On Jan 18, 2008, at 3:44 PM, William Stein wrote: > >> But then for "convenience of users", division by a unit is carried >> out >> in the same ring: >> >>> Parent(1/(1+q)); >> Power series ring in q over Rational Field >> >> In writing code, it becomes necessary to test the invertibility of >> the >> denominator in order to know what the output type will be. >> >> Moreover, the conventions for power series ring are not the same for >> p-adic rings, so writing generic code becomes difficult. >> >> I strongly suggest that some fixed convention exists for all rings, >> before things become too muddled. I prefer: >> >> 1/x = constructor for the ring of fractions > > Yes.
I think it's nice that 1/(1+q) is still a power series, but there should be a convention adopted here. My proposal is that division is a constructor for fraction fields when generic elements are non- units, and happens in the ring (and raises error on failure) when they're not. This seems to be consistent with the current status of Sage, and is clear-cut and (IMHO) usually does what one wants. >> x^-1 = x.inverse() the inverse in the ring (error for non-units) > > I'm not so sure. > >> If you think SAGE should be more lenient with the notation x^-1, then > > I do. Not allowing 3^(-1) seems too mean to me. > >> 1/x = x^-1 constructor for the ring of fractions >> x.inverse() the inverse in the ring >> But x.inverse() should not return an inverse if one does not exist; >> this should be reserved for the operation on units in the ring or >> give an error. I really want to be able to do: > > I would be OK with this, but I think the name should be more > explicit, e.g., > x.inverse_in_parent() There is currently an inverse_of_unit command. ZZ(-1).inverse_of_unit().parent() Integer Ring sage: QQ[x](2).inverse_of_unit().parent() Univariate Polynomial Ring in x over Rational Field sage: matrix(ZZ, 2, 2, [1,5,0,-1]).inverse_of_unit() # not implemented... ------------------------------------------------------------ Traceback (most recent call last): File "<ipython console>", line 1, in <module> <type 'exceptions.AttributeError'>: 'sage.matrix.matrix_integer_dense.Matrix_integer_de' object has no attribute 'inverse_of_unit' It would be nice (perhaps) to have an easier way to get a unit in self.parent(), if one exists. E.g. the ~ operator could do this. (Perhaps this would be too confusing.) >> In general I am opposed to functions returning values of different >> types depending on the values of the arguments, unless there is some >> overriding reason and convention in place for doing otherwise. > > Same here. And in the case of exponentiation I think there is > such an overriding reason and convention in place for doing otherwise. Exponentiation is particularly thorny, which is why it has been difficult to put it into the coercion model... However, I think that x^(-1) != 1/x would cause a lot of confusion, as would parent(x) != parent(x^n) for positive n. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
