121*a143*a234-a143*a233*a234-a121*a134*a243-a134*a233*a243-2*a122*a234*a243+2*a133*a234*a243+2*a144*a234*a243+a121*a133*a244+2*a122*a233*a244-a133*a233*a244-a144*a233*a244-a143*a234*a244-a134*a243*a244+a133*a244^2+a121*a124*a343+a124*a233*a343-4*a123*a234*a343-3*a124*a244*a343-a121*a123*a344+3*a123*a233*a344+4*a124*a243*a344-a123*a244*a344, a121*a142*a233+a131*a143*a233-a143*a232*a233+a142*a233^2+a141*a143*a234+a122*a233*a242-a133*a233*a242-a144*a233*a242-a143*a234*a242-a121*a132*a243-a131*a133*a243-a122*a232*a243+2*a133*a232*a243+a144*a232*a243-a132*a233*a243+2*a142*a234*a243-a131*a143*a244+a133*a242*a244-2*a132*a243*a244+2*a123*a233*a342+2*a124*a243*a342+a123*a244*a342+a121*a122*a343+a121*a133*a343-4*a123*a232*a343+2*a122*a233*a343-2*a124*a242*a343+a134*a243*a343-a124*a343^2+a121*a143*a344-2*a123*a242*a344+2*a122*a243*a344-a133*a243*a344+a123*a343*a344, 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a121*a122*a132+2*a121*a132*a133+a131*a133^2+2*a121*a132*a144+2*a131*a133*a144+a131*a144^2+a122^2*a232-a122*a133*a232-a133^2*a232-4*a134*a143*a232+2*a133*a144*a232-a144^2*a232+3*a122*a132*a233+2*a132*a133*a233+4*a134*a142*a233-2*a132*a144*a233+a122*a142*a234-4*a133*a142*a234+4*a132*a143*a234-a122*a134*a242+2*a122*a132*a244+2*a132*a133*a244+2*a132*a144*a244-3*a122*a124*a342-4*a123*a134*a342-4*a124*a144*a342-4*a124*a132*a343-4*a133*a134*a343-4*a134*a144*a343+a122^2*a344+4*a123*a132*a344+3*a133^2*a344+2*a133*a144*a344-a144^2*a344, a121^2*a132+a121*a131*a133+a121*a131*a144+a121*a122*a232-2*a121*a133*a232+2*a121*a132*a233-a131*a133*a233-a122*a232*a233+2*a133*a232*a233+a144*a232*a233-3*a132*a233^2-a131*a143*a234+a143*a232*a234-2*a142*a233*a234-2*a121*a134*a242-2*a122*a234*a242+2*a133*a234*a242+2*a144*a234*a242-a131*a134*a243+a134*a232*a243-4*a132*a234*a243+2*a121*a132*a244-a131*a144*a244+a122*a232*a244-a133*a232*a244-2*a142*a234*a244-a132*a244^2-2*a121*a124*a342-4*a124*a233*a342+4*a123*a234*a342-3*a121*a134*a343+6*a124*a232*a343+3*a134*a233*a343-5*a122*a234*a343-a133*a234*a343+a144*a234*a343+a134*a244*a343+2*a121*a133*a344-a121*a144*a344-2*a123*a232*a344+3*a122*a233*a344-a133*a233*a344+4*a124*a242*a344+2*a134*a243*a344-2*a122*a244*a344-2*a133*a244*a344+a144*a244*a344+a124*a343*a344-a123*a344^2, a131^3+4*a131*a132*a231-a131^2*a232+4*a132*a231*a232-a131*a232^2+a232^3-4*a131*a134*a341+4*a134*a232*a341-8*a132*a234*a341-8*a134*a231*a342+4*a131*a234*a342-4*a232*a234*a342+a131^2*a344+4*a132*a231*a344-2*a131*a232*a344+a232^2*a344+4*a134*a341*a344+4*a234*a342*a344-a131*a344^2-a232*a344^2-a344^3, a121*a131^2-4*a131*a133*a231+2*a121*a131*a232-4*a133*a231*a232+a121*a232^2+3*a131^2*a233+2*a131*a232*a233-a232^2*a233+4*a141*a232*a234-4*a131*a134*a241-12*a132*a234*a241-4*a134*a231*a242+4*a131*a234*a242-4*a232*a234*a242+3*a131^2*a244+12*a132*a231*a244-6*a131*a232*a244+3*a232^2*a244+12*a124*a232*a341+8*a134*a233*a341-4*a133*a234*a341+12*a144*a234*a341-8*a134*a244*a341-12*a124*a231*a342+4*a121*a234*a342+8*a233*a234*a342+8*a234*a244*a342-8*a134*a231*a343+4*a131*a234*a343-8*a232*a234*a343-2*a121*a131*a344+8*a133*a231*a344-2*a121*a232*a344-6*a131*a233*a344+2*a232*a233*a344-4*a141*a234*a344-8*a234*a242*a344+2*a131*a244*a344+2*a232*a244*a344+12*a124*a341*a344-4*a234*a343*a344-3*a121*a344^2+3*a233*a344^2-a244*a344^2, a121^2*a131-4*a121*a133*a231+a121^2*a232+2*a121*a131*a233+4*a133*a231*a233-2*a121*a232*a233-3*a131*a233^2+a232*a233^2-4*a141*a233*a234-4*a121*a134*a241+4*a134*a233*a241+8*a133*a234*a241+8*a144*a234*a241-4*a121*a234*a242+8*a233*a234*a242-4*a131*a234*a243-4*a232*a234*a243+2*a121*a131*a244-4*a133*a231*a244+2*a121*a232*a244+2*a131*a233*a244-2*a232*a233*a244-4*a141*a234*a244-4*a134*a241*a244+a131*a244^2+a232*a244^2-8*a124*a233*a341+8*a124*a231*a343-4*a121*a234*a343-8*a234*a244*a343-a121^2*a344+2*a121*a233*a344-a233^2*a344+8*a124*a241*a344+4*a234*a243*a344-2*a121*a244*a344+2*a233*a244*a344-a244^2*a344, a122^3+4*a122*a123*a132-a122^2*a133+4*a123*a132*a133-a122*a133^2+a133^3+4*a122*a124*a142-4*a124*a133*a142+8*a123*a134*a142+8*a124*a132*a143-4*a122*a134*a143+4*a133*a134*a143-a122^2*a144-4*a123*a132*a144+2*a122*a133*a144-a133^2*a144+4*a124*a142*a144+4*a134*a143*a144-a122*a144^2-a133*a144^2+a144^3, a121*a122^2+2*a121*a122*a133+a121*a133^2+2*a121*a122*a144+2*a121*a133*a144+a121*a144^2-4*a122*a123*a232-4*a123*a133*a232+3*a122^2*a233+2*a122*a133*a233-a133^2*a233+8*a124*a142*a233+8*a134*a143*a233-2*a122*a144*a233-2*a133*a144*a233+3*a144^2*a233-4*a123*a142*a234-4*a133*a143*a234-4*a122*a124*a242-4*a124*a133*a242-4*a123*a134*a242-4*a124*a144*a242-8*a124*a132*a243+4*a122*a134*a243-8*a133*a134*a243-4*a134*a144*a243+3*a122^2*a244+4*a123*a132*a244+2*a122*a133*a244+3*a133^2*a244+2*a122*a144*a244-2*a133*a144*a244-a144^2*a244+4*a123*a124*a342-4*a124*a133*a343+8*a123*a134*a343+4*a123*a144*a344, a121^2*a122+a121^2*a133+a121^2*a144-4*a121*a123*a232+2*a121*a122*a233-2*a121*a133*a233+4*a123*a232*a233-3*a122*a233^2+a133*a233^2-a144*a233^2-2*a121*a143*a234+2*a143*a233*a234-4*a121*a124*a242-4*a124*a233*a242+8*a123*a234*a242-2*a121*a134*a243+8*a124*a232*a243+2*a134*a233*a243-8*a122*a234*a243+2*a121*a122*a244-2*a121*a144*a244-4*a123*a232*a244+2*a122*a233*a244+2*a143*a234*a244+4*a124*a242*a244+2*a134*a243*a244-3*a122*a244^2-a133*a244^2+a144*a244^2-2*a121*a124*a343+2*a124*a233*a343+2*a124*a244*a343+2*a121*a123*a344-2*a123*a233*a344-2*a123*a244*a344, a121^3-4*a121*a123*a231+a121^2*a233+4*a123*a231*a233-a121*a233^2-a233^3-4*a121*a124*a241-4*a124*a233*a241+8*a123*a234*a241+8*a124*a231*a243-4*a121*a234*a243-4*a233*a234*a243+a121^2*a244-4*a123*a231*a244+2*a121*a233*a244+a233^2*a244+4*a124*a241*a244-4*a234*a243*a244-a121*a244^2+a233*a244^2-a244^3); C3 = ideal(a122*a341+a133*a341+a144*a341-a121*a342+a233*a342+a244*a342-a131*a343-a232*a343-a141*a344-a242*a344, a232*a241-a231*a242+a233*a341+a244*a341-a231*a343-a241*a344, a122*a241+a133*a241+a144*a241-a121*a242+a233*a242-a131*a243-a232*a243-a141*a244-a244*a343+a243*a344, a144*a234-a134*a244+a124*a344, a141*a234+a234*a242-a131*a244-a232*a244+a234*a343+a121*a344-a233*a344, a144*a233+a143*a234-a134*a243-a133*a244+a124*a343+a123*a344, a143*a233-a133*a243+a123*a343, a141*a233+a233*a242-a131*a243-a232*a243+a121*a343-a244*a343+a243*a344, a144*a232+a142*a234-a134*a242-a132*a244+a124*a342+a122*a344, a143*a232+a142*a233-a133*a242-a132*a243+a123*a342+a122*a343, a142*a232-a132*a242+a122*a342, a141*a232-a131*a242+a121*a342-a233*a342-a244*a342+a232*a343+a242*a344, a144*a231-a134*a241-a234*a242+a232*a244+a124*a341-a234*a343+a233*a344, a143*a231-a133*a241-a233*a242+a232*a243+a123*a341+a244*a343-a243*a344, a142*a231-a132*a241-a133*a341-a144*a341+a121*a342+a131*a343+a141*a344, a141*a231-a131*a241+a121*a341, a122*a231+a133*a231-a121*a232-a131*a233+a134*a241+a234*a242-a131*a244-a232*a244-a124*a341+a234*a343+a121*a344-a233*a344, a134*a141-a131*a144+a142*a234-a132*a244+a124*a342+a134*a343-a133*a344, a133*a141-a131*a143+a142*a233-a132*a243+a123*a342-a144*a343+a143*a344, a132*a141-a131*a142-a133*a342-a144*a342+a132*a343+a142*a344, a124*a141-a121*a144-a143*a234+a124*a242+a134*a243-a122*a244-a123*a344, a123*a141-a121*a143+a123*a242-a122*a243-a144*a243+a143*a244, a122*a141-a121*a142+a142*a233-a133*a242-a144*a242+a142*a244+a122*a343, a124*a131-a121*a134+a124*a232+a134*a233-a122*a234-a133*a234, a123*a131-a121*a133+a123*a232-a122*a233+a143*a234-a134*a243+a124*a343, a122*a131-a121*a132-a133*a232+a132*a233+a142*a234-a134*a242+a124*a342, a234*a243*a342-a233*a244*a342-a234*a242*a343+a232*a244*a343+a233*a242*a344-a232*a243*a344, a143*a234*a342-a133*a244*a342-a142*a234*a343+a132*a244*a343+a142*a233*a344-a132*a243*a344+a123*a342*a344, a134*a143*a342-a133*a144*a342-a134*a142*a343+a132*a144*a343+a133*a142*a344-a132*a143*a344, a234*a243*a341-a233*a244*a341-a234*a241*a343+a231*a244*a343+a233*a241*a344-a231*a243*a344, a234*a242*a341-a232*a244*a341-a234*a241*a342+a231*a244*a342-a233*a341*a344-a244*a341*a344+a231*a343*a344+a241*a344^2, a233*a242*a341-a232*a243*a341-a233*a241*a342+a231*a243*a342-a233*a341*a343-a244*a341*a343+a231*a343^2+a241*a343*a344, a133*a242*a341+a144*a242*a341-a132*a243*a341-a142*a244*a341-a133*a241*a342-a144*a241*a342+a131*a243*a342+a141*a244*a342+a132*a241*a343-a131*a242*a343+a142*a241*a344-a141*a242*a344, a124*a242*a341+a134*a243*a341+a144*a244*a341-a124*a241*a342+a233*a244*a342+a244^2*a342-a134*a241*a343-a232*a244*a343-a144*a241*a344-a233*a242*a344+a232*a243*a344-a242*a244*a344+a244*a343*a344-a243*a344^2, a123*a242*a341+a133*a243*a341+a143*a244*a341-a123*a241*a342+a233*a243*a342+a243*a244*a342-a133*a241*a343-a233*a242*a343+a244*a343^2-a143*a241*a344-a242*a243*a344-a243*a343*a344, a143*a234*a341-a133*a244*a341+a234*a242*a343-a232*a244*a343+a234*a343^2-a233*a242*a344+a232*a243*a344+a123*a341*a344-a233*a343*a344+a244*a343*a344-a243*a344^2, a142*a234*a341-a132*a244*a341+a234*a242*a342-a232*a244*a342+a234*a342*a343-a133*a341*a344-a144*a341*a344+a121*a342*a344-a233*a342*a344+a131*a343*a344+a141*a344^2, a124*a232*a341+a134*a233*a341+a134*a244*a341-a124*a231*a342+a233*a234*a342+a234*a244*a342-a134*a231*a343-a232*a234*a343-a134*a241*a344-a234*a242*a344, a123*a232*a341+a133*a233*a341+a133*a244*a341-a123*a231*a342+a233^2*a342+a233*a244*a342-a133*a231*a343-a232*a233*a343-a133*a241*a344-a233*a242*a344, a134*a143*a341-a133*a144*a341+a142*a234*a343-a132*a244*a343+a124*a342*a343+a134*a343^2-a142*a233*a344+a132*a243*a344-a123*a342*a344-a133*a343*a344+a144*a343*a344-a143*a344^2, a124*a143*a341-a123*a144*a341+a124*a243*a342-a123*a244*a342-a143*a234*a343+a134*a243*a343+a144*a243*a344-a143*a244*a344-a123*a343*a344, a134*a142*a341-a132*a144*a341+a142*a234*a342-a132*a244*a342+a124*a342^2+a134*a342*a343+a144*a342*a344-a132*a343*a344-a142*a344^2, a133*a142*a341-a132*a143*a341+a142*a233*a342-a132*a243*a342+a123*a342^2+a133*a342*a343-a132*a343^2+a143*a342*a344-a142*a343*a344, a124*a142*a341+a133*a144*a341+a144^2*a341-a121*a144*a342+a124*a242*a342+a134*a243*a342-a122*a244*a342+a144*a244*a342-a131*a144*a343-a142*a234*a343-a141*a144*a344+a142*a233*a344-a132*a243*a344-a142*a244*a344, a123*a142*a341+a133*a143*a341+a143*a144*a341-a121*a143*a342+a123*a242*a342-a122*a243*a342+a133*a243*a342+a143*a244*a342-a131*a143*a343-a132*a243*a343-a141*a143*a344-a142*a243*a344, a124*a133*a341-a123*a134*a341+a124*a233*a342-a123*a234*a342+a134*a233*a343-a133*a234*a343-a143*a234*a344+a134*a243*a344-a124*a343*a344, a124*a132*a341+a133*a134*a341+a134*a144*a341-a121*a134*a342+a124*a232*a342+a134*a233*a342-a122*a234*a342+a134*a244*a342-a131*a134*a343-a132*a234*a343-a131*a144*a344-a132*a244*a344+a134*a343*a344-a133*a344^2, a123*a132*a341+a133^2*a341+a133*a144*a341-a121*a133*a342+a123*a232*a342-a122*a233*a342+a133*a233*a342+a133*a244*a342-a131*a133*a343-a132*a233*a343-a131*a143*a344-a132*a243*a344-a144*a343*a344+a143*a344^2, a143*a234*a242-a142*a234*a243+a142*a233*a244-a133*a242*a244+a122*a244*a343+a123*a242*a344-a122*a243*a344, a134*a233*a242-a133*a234*a242-a134*a232*a243+a132*a234*a243+a133*a232*a244-a132*a233*a244-a124*a233*a342+a123*a234*a342+a124*a232*a343-a122*a234*a343-a123*a232*a344+a122*a233*a344, a134*a143*a242-a133*a144*a242-a134*a142*a243+a132*a144*a243+a133*a142*a244-a132*a143*a244+a124*a143*a342-a123*a144*a342-a124*a142*a343+a122*a144*a343+a123*a142*a344-a122*a143*a344, a124*a143*a242-a123*a144*a242-a124*a142*a243+a122*a144*a243+a123*a142*a244-a122*a143*a244, a143*a234*a241+a234*a242*a243-a133*a241*a244-a233*a242*a244+a234*a243*a343+a244^2*a343+a123*a241*a344-a233*a243*a344-a243*a244*a344, a133*a234*a241+a233*a234*a242-a133*a231*a244-a232*a233*a244-a123*a234*a341+a233*a234*a343+a123*a231*a344-a233^2*a344, a124*a143*a241-a123*a144*a241-a143*a234*a243+a124*a242*a243+a134*a243^2-a123*a242*a244+a144*a243*a244-a143*a244^2-a123*a243*a344, a124*a142*a241+a133*a144*a241+a144^2*a241-a121*a144*a242+a124*a242^2-a131*a144*a243-a142*a234*a243+a134*a242*a243-a141*a144*a244+a142*a233*a244-a122*a242*a244+a144*a242*a244-a132*a243*a244-a142*a244^2+a124*a243*a342-a124*a242*a343+a122*a244*a343-a144*a244*a343-a122*a243*a344+a144*a243*a344, a123*a142*a241+a133*a143*a241+a143*a144*a241-a121*a143*a242+a123*a242^2-a131*a143*a243-a122*a242*a243+a133*a242*a243-a132*a243^2-a141*a143*a244+a143*a242*a244-a142*a243*a244+a123*a243*a342-a123*a242*a343-a143*a244*a343+a143*a243*a344, a124*a133*a241-a123*a134*a241+a124*a233*a242-a123*a234*a242+a134*a233*a243-a133*a234*a243-a143*a234*a244+a134*a243*a244-a124*a244*a343, a124*a132*a241+a133*a134*a241+a134*a144*a241-a121*a134*a242+a124*a232*a242-a122*a234*a242+a133*a234*a242-a131*a134*a243+a134*a232*a243-2*a132*a234*a243-a131*a144*a244-a133*a232*a244+a132*a233*a244+a134*a242*a244-a132*a244^2+a124*a233*a342-a123*a234*a342-a124*a232*a343+a122*a234*a343+a123*a232*a344-a122*a233*a344+a134*a243*a344-a133*a244*a344, a123*a132*a241+a133^2*a241+a133*a144*a241-a121*a133*a242+a123*a232*a242-a122*a233*a242+a133*a233*a242-a131*a133*a243-a132*a233*a243-a131*a143*a244+a133*a242*a244-a132*a243*a244-a133*a244*a343-a144*a244*a343+a133*a243*a344+a143*a244*a344, a134*a142*a233-a133*a142*a234+a132*a143*a234-a132*a134*a243-a124*a133*a342+a123*a134*a342+a124*a132*a343, a124*a142*a233-a123*a142*a234+a122*a143*a234-a124*a133*a242+a123*a134*a242-a122*a134*a243+a122*a124*a343, a124*a133*a232-a123*a134*a232-a124*a132*a233+a122*a134*a233+a123*a132*a234-a122*a133*a234, a124*a133*a231-a123*a134*a231+a124*a232*a233+a134*a233^2-a123*a232*a234-a133*a233*a234+a134*a233*a244-a133*a234*a244-a124*a233*a344+a123*a234*a344, a124*a132*a231+a133*a134*a231-a121*a134*a232+a124*a232^2-a131*a134*a233+a134*a232*a233-a122*a232*a234-a132*a233*a234+a134^2*a241+a134*a234*a242-a131*a134*a244-a132*a234*a244-a124*a134*a341+a134*a234*a343+a121*a134*a344-a124*a232*a344-a134*a233*a344+a122*a234*a344, a123*a132*a231+a133^2*a231-a121*a133*a232+a123*a232^2-a131*a133*a233-a122*a232*a233+a133*a232*a233-a132*a233^2+a133*a134*a241+a133*a234*a242-a131*a133*a244-a132*a233*a244-a123*a134*a341+a124*a233*a342-a123*a234*a342+a134*a233*a343+a121*a133*a344-a123*a232*a344+a122*a233*a344-a133*a233*a344-a143*a234*a344+a134*a243*a344-a124*a343*a344); C4 = I + minors(3,M); time dim C1, degree C1, betti mingens C1 hilbertPolynomial C1 time isPrime C1 time dim C3, degree C3, betti mingens C3 hilbertPolynomial C3 time isPrime C3 time dim C4, degree C4, betti mingens C4 hilbertPolynomial C4 time # minimalPrimes C4 time radical C4 == C4 time dim C2, degree C2, betti mingens C2 hilbertPolynomial C2 time T = intersect(C1,C3); betti mingens T dim T, degree T time T = intersect(T,C4); betti mingens T dim T, degree T time T = intersect(T,C2); betti mingens T dim T, degree T