[Axiom-mail] Re: Power series with coeffs in positive characteristic

[Marcus Better]

I managed to solve the problem with power series with variable 
coefficients over a field as follows, but I still don't know why the 
first approach didn't work. Here is what I did:

First I define some coefficient function ycoeff with a nice recursive 
definition:

      ycoeff: Integer -> FRAC POLY PrimeField 2;
      ycoeff(0)==1; ycoeff(1)==a;
      ycoeff(n | n>1 and even? n)==0;
      ycoeff(n | n>1 and odd? n) == b*ycoeff((n-1)/2-1)^2;

Then I try to form a power series from it using the GENUPS package:

      series(n +-> ycoeff(n), z=0)

which gives me

      1+az+bz^3+a^2bz^5+b^3z^9+O(z^11)

with type UnivariatePuiseuxSeries(Expression Integer, z, 0), so here the 
coefficients have been turned into Expression Integer, whereas I still 
want them to be FRAC POLY PrimeField 2.

However, I get the correct result by forming a stream manually:
      stream := [ycoeff(n) for n in 0..];
      series(stream)$UTS(FRAC POLY PrimeField 2, z, 0)

This should be more or less equivalent to what GENUPS does, but seems to 
 retain the coefficient type.

--
-----------------------------------------------------------------
Marcus Better
Department of Mathematics                      Tel. +46 8 164539
Stockholm University                           Fax +46 8 6126717
SE-106 91 Stockholm
Sweden                                     http://www.math.su.se
-----------------------------------------------------------------