Lösen-Algebraischer-GLS-händisch
system:sage


{{{id=1|
R.<x,y>=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
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}2 x^{2} y + 4 y + 3 x</span></html>
}}}

{{{id=10|
f2
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}3 x y^{2} + 5 y + 4 x</span></html>
}}}

{{{id=11|
f3=3*y*f1-2*x*f2;f3
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}12 y^{2} - x y - 8 x^{2}</span></html>
}}}

{{{id=12|
f4=f1*4+y*f3;f4
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}12 y^{3} - x y^{2} + 16 y + 12 x</span></html>
}}}

{{{id=13|
f5=f2+3*f4;f5
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}36 y^{3} + 53 y + 40 x</span></html>
}}}

{{{id=14|
f6=x*f5+5*f3;f6
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}36 x y^{3} + 60 y^{2} + 48 x y</span></html>
}}}

{{{id=15|
f6-12*f2*y
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}0</span></html>
}}}

{{{id=16|
f7=y^2*f5+40*f4;f7
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}36 y^{5} + 533 y^{3} + 640 y + 480 x</span></html>
}}}

{{{id=17|
f8=12*f5-f7;f8
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}-36 y^{5} - 101 y^{3} - 4 y</span></html>
}}}

{{{id=18|
f8.factor()
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}\left(-1\right) \cdot y \cdot (36 y^{4} + 101 y^{2} + 4)</span></html>
}}}

{{{id=20|
R(f8)
///
<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}-36 y^{5} - 101 y^{3} - 4 y</span></html>
}}}

{{{id=21|

///
}}}

{{{id=22|

///
}}}