I sometimes illustrate techniques of polynomial factorization in a class by starting with a polynomial in ZZ[x] and converting it to a polynomial in GF(insert_large_prime)[x]. I realize this is not an instance of two _finite_ fields, but (a) you mention "the characteristics are different", and (b) _are_ there similar applications for finite fields, when the characteristics are different?
Or am I misunderstanding the proposal? john perry On Tuesday, December 31, 2013 6:59:03 AM UTC-5, Jean-Pierre Flori wrote: > > Dear all, > > Currently one can obtain surprising results in Sage when converting > polynomial over finite fields (or elements of quotient rings of univariate > polynomial ring even though tht's not the primary concern of the ticket). > See http://trac.sagemath.org/ticket/11239 > Basically the generators of the finite fields are just exchanged, even > when the characteristics are different. > The changes suggested in this ticket would more or less only let a > coercion be used if there is one, and rant if the characteristics are > different or the base finite fields are not part of a common lattice when > there is no canonical embedding. > > Note though that the original disturbing conversion fits with the current > behavior described in the doc: > * > http://www.sagemath.org/doc/reference/coercion/index.html#maps-between-parents > where it's stated that > > "Conversions need not be canonical (they may for example involve a choice > of lift) or even make sense mathematically (e.g. constructions of some > kind)." > > Anyone has a strong opinion about what we should let Sage do in such a > situation? > > Should we leave the old conversion when there is no coercion even though > that might easily to wrong mathematical results for a careless user? Or > never look for a coercion unless the user explicitly asks for it (i.e. what > the situation is currently in Sage without the patches of the ticket)? > > Best, > > JP > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
