Let's construct a series that is zero to all orders:
ser := series(exp(x),x=0)
zeroSeries := ser-ser
I would like to check if the first 10 coefficients are zero, so I truncate
trunc := truncate(zeroSeries,10)
test(trunc = 0$UnivariatePuiseuxSeries(Expression(Integer),x,0))
and the comparison with 0 is indeed true.
On the other hand
zero?(trunc) is false because of the way it checks the coefficients stream.
I am not sure if you consider this a bug, but I wanted to have it
mentioned, since it seems on the unexpected-behavior side for a finite
stream, at least for me.
zero? x ==
empty? (coefs := coefficients x) => true
(zero? frst coefs) and (empty? rst coefs) => true
false
Now the interesting behavior goes on:
test(truncate(zeroSeries,10) =
0$UnivariatePuiseuxSeries(Expression(Integer),x,0))
is true
but
test(truncate(zeroSeries,20) =
0$UnivariatePuiseuxSeries(Expression(Integer),x,0))
is false
So there also seems to be some cutoff built in?
It seems, the safest way is to directly check the first N terms of
coefficients(zeroSeries) and not rely on truncate and "zero?".
Best wishes,
Tobias
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