On 6 May 2014 16:24, Charles Bouillaguet <charles.bouillag...@gmail.com> wrote: > Dear all, > > I would like to make a case for the quo_rem() method to actually implement > euclidean division when it makes sense, or to raise an exception when the > result is not defined. After all, this is what it is **supposed** to do, at > least according to the docstring in > sage/ring/polynomial/polynomial_element.pyx : > > """ > @coerce_binop > def quo_rem(self, other): > """ > Returns the quotient and remainder of the Euclidean division of > ``self`` and ``other``. > > Raises ZerodivisionError if ``other`` is zero. Raises ArithmeticError > if ``other`` has > a nonunit leading coefficient. > """ > > I personally think that this specification is correct and decent. > > Presently, depending on the domain, quo_rem does not always behave the same, > and not according to the same specification. Examples : > > In ZZ[X] or ZZ[X,Y] : > ------- > > sage: R.<X> = ZZ[] > sage: (X^100).quo_rem(2*X+1) > (0, X^100) > > ---> Result is not defined, but quo_rem() does not complain. It tries to > reduce "as much as possible". > > in QQ[x][y] : > ---------------- > > sage: P.<x> = QQ[] > sage: R.<y> = P[] > sage: f = R.random_element(10) > sage: g = y^5+R.random_element(5) > sage: q,r = f.quo_rem(g) > sage: f == q*g + r > True > sage: g = x*y^5 > sage: f.quo_rem(g) > Traceback (most recent call last): > ... > ArithmeticError: Nonunit leading coefficient > > ---> quo_rem() complains when result is not defined. > > So, I suggest that : > a) we stick to the spec (what happens in QQ[x][y]). > b) we fix the cases like ZZ[X] that do not stick to the spec > c) we make sure, eventually by adding a "reduce" method or something like > that, that the previous behavior is still available somehow. > > I am willing to implement these changes. Do we agree on this?
+1 from me. Will this replace he current patch/branch at #16276? John > > --- > Charles Bouillaguet > http://www.lifl.fr/~bouillaguet/ > > > > -- > 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/d/optout. -- 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/d/optout.
