2013/10/7 Jori Mantysalo <jori.mantys...@uta.fi> > On Mon, 7 Oct 2013, John Cremona wrote: > > sage: R.<x,y> = ZZ[]; print (4*x^2-1).factor() >> ------------------------------**------------------------------** >> --------------- >> NotImplementedError Traceback (most recent call >> last) >> > > But that is just what I would like to "implement", i.e. make few lines of > code that converts polynomial to QQ, factors it and then convert back to ZZ. > > Great, when you do, make sure to mention the ticket number on this thread.
> (But my first suggestion lacks .unit(), which need to be added.) It's not just a matter of units. In polynomial rings over QQ, all non-zero constants are units. In polynomial rings over ZZ, only +/- 1 are units, prime numbers are primes, and composite numbers are neither units nor primes (hence need to be factored). This is correctly implemented for ZZ[x], QQ[x] and QQ[x,y]: sage: P.<x> = ZZ[] sage: p = -15*(3*x+2)*(7*x-5) sage: f = p.factor() sage: f.unit() -1 sage: list(f) [(3, 1), (5, 1), (3*x + 2, 1), (7*x - 5, 1)] sage: P.<x> = QQ[] sage: p = -15*(3*x+2)*(7*x-5) sage: f = p.factor() sage: f.unit() -315 sage: list(f) [(x - 5/7, 1), (x + 2/3, 1)] sage: P.<x,y> = QQ[] sage: p = -15*(3*x+2)*(7*x-5) sage: f = p.factor() sage: f.unit() -15 sage: list(f) [(3*x + 2, 1), (7*x - 5, 1)] > > > -- > Jori Mäntysalo > > -- > 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 > sage-devel+unsubscribe@**googlegroups.com<sage-devel%2bunsubscr...@googlegroups.com> > . > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at > http://groups.google.com/**group/sage-devel<http://groups.google.com/group/sage-devel> > . > For more options, visit > https://groups.google.com/**groups/opt_out<https://groups.google.com/groups/opt_out> > . > -- 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 sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
