I want to plot the two surfaces which are defined in $ \mathbb{ R }^3 \ni ( x, y, z ) $ via the equations $ 0 = y^2 - x\*(x^2 + 1) $ and $ 0 = z^2 - y\*(y^2 + 1) $, respectively.
Moreover, I want also to highlight the intersection curve of these surfaces.


Any tool is ok for me, but I know that sage has some functions for plotting implicit functions in 3d:
The commands



```
var('x, y, z') 
s1 = implicit_plot3d(0 == y^2 - x*(x^2 + 1), (x,-3,3), (y,-3,3), (z,-3,3))
s2 = implicit_plot3d(0 == z^2 - y*(y^2 + 1), (x,-3,3), (y,-3,3), (z,-3,3))
plot(s1 + s2) 

```

plot both surfaces.
But I would like to highlight the intersection curve or at least change the transparency-level of the surfaces (changing the alpha-values seems not to do anything)


A bonus would also be if there were a way to directly plot the intersection of these surfaces.


Does anybody know a tool to do this?



Plot two implicit surfaces in 3D and highlight their intersection
Something like this?


![](https://i.stack.imgur.com/rJ9IL.png) 
 
Blue curve is the intersection of the two surfaces $ 0 = y^2 - x(x^2 + 1) $ and $ 0 = z^2 - y(y^2 + 1) $.
The 3D plots were generated with Mathematica, as documented [here.](https://reference.wolfram.com/language/example/HighlightTheIntersectionOfTwoSurfaces.html)


