︠ed204d86-55e9-4ec1-bcee-f06f734083b8︠ # I want to do something like this: R = PolynomialRing(QQ,'x') S.=R.quotient(x^3+x+1) T.=QQ[] b*a ︡b5fc0ae0-3dc2-417b-8f69-3c8cb1137f2b︡{"md":"I want to do something like this:"}︡{"stderr":"Error in lines 5-5\nTraceback (most recent call last):\n File \"/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/.sagemathcloud/sage_server.py\", line 875, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \n File \"sage/structure/element.pyx\", line 1841, in sage.structure.element.RingElement.__mul__ (build/cythonized/sage/structure/element.c:17183)\n return coercion_model.bin_op(left, right, mul)\n File \"sage/structure/coerce.pyx\", line 850, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (build/cythonized/sage/structure/coerce.c:8045)\n raise TypeError, arith_error_message(x,y,op)\nTypeError: unsupported operand parent(s) for '*': 'Univariate Polynomial Ring in b over Rational Field' and 'Univariate Quotient Polynomial Ring in a over Rational Field with modulus x^3 + x + 1'\n"}︡ ︠0975d7ff-3058-4a8f-b5a2-e8e2e33ac2b7︠ # Instead, do this: R. = QQ[] S. = NumberField(x^3 + x + 1) T. = QQ[] a*b ︡4d999ca6-3a09-44a3-8cd7-3d2ed9ecc322︡{"stdout":"a*b\n"}︡ ︠20401a55-477e-43ec-b33e-08d937c69db6︠ parent(a*b) ︡81b8abd8-1fbd-4523-89e1-a67d3903d9c9︡{"stdout":"Univariate Polynomial Ring in b over Number Field in a with defining polynomial x^3 + x + 1\n"}︡ ︠69b56b60-4d79-488c-8701-3db59e924c70︠