In [20]:
load("/Users/vincentdouce/Dropbox/LWS_FTP/jupyter/hessienne/code_general.sage")
fonction P
paramètres généraux
| f | \(\left( x, y \right) \ {\mapsto} \ x^{2} y - x y^{2} - x y\) |
| grad f= | \(\left[{\left(2 \, x - 1\right)} y - y^{2}, x^{2} - 2 \, x y - x\right]\) |
| H= | \(\left(\begin{array}{rr} 2 \, y & 2 \, x - 2 \, y - 1 \\ 2 \, x - 2 \, y - 1 & -2 \, x \end{array}\right)\) |
points critiques
| ( | x | = | \(0\) | ; | y | = | \(0\) | ) | \(\left(\begin{array}{rr} 0 & -1 \\ -1 & 0 \end{array}\right)\) |
| ( | x | = | \(0\) | ; | y | = | \(-1\) | ) | \(\left(\begin{array}{rr} -2 & 1 \\ 1 & 0 \end{array}\right)\) |
| ( | x | = | \(1\) | ; | y | = | \(0\) | ) | \(\left(\begin{array}{rr} 0 & 1 \\ 1 & -2 \end{array}\right)\) |
| ( | x | = | \(\frac{1}{3}\) | ; | y | = | \(-\frac{1}{3}\) | ) | \(\left(\begin{array}{rr} -\frac{2}{3} & \frac{1}{3} \\ \frac{1}{3} & -\frac{2}{3} \end{array}\right)\) |
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