Re: digits(0)

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sat, Oct 20, 2012 at 05:12:22PM +0200, Joerg Arndt wrote:
> * Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr> [Oct 19. 2012 20:02]:
> > On Fri, Oct 19, 2012 at 05:36:04PM +0200, Karim Belabas wrote:
> > > 
> > > In our normalization, the "0" numeral has no digit. We already have
> > > similar behaviour for polynomials : the 0 polynomial has no
> > > coefficients.
> > > 
> > >   (17:25) gp > Vec(x + 2)    \\ Vec(t_POL) returns the polynomial's coeffs
> > >   %1 = [1, 2]
> > >   (17:25) gp > Vec(Pol(1,'x))
> > >   %2 = [1]
> > >   (17:26) gp > Vec(Pol(0,'x))
> > >   %3 = []
> > > 
> > > So the current definition of digits() is consistent with what we already do.
> > > On the other hand, it is sometimes convenient to consider polynomials
> > > with respect to a fixed basis, and "degree drops" are inconvenient.
> > > So Vec() has an optional argument to fix the vector length:
> > >   (17:25) gp > Vec(Pol(1,'x), 5)
> > >   %4 = [1, 0, 0, 0, 0]   \\ 0*x^4 + 0*x^3 + 0*x^2 + 0*x + 1
> >  
> > Maybe we should return the digits in the other order, so that the relation
> > between the indices in the vector and the weight in the number is more
> > straightforward.
> 
> Make that an *option*.

Well, one can always use Vecrev(digits(n)). Really the question is the standard
order.

> Similarly with Vec(poly), one should have the choice to get
> falling or rising powers (and another option to set the
> range of powers would be useful).

All of that is implemented, see the function Vec(x,n) and Vecrev(x,n).

> While we are at it, the omission of leading zero
> coefficients with Vec(powseries) should also be avoidable IMHO
> (this ugly-fies much of my code for OEIS sequences).

Maybe you can use truncate.

Cheers,
Bill.