︠c9afd941-d292-416b-9b69-866d217f34f2︠ KK.=QQ[] I=Ideal([x^4-3*x*y+y^2,x^5-4*x*y+3*x*y^2]) ︠0c007b62-f9cc-4c6a-9450-7c5ea12e8844︠ x^2 in I ︡6decdea9-bc75-443b-b9d2-30bb1f687235︡{"stdout":"False\n"}︡ ︠be922dce-65da-4dfa-b502-5b74e60e343fs︠ x^3 in I ︡f778b5c7-3186-4c38-a25f-bfb59fb3df0d︡{"stdout":"False\n"}︡ ︠3e04e975-44ec-4d1f-8ade-d0208a9546e6s︠ x^4 - 3*x*y + y^2 in I ︡b1e9b554-22c6-4e2c-9ae4-96280750c4cc︡{"stdout":"True\n"}︡ ︠764ab330-dd89-4703-a43b-48b4d0877f52s︠ I.groebner_basis() ︡5bcd2847-cd10-4ad9-aa62-28e8b2b7be96︡{"stdout":"[y^5 - 8*y^4 - 531/16*x*y^2 + 273/16*y^3 + 12*x*y, x^4 - 3*x*y + y^2, x*y^3 + 2/3*y^4 - 4/3*y^3, x^2*y + 2/3*x*y^2 - 4/3*x*y]\n"}︡ ︠b4311e52-d25d-4c13-8acb-9e5d4a2e4dad︠