Taylor.sagews

%typeset_mode True

Exemple : calcul du polynôme de Taylor de degré 3 de $f(x,y) = e^x \cos (y)$ autour de $(0,0)$.

f(x,y) = e^x * cos(y)

P3(x,y) = f.taylor((x,0),(y,0),3)
P3(x,y)

$\displaystyle \frac{1}{6} \, x^{3} - \frac{1}{2} \, x y^{2} + \frac{1}{2} \, x^{2} - \frac{1}{2} \, y^{2} + x + 1$

Surff = plot3d(f(x,y),(x,-1,1),(y,-pi,pi), color="blue", opacity = 0.5)
SurfP3 = plot3d(P3(x,y),(x,-1,1),(y,-pi,pi), color="red", opacity = 0.5)
show(Surff+ SurfP3, frame_aspect_ratio = [2,2,1])

3D rendering not yet implemented