In recent work trying to visualize the graph of a function from RP^1 to RP^1 on the torus, the code I used gave a DeprecationWarning that I have not been able to interpret.
/home/sageserver/sage/sagecell-main/interact_sagecell.py:422: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...) See http://trac.sagemath.org/5930 for details. returned = f(args, *control_vals)
The graph also seemed to hang up-- though it now seems ok. Any assistance would be appreciated, THANKS.
Here's the permalink:
https://sagecell.sagemath.org/?z=eJyNUd1qwyAYvS_0HQ6hUG0dTUyvSlJ2t9uxB-iwRkloGsUYu739lLZsgzImyPn8OD9-OjEEMI8aQTiynFhgfknns9afe4Kskmrwyu1RHeNu-R4vTtgWRmOhscPb66FYwBssrlW1iZxqc9xn0eO5S1ohPeazRmmchSU6Jn0cON3NZ4hLFzUIKbGGNCMJlK4STpT96o3dkHoJAgW9Scv6W8lXwkkvBqJjmTBgA04j-WYZp6QM_-NfcxgS_kG8X8TGGaxw4qy86-S77Y0vG5Jmi4ETQ87AV7ZL8eHnSZreuBrZp-p7c8nubrwWzplLsiA5y9nTNr5GKrb0TikfBurycULmVJMx33byNKhxjB9Q5KDJ6Go3tuZCbLG2fG1LGptfnWWK-w==&lang=sage
And here's the Code:
u, v ,t = var('u,v,t')
html( "<center> <b> <h2> Graph of $f : RP^1$ to $RP^1$ </h2></b>")
@interact
def map(f = x^2):
f1= ((3 + cos(v))*cos(u),(3 + cos(v))*sin(u),sin(v) )
f3=((3 + cos(2*arctan(f(2*tan(v / 2)) )))*cos( v ), (3 + cos(2*arctan(f(2*tan(v / 2)) )))*sin(v), sin(2*arctan(f(2*tan(v / 2)) )) )
p1= parametric_plot3d( f1, (u, 0, 2*pi), (v, 0, 2*pi), color= "yellow")
p2=arrow3d( (0,0,-4),(0,0,4))
p3= parametric_plot3d( f3, (v, 0, 2*pi), color="red",thickness = 10 )
show(p1+p2+p3)
