Martin R wrote:
>
> Dear all!
>
> the question fits into the title :-)
>
Does not fit: it is truncated by many viewers. Fixed:
> shouldn't UTS(F, x, 0) export EuclideanDomain if F is
> a Field?
That is a tricky question. I see that you gave an
implementation, but there is a core problem:
EuclideanDomain implies BasicType and this already
is a lie. That is equality for power series is
noncomputable. Which means that generic algorithms
may have very poor performance or fail. To explain
it better, consider Gaussian elimination applied
to invertible matrix of power series. Generic algorithm
will struggle trying to find out if an element is suitable
pivot. Algorithm aware of power series will try increasing orders
and checking all elements of a column for given order.
In this way it will find pivot of best order, without
wasting time examining many entries of zero or nearly
zero series.
So question is if after lying several times we want
to keep lying, or if we want to clean up things.
Pragmatically lying may look attractive as it gives
immediate rewards, while punishment is delayed.
OTOH most had to fix bugs comes from original developers
ignoring problems and opting for immediate "progress".
--
Waldek Hebisch
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