Irgendwas

685 days ago by supasnashbuhl

Irgendwas system:sage
f(x,y)=(6*x^2 + 7*x - 15) * cos(y) 
       
show(f) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\left( x, y \right) \ {\mapsto} \ {\left(6 \, x^{2} + 7 \, x - 15\right)} \cos\left(y\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\left( x, y \right) \ {\mapsto} \ {\left(6 \, x^{2} + 7 \, x - 15\right)} \cos\left(y\right)
 
       
show(diff(f,x,y)) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\left( x, y \right) \ {\mapsto} \ -{\left(12 \, x + 7\right)} \sin\left(y\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\left( x, y \right) \ {\mapsto} \ -{\left(12 \, x + 7\right)} \sin\left(y\right)
show(integral(f,x,y)) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, {\left(4 \, x^{3} + 7 \, x^{2} - 4 \, y^{3} - 7 \, y^{2} - 30 \, x + 30 \, y\right)} \cos\left(y\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, {\left(4 \, x^{3} + 7 \, x^{2} - 4 \, y^{3} - 7 \, y^{2} - 30 \, x + 30 \, y\right)} \cos\left(y\right)
g(x) = (x^3 + 2*x + 1)/(3*x^2 + x + 1); show(g) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}x \ {\mapsto}\ \frac{{\left(x^{3} + 2 \, x + 1\right)}}{{\left(3 \, x^{2} + x + 1\right)}}
\newcommand{\Bold}[1]{\mathbf{#1}}x \ {\mapsto}\ \frac{{\left(x^{3} + 2 \, x + 1\right)}}{{\left(3 \, x^{2} + x + 1\right)}}
temp = solve(g,x); show(temp) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{2} \, {\left(I \, \sqrt{3} + 1\right)} {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{1}{3} \, \frac{{\left(I \, \sqrt{3} - 1\right)}}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}, x = -\frac{1}{2} \, {\left(-I \, \sqrt{3} + 1\right)} {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{1}{3} \, \frac{{\left(-I \, \sqrt{3} - 1\right)}}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}, x = {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{2}{3} \, \frac{1}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{2} \, {\left(I \, \sqrt{3} + 1\right)} {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{1}{3} \, \frac{{\left(I \, \sqrt{3} - 1\right)}}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}, x = -\frac{1}{2} \, {\left(-I \, \sqrt{3} + 1\right)} {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{1}{3} \, \frac{{\left(-I \, \sqrt{3} - 1\right)}}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}, x = {\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)} - \frac{2}{3} \, \frac{1}{{\left(\frac{1}{18} \, \sqrt{3} \sqrt{59} - \frac{1}{2}\right)}^{\left(\frac{1}{3}\right)}}\right]
k = 5 + 2*I show(k); 
        
\newcommand{\Bold}[1]{\mathbf{#1}}2 I + 5
\newcommand{\Bold}[1]{\mathbf{#1}}2 I + 5
show(k*(5-2*I)); 
        
\newcommand{\Bold}[1]{\mathbf{#1}}29
\newcommand{\Bold}[1]{\mathbf{#1}}29