Manifold that is the union of 2 manifolds

In [7]:
var("x y")
F(x,y)=4*(x^4 + x^2 *y^2)-12*x^3*y + x^2
implicit_plot(F(x,y), (x,-2,2), (y,-1,1))+implicit_plot(x, (x,-2,2), (y,-1,1)) #computer makes an error x=0 added artificially
Out[7]:

Non-submanifold that is the union of 2 submanifolds

In [9]:
implicit_plot(x^2+y^2-1, (x,-2,2), (y,-1,1))+implicit_plot(x, (x,-2,2), (y,-2,2))
Out[9]:

graph from both axes perspective

In [10]:
implicit_plot(y*log(x)-x*cos(y), (x,-2,2), (y,-1,1))
Out[10]:
In [21]:
u = var('u')
circle = (cos(u)+2, sin(u))
In [22]:
revolution_plot3d(circle, (u,0,2*pi), axis=(0,0), show_curve=True, opacity=0.5).show(aspect_ratio=(1,1,1))
In [ ]: