On Fri, Sep 24, 2010 at 6:56 PM, kcrisman <kcris...@gmail.com> wrote: > If I make a polynomial ring using > > sage: b = PolynomialRing(ZZ, 'x') > > I get some odd behavior. Namely, > > sage: bool(b(x)==x) > True > sage: b(x) > x > sage: type(b(x)) > <something about element of the ring> > sage: type(x) > <symbolic expression> > > This isn't really that odd, but still I don't know whether it is good > that one can still use x as a symbolic variable. Probably this was a > design decision.
There is the distinction between x the Python variable and x the symbol (aka symbolic variable). For example, in the code below x and y both "store" the symbol x. sage: y = x sage: y x x just happens to start out as a symbolic variable with the same name as the Python variable. In general, we try to avoid overwriting the namespace, so when you do sage: x = 3 sage: PolynomialRing(ZZ, 'x') Univariate Polynomial Ring in x over Integer Ring sage: x 3 you don't have any surprises. You can change this with inject_on() sage: inject_on() Redefining: FiniteField Frac FractionField FreeMonoid GF LaurentSeriesRing NumberField PolynomialRing quo quotient sage: PolynomialRing(ZZ, 'x') Defining x Univariate Polynomial Ring in x over Integer Ring sage: x x sage: type(x) <type 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'> (And whatever used to be in x is now gone.) Of course most people just write sage: R.<x> = ZZ[] which defines the ring and assigns the generator in one step. > Anyway, what I really don't like is when you make > > sage: a = FractionField(PolynomialRing(ZZ, 'x')) > sage: a(1/x) > <weird error that seems to imply it has not coerced x to the > polynomial ring> We should certainly raise a better error here (or accept it). Automatic coercion is always a compromise between convenience and surprise. For example, if we didn't have any coercions there than sage: a = ZZ['x'].gen() sage: a = ZZ['x'](2) sage: b = SR(2) sage: a 2 sage: b 2 sage: bool(a == b) False # hypothetically would be especially confusing, especially if the context weren't so clear (e.g. trying to debug something when a and b were generated by completely different functions at completely different times.) Even if one made an exception for "constants" sage: a x sage: b x sage: bool(a == b) False # hypothetically I think would still cause more confusion than the current behavior. > Did I do something wrong, or is this a bug? Because of the initial > behavior, maybe I shouldn't expect to be able to do this. > > Thanks, > - kcrisman > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
