{{{id=1| R.=PolynomialRing(QQ,2,order='lex') /// }}} {{{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 + 3 x + 4 y }}} {{{id=10| f2 /// \newcommand{\Bold}[1]{\mathbf{#1}}3 x y^{2} + 4 x + 5 y }}} {{{id=11| f3=3*y*f1-2*x*f2;f3 /// \newcommand{\Bold}[1]{\mathbf{#1}}-8 x^{2} - x y + 12 y^{2} }}} {{{id=12| f4=f1*4+y*f3;f4 /// \newcommand{\Bold}[1]{\mathbf{#1}}- x y^{2} + 12 x + 12 y^{3} + 16 y }}} {{{id=23| f4a=f4*3+f2;f4a /// \newcommand{\Bold}[1]{\mathbf{#1}}40 x + 36 y^{3} + 53 y }}} {{{id=24| f5=f4a*x+5*f3;f5 /// \newcommand{\Bold}[1]{\mathbf{#1}}36 x y^{3} + 48 x y + 60 y^{2} }}} {{{id=25| f5a=f5-y^3*36/40*f4a; f5a /// \newcommand{\Bold}[1]{\mathbf{#1}}48 x y - \frac{162}{5} y^{6} - \frac{477}{10} y^{4} + 60 y^{2} }}} {{{id=26| f5b=f5a-48/40*y*f4a;f5b /// \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{162}{5} y^{6} - \frac{909}{10} y^{4} - \frac{18}{5} y^{2} }}} {{{id=27| usw /// }}} {{{id=28| Id=(f1,f2)*R; Id /// Ideal (2*x^2*y + 3*x + 4*y, 3*x*y^2 + 4*x + 5*y) of Multivariate Polynomial Ring in x, y over Rational Field }}} {{{id=29| Id.groebner_basis() /// [x + 9/10*y^3 + 53/40*y, y^5 + 101/36*y^3 + 1/9*y] }}} {{{id=20| /// }}} {{{id=21| /// }}} {{{id=22| /// }}}