I'm trying to sum over the coefficients of an expansion but the sum gives zero. I use the taylor method to expand a function f:
f=sin(x)
ft=f.taylor(x,0,6)
then I need to use the coefficients in a sum, but if I for example do the following:
sum(x^(i)*ft.coefficient(x,i),i,0,5)
I get zero. Any idea why this is happening?
You should use instead:
sage: sum(x^i*ft.coefficient(x, i) for i in [0..5])
1/120*x^5 - 1/6*x^3 + x
Explanation: your original code involves Sage's symbolic sum and i has to be a symbolic variable (you probably declared it as such via var('i')). Now, the method coefficient is expecting an integer, not a symbolic variable. For some reason, it returns always zero for a symbolic variable (IMHO an error message would be more appropriate here):
sage: i = var('i')
sage: ft.coefficient(x, i)
0
Hence the result that you get. On the contrary, the command
sum(x^i*ft.coefficient(x, i) for i in [0..5])
involves Python's sum, for which i is an integer, so that ft.coefficient behaves correctly. For more details, see the documentation returned by sum? (in particular the warning in it).
Asked: 2018-05-24 02:40:44 +0100
Seen: 507 times
Last updated: May 26 '18
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