Re: Vec() and leading zeros of generating function

[Joerg Arndt <arndt@jjj.de>]

* Kevin Ryde <user42_kevin@yahoo.com.au> [Aug 16. 2014 07:58]:
> Vec() can give terms from a polynomial generating function but it
> doesn't include leading zeros.  Eg.
> 
>     Vec(x^2/(1-2*x) + O(x^5))
>     =>
>     [1, 2, 4]
> 
> Is there a good way to start from the zero'th term so I would get
> 
>     [0, 0, 1, 2, 4]

I'd use
  concat([0,0], Vec(x^2/(1-2*x) + O(x^5)))

The drawback is that you have to manually put in the right
number of zeros.  With any method to obtain the smallest
exponent of a power series with nonzero coefficient this
could be done as follows:

 gf = x^2/(1-2*x) + O(x^5))
 e = magic(gf)  \\ anyone?
 concat( vector(e), Vec(gf) )

That magic() would be useful in many places in the OEIS.

Would  e = valuation(gf,x)  do the trick _reliably_?


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