{{{id=1| R.=PolynomialRing(QQ,2,order='invlex') /// }}} {{{id=2| f1=2*x^2*y+3*x+4*y f2=3*x*y^2+4*x+5*y /// }}} {{{id=9| f1 /// \newcommand{\Bold}[1]{\mathbf{#1}}2 x^{2} y + 4 y + 3 x }}} {{{id=10| f2 /// \newcommand{\Bold}[1]{\mathbf{#1}}3 x y^{2} + 5 y + 4 x }}} {{{id=11| f3=3*y*f1-2*x*f2;f3 /// \newcommand{\Bold}[1]{\mathbf{#1}}12 y^{2} - x y - 8 x^{2} }}} {{{id=12| f4=f1*4+y*f3;f4 /// \newcommand{\Bold}[1]{\mathbf{#1}}12 y^{3} - x y^{2} + 16 y + 12 x }}} {{{id=13| f5=f2+3*f4;f5 /// \newcommand{\Bold}[1]{\mathbf{#1}}36 y^{3} + 53 y + 40 x }}} {{{id=14| f6=x*f5+5*f3;f6 /// \newcommand{\Bold}[1]{\mathbf{#1}}36 x y^{3} + 60 y^{2} + 48 x y }}} {{{id=15| f6-12*f2*y /// \newcommand{\Bold}[1]{\mathbf{#1}}0 }}} {{{id=16| f7=y^2*f5+40*f4;f7 /// \newcommand{\Bold}[1]{\mathbf{#1}}36 y^{5} + 533 y^{3} + 640 y + 480 x }}} {{{id=17| f8=12*f5-f7;f8 /// \newcommand{\Bold}[1]{\mathbf{#1}}-36 y^{5} - 101 y^{3} - 4 y }}} {{{id=18| f8.factor() /// \newcommand{\Bold}[1]{\mathbf{#1}}\left(-1\right) \cdot y \cdot (36 y^{4} + 101 y^{2} + 4) }}} {{{id=20| R(f8) /// \newcommand{\Bold}[1]{\mathbf{#1}}-36 y^{5} - 101 y^{3} - 4 y }}} {{{id=21| /// }}} {{{id=22| /// }}}