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x, y=var('x y')
f(x,y)=sqrt(1-x^2-y^2)
plot3d(f(x,y),(x,-1,1),(y,-1,1))
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contour_plot(f(x,y), (x,-1,1), (y,-1,1), contours=(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9))
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contour_plot(f(x,y), (x,-1,1), (y,-1,1), contours=(0,sqrt(3)/2))
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gradient=f.gradient()
gradient(x,y)
(-x/sqrt(-x^2 - y^2 + 1), -y/sqrt(-x^2 - y^2 + 1)) (-x/sqrt(-x^2 - y^2 + 1), -y/sqrt(-x^2 - y^2 + 1)) |
[diff(f(x,y),x),diff(f(x,y),y)]
[-x/sqrt(-x^2 - y^2 + 1), -y/sqrt(-x^2 - y^2 + 1)] [-x/sqrt(-x^2 - y^2 + 1), -y/sqrt(-x^2 - y^2 + 1)] |
# de twee onderstaande commando's produceren net hetzelfde
p1=plot_vector_field([diff(f(x,y),x),diff(f(x,y),y)], (x,-1,1), (y,-1,1))
# p2=plot_vector_field(gradient(x,y), (x,-1,1), (y,-1,1))
show(p1)
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pretty_print(gradient(0.5,0))
pretty_print(gradient(-0.5,0))
pretty_print(gradient(0,0.5))
pretty_print(gradient(0,-0.5))
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