More generally, The % operator tends to return the "remainder" term, in the same ring. mod(a, b) constructs an element of the quotient ring. So, the behavior you're observing is intended, though perhaps a bit unexpected. David
On Sun, Feb 21, 2010 at 11:32 AM, John Cremona <john.crem...@gmail.com>wrote: > On 21 February 2010 16:05, Minh Nguyen <nguyenmi...@gmail.com> wrote: > > On Mon, Feb 22, 2010 at 3:01 AM, slabbe <sla...@gmail.com> wrote: > > > > <SNIP> > > > >> sage: 15.mod(4) == 7 > >> False > >> sage: mod(15, 4) == 7 > >> True > > > > Is the following the intended behaviour? > > > > sage: type(15.mod(4)) > > <type 'sage.rings.integer.Integer'> > > sage: type(mod(15, 4).lift()) > > <type 'sage.rings.integer.Integer'> > > sage: 15.mod(4) == 7 > > False > > sage: mod(15, 4).lift() == 7 > > False > > > > This is entirely consistent, though possibly unexpected. Both > a.mod(n) and a%n return an integer which is "a reduced modulo n", > while mod(a,n) returns an element of Z/nZ. > > Now the only surprising thing, perhaps, is the test that mod(15, 4) > == 7 which yields True. This is because Sage tries, and succeeds, to > find a place where both the objects being compared map to -- here an > integer mod 4 and an integer can both be mapped to integers mod 4 > (i.e. elements of Z/4Z) where they are compared and found equal. > > The warning is that "==" does *not* correspond to equality in any > mathematical sense (it is not transitive, for example): > > sage: 0 == mod(0,2) > True > sage: mod(0,2) == 2 > True > sage: 0 == 2 > False > > John > > > > -- > > Regards > > Minh Van Nguyen > > > > -- > > To post to this group, send an email to sage-devel@googlegroups.com > > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com<sage-devel%2bunsubscr...@googlegroups.com> > > For more options, visit this group at > http://groups.google.com/group/sage-devel > > URL: http://www.sagemath.org > > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com<sage-devel%2bunsubscr...@googlegroups.com> > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
