reset()
var('x r h ')
p1=implicit_plot3d(h+r*x-x^3==0, (r,-3,5), (h,-3,3),(x,-3,3),color='red')
p2=implicit_plot3d(r-1, (r,-3,5), (h,-3,3),(x,-3,3),color='blue')
p3=implicit_plot3d(h-2, (-r,-3,5), (h,-3,3),(x,-3,3),color='green')
p=p1+p2+p3
show(p,axes_labels=['r','h','x'])
# p.save('i.bmp')
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reset()
var('r h')
r=-2
p1=implicit_plot(h+r*x-x^3==0, (h,-3,3), (x,-3,3),fill=true,fillcolor='pink',color='red',axes_labels=['$h$','$x$'])
p=p1
if r>0:
p2=implicit_plot(h+r*x-x^3==0, (h,-2/3*sqrt(1/3)*r^(3/2),
2/3*sqrt(1/3)*r^(3/2)), (x,-sqrt(r/3),sqrt(r/3)),
fill=true,fillcolor='pink',color='red',linestyle='dashed')
p=p1+p2
end
arr1=arrow((-2.5,2.5), (-2.5,2),color='black',width=1)
arr2=arrow((2.5,-2.5), (2.5,-2),color='black',width=1)
show(p+arr1+arr2)
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reset()
var ('r')
h=0.5;
p1=implicit_plot(h+r*x-x^3==0, (r,-3,3), (x,-3,3),fill=true,fillcolor='pink',color='red',axes_labels=['$r$','$x$'])
p2=implicit_plot(h+r*x-x^3==0, (r,3*(1/2)^(2/3)*(abs(h))^(1/3),3), (x,-(1/2)^(1/3)*(abs(h))^(1/3),(1/2)^(1/3)*(abs(h))^(1/3)), fill=true,fillcolor='pink',color='red',linestyle='dashed')
arr1=arrow((-2.5,2.5), (-2.5,2),color='black',width=1)
arr2=arrow((2.5,-2.5), (2.5,-2),color='black',width=1)
show(p1+p2+arr1+arr2)
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# dit hoort bij het voorbeeld van de insectenplaag
r= 2*x^3/(1+x^2)^2
k= 2*x^3/(x^2-1)
p=parametric_plot([k/10,5*r], (x, 1.0001, 45),fill=true,fillcolor='lightblue',color='blue',axes_labels=['$k$','$r$'])
p.show(xmin=0, xmax=8, ymin=0, ymax=3.5)
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