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

[root]

Marcus,


>I am trying to compute with Laurent series over some unspecified field 
>of postitive characteristic, where the coefficients may be indeterminate 
>variables. I declare my power series as follows:
>
>   z: ULS(FRAC POLY PrimeField 2, z, 0) := z
>
>I can now create expressions like
>
>   1/a*z^(-1)  + 1 + z^2 + b*z^4
>
>which works nicely. The problem is to use GenerateUnivariatePowerSeries 
>to generate series of this type. It seems that there is no such thing as 
>Expression(PrimeField 2) which this package would expect.
>
>I have defined a function
>   coeffs: Integer -> FRAC POLY PrimeField 2
>which computes the coefficients. How can I put them together into a 
>power (or Laurent) series? The command
>   series(n +-> coeffs(n), z=0)
>just gives the error message
>"Cannot find a definition or applicable library operation named series 
>with argument type(s)
>   AnonymousFunction
>   Equation UnivariateLaurentSeries(Fraction Polynomial PrimeField 2,z,0)
>"
>
>There is a similar error if I declare z simply as FRAC POLY PrimeField 2.
>
>Also, if I don't declare z at all, the above command gives me a UTS(EXPR 
>INT,z,0) with the correct coefficients but treated as EXPR INT, which is 
>not what I want. Is there any way I can get around this?

EXPR is basically Axiom's attempt at a "typeless" place to work.
Axiom ends up there when it has to guess and can't find anything
else useful. You may be confusing the interpreter by overusing z in:

>   z: ULS(FRAC POLY PrimeField 2, z, 0) := z

I'm not sharp enough at the moment to see exactly what is failing.
I'll have to read the code in GenerateUnivariatePowerSeries to get
up to speed on what you are trying to do. Unfortunately that won't be
until later this evening. I'll get back to you.

Tim Daly
address@hidden
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