load("/Users/vincentdouce/Dropbox/LWS_FTP/jupyter/hessienne/code_general.sage")

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f	$\left( x, y \right) \ {\mapsto} \ x^{5} + y^{5} - 5 \, x^{3} - 5 \, y^{3} + 10 \, x + 10 \, y$
grad f=	$\left[5 \, x^{4} - 15 \, x^{2} + 10, 5 \, y^{4} - 15 \, y^{2} + 10\right]$
H=	$\left(\begin{array}{rr} 20 \, x^{3} - 30 \, x & 0 \\ 0 & 20 \, y^{3} - 30 \, y \end{array}\right)$

(	x	=	$1$	;	y	=	$1$	)	$\left(\begin{array}{rr} -10 & 0 \\ 0 & -10 \end{array}\right)$
(	x	=	$-1$	;	y	=	$1$	)	$\left(\begin{array}{rr} 10 & 0 \\ 0 & -10 \end{array}\right)$
(	x	=	$-\sqrt{2}$	;	y	=	$1$	)	$\left(\begin{array}{rr} -10 \, \sqrt{2} & 0 \\ 0 & -10 \end{array}\right)$
(	x	=	$\sqrt{2}$	;	y	=	$1$	)	$\left(\begin{array}{rr} 10 \, \sqrt{2} & 0 \\ 0 & -10 \end{array}\right)$
(	x	=	$1$	;	y	=	$-1$	)	$\left(\begin{array}{rr} -10 & 0 \\ 0 & 10 \end{array}\right)$
(	x	=	$-1$	;	y	=	$-1$	)	$\left(\begin{array}{rr} 10 & 0 \\ 0 & 10 \end{array}\right)$
(	x	=	$-\sqrt{2}$	;	y	=	$-1$	)	$\left(\begin{array}{rr} -10 \, \sqrt{2} & 0 \\ 0 & 10 \end{array}\right)$
(	x	=	$\sqrt{2}$	;	y	=	$-1$	)	$\left(\begin{array}{rr} 10 \, \sqrt{2} & 0 \\ 0 & 10 \end{array}\right)$
(	x	=	$1$	;	y	=	$-\sqrt{2}$	)	$\left(\begin{array}{rr} -10 & 0 \\ 0 & -10 \, \sqrt{2} \end{array}\right)$
(	x	=	$1$	;	y	=	$\sqrt{2}$	)	$\left(\begin{array}{rr} -10 & 0 \\ 0 & 10 \, \sqrt{2} \end{array}\right)$
(	x	=	$-1$	;	y	=	$-\sqrt{2}$	)	$\left(\begin{array}{rr} 10 & 0 \\ 0 & -10 \, \sqrt{2} \end{array}\right)$
(	x	=	$-1$	;	y	=	$\sqrt{2}$	)	$\left(\begin{array}{rr} 10 & 0 \\ 0 & 10 \, \sqrt{2} \end{array}\right)$
(	x	=	$-\sqrt{2}$	;	y	=	$-\sqrt{2}$	)	$\left(\begin{array}{rr} -10 \, \sqrt{2} & 0 \\ 0 & -10 \, \sqrt{2} \end{array}\right)$
(	x	=	$\sqrt{2}$	;	y	=	$-\sqrt{2}$	)	$\left(\begin{array}{rr} 10 \, \sqrt{2} & 0 \\ 0 & -10 \, \sqrt{2} \end{array}\right)$
(	x	=	$-\sqrt{2}$	;	y	=	$\sqrt{2}$	)	$\left(\begin{array}{rr} -10 \, \sqrt{2} & 0 \\ 0 & 10 \, \sqrt{2} \end{array}\right)$
(	x	=	$\sqrt{2}$	;	y	=	$\sqrt{2}$	)	$\left(\begin{array}{rr} 10 \, \sqrt{2} & 0 \\ 0 & 10 \, \sqrt{2} \end{array}\right)$

fonction C : Vénus…

paramètres généraux

points critiques