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Taylor expansion twice for a general function cause problem?

asked 2011-12-16 08:13:28 -0600

updated 2011-12-16 09:27:26 -0600

kcrisman gravatar image


I met a problem when expanding a general function twice:

y = var('y')
f = function('f',var('x'))
g = f(x=var('eps')*y)
h = taylor(g, eps, 0, 1)
taylor(h, eps, 0, 1)

The last expression ends up with an error: NotImplementedError: arguments must be distinct variables

Is it a bug or I got anything wrong? Thanks!

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answered 2011-12-23 13:09:36 -0600

gabriel gravatar image

Hello, I'm new to Sage and running into the same problem as you. I think this error happens when the object that you want to Taylor expand has a derivative that is evaluated at a specified point:

x = var('x')
u = function('u', x)
v(x) = u.diff(x)
taylor(u(x = 0), x, 0, 2) #works
taylor(v(x), x, 0, 2) #works
taylor(v(x = 0), x, 0, 2) #doesn't work

v(0) = D[0](u)(0) seems to be the problem, just like, in your case, there is a D[0](f)(0) in the Taylor expansion of g

So my guess is that issue resides in how derivatives evaluated at a fixed point are passed to Maxima..

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Asked: 2011-12-16 08:13:28 -0600

Seen: 158 times

Last updated: Dec 23 '11