Function-call syntax deprecation

[Federico Galetto]

Hello, I get a warning due to function-call syntax deprecation and I don't understand how to fix it despite looking at other similar conversations.

Here is the setup for my code:

t=var('t')

gamma=vector([t,t^2,t^3])

curve=parametric_plot(gamma,(t,-2,2),color='black',radius=0.02)

v=derivative(gamma,t)

T=v/v.norm()

Tp=derivative(T,t)

N=Tp/Tp.norm()

B=T.cross_product(N)

This code creates the plot of a space curve and computes T,N,B which are unit tangent, normal, and binormal vectors. Now I want to create an interactive 3d plot:

def frame(x):

    pT = T(x).plot(start=gamma(x),radius=0.02)

    pN = N(x).plot(color='red',start=gamma(x),radius=0.02)

    pB = B(x).plot(color='green',start=gamma(x),radius=0.02)

    frenet = pT + pN + pB

    whole = frenet + curve

    return whole

a = animate([frame(x) for x in srange(-0.5,1.5,.02)])

a.show()

Although this works, I get the syntax deprecation warning at the line 'a = animate(...'.

Any help is greatly appreciated!

Fred

[Matthias Koeppe]

Instead of:

gamma=vector([t,t^2,t^3])

use:

gamma=vector([t,t^2,t^3]).function(t)

Alternatively, keep gamma as is and use gamma(t=x) instead of gamma(x).

[Kwankyu]

gamma(t) = vector([t,t^2,t^3])

is a bit simpler.

[Federico Galetto]

Thank you both for your suggestions!

The gamma(t)=... solution gave me some other error down the line, while appending .function(t) to the definition of gamma worked but raised errors from later calls to simplify_full(). In the end, replacing x with t=x in the definition of my 'frame' function got rid of all warnings and allowed me to keep everything else in place.

Cheers,

Fred.