Re: converting a multivariate series to a polynomial

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Jan 04, 2022 at 05:20:34PM -0500, Max Alekseyev wrote:
> Dear Bill,
> 
> Thank you for a neat solution!
> 
> As a side note, can you please elaborate on the "you should use truncate"
> suggestion?
> PARI documentation says
> "Pol(t,{v='x}): convert t (usually a vector or a power series) into a
> polynomial..."
> and thus it implies that Pol() is usually used for converting power series
> into a polynomial. 

Not really, it only implies that the argument of Pol is usually a vector
or a power series.

> If that is bad for some reason, it should be reflected
> in the documentation.

'convert' is a structural operation without much mathematic meaning, while
'truncate' is a mathematical operation:

For example

? truncate(1/x+1+x+O(x^2))
%1 = (x^2+x+1)/x
? Pol(1/x+1+x+O(x^2))
  ***   at top-level: Pol(1/x+1+x+O(x^2))
  ***                 ^-------------------
  *** Pol: domain error in gtopoly: valuation < 0

as an aside, you might want to use this variant of truncateall:

truncateall(x)=if(type(x)=="t_SER",truncate(apply(truncateall,x)),x)

Cheers,
Bill.