Problem in SageMath 10.6?

[Fernando Gouvea]

I'm trying to run this code, a simple-minded implementation of Newton's method:

g(x) = cos(x)-x
g_prime(x) = g.diff()
start = 1
number_of_steps = 5
x = start
for n in range(number_of_steps+1):
    print('step number: ',n,'; Newton estimate: ',x.n())
    if g_prime(x)!=0:
       x = x - g(x)/g_prime(x)

On my old Windows based 9.2 (terminal), it takes a minute but prints out steps 0 to 5 and gives me a new prompt.

On 10.6, however (running in WSL, Jupyter notebook), it prints out steps 0 to 4, waits quite a while, prints out step 5, and then the notebook prompt stays [*] indicating that the kernel is still running. 

If I change the number of steps to 8, even in 9.2 it hangs. And it slows down dramatically in the later steps. I'm clearly doing something wrong. What?

Thanks,

Fernando

-- 
=============================================================
Fernando Q. Gouvea         http://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics
Colby College              
5836 Mayflower Hill        
Waterville, ME 04901       

You can go wrong by being too skeptical as readily as by being too trusting.
  -- Robert A. Heinlein

[Fernando Gouvea]

Update: I left it running and yes, it does eventually exit. So perhaps the question is why it takes so much longer to do the next step when n=5 than when n=4. The values of x seem to be identical in both steps.

Fernando

[Fernando Gouvea]

Ah, I think I see it. The step should be x = (x - g(x)/g_prime(x)).n(); otherwise x is becoming an immensely long expression with sin(1) and cos(1).

Sorry to bother y'all.

Fernando

Carter Professor of Mathematics
Dept. of Mathematics
Colby College              
5836 Mayflower Hill        
Waterville, ME 04901       

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