On Wed, Oct 21, 2020 at 09:51:35PM +0200, Ralf Hemmecke wrote:
> It is clear that in general there is no decidable zero test for power
> series, however, we have the function truncate: (%, INT) -> % that
> basically creates a finite series. I hoped that it were possible to use
> UnivariateLaurentSeries together with this truncate function to
> essentially work with Laurent polynomials.
I do not know what you really want. We have LaurentPolynomial.
The whole point of our series is that they are lazy. In
particular 'truncate' is lazy and other stream operations
can not see that stream is finite.
> I ran into a problem that I
> did not expect.
>
> With the attached file I get.
>
> (9) -> zero? l0
>
> (9) false
>
> (13) -> zero? t0
>
> (13) false
>
> In fact, I consider this a bug. It is clearly possible to decide that l0
> and t0 are 0 since their corresponding stream should be finite and at
> most contain zeros.
>
> Waldek, I can look into it if you also want the above return true.
I would prefer to remove 'zero?' and equality for series...
ATM equality gives different result than 'zero?', that is not
nice. OTOH this is something that original developers apparently
wanted, the offending 'zero?' is implemented as categry
default in UnivariateTaylorSeriesCategory, while otherwise we
would use 'zero?' from AbelianMonoid. The only reason I see
for adding such 'zero?' is that 'zero?' may be called
without need.
It would make some sense to remove definition from
UnivariateTaylorSeriesCategory, but in general, if
you want reliable equality then use finite domain...
--
Waldek Hebisch
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