Igor Schein on Sun, 22 May 2005 00:19:36 +0200

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tough family of fields for polredxxx() functions


In the past I reported, among others, 1 polred() and 1 polredabs()
bug.  For certain polynomials polred() returns only proper subfields,
and not a reduced isomorphic once.  And, for certain polynomials
polredabs() takes very long time.  The former has to do with a fact
that polred() is not guaranteed to return a reduced isomorphism.  The
latter has to do with the current design and could be improved.  Now,
I realized there's a whole family of fields which exhibit both bugs


polred(f(k)) always returns proper subfields, and in order to exhibit
polredabs() taking very long time, just do something like
polredabs(poltschirnhaus(poltschirnhaus(f(k))),16).  The first few
*slow* values of k are 2 5 6 8 10 13 14 17 18 20 ( basically eliminate
all k's in shape of 16*j+3, 16*j+7, 16*j+11, 16*j+12, 16*j+15 and some
more - can be formalized if necessary ).