John Cremona on Thu, 25 Jun 2015 11:37:25 +0200

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The function bnfissunit() returns the coordinate vector if given an
S-unit and the empty vector if the element given is not as S-unit.  If
all I want is to check for being an S-unit, without needing the
exponent vector, is it possible that this could be done faster?  The
situation I have is that I have a lot of elements to test, and most of
them will not be S-units, and I want it to be fast (of course).  If S
is empty, one can check for being a unit just by looking at the norm.
Here one could first check that the norm is only divisible by the
correct rational primes, but that is not sufficient of course (would
it be faster to do that?  the elements will be large and computing
their norms not so trivial).