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[Axiom-mail] Re: Power series with coeffs in positive characteristic
From: |
Marcus Better |
Subject: |
[Axiom-mail] Re: Power series with coeffs in positive characteristic |
Date: |
Thu, 12 Feb 2004 15:01:14 +0100 |
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Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.6) Gecko/20040115 |
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
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