I tried with both fields, and the output is identical. In fact, I think that when you create a NumberField from a quadratic polynomial, the resulting field is actually of the subclass QuadraticField, and in both cases it is the same function. Looking into the code, you see that one of the differences is that when you use the QuadraticField constructor, the polynomial comes from a ring that is defined in a different way, and with a different name of the indeterminate. It turns out that where R.<X> = PolynomialRing(QQ) K.<u> = NumberField(X^2 + 5) L.<v> = K.hilbert_class_field() fails, R.<x> = PolynomialRing(QQ) K.<u> = NumberField(x^2 + 5) L.<v> = K.hilbert_class_field() works. The only difference is that in the first case a capital X is used, in the second a lowercase.
On Jun 1, 7:03 am, "Justin C. Walker" <[EMAIL PROTECTED]> wrote: > On May 31, 2007, at 16:58 , Utpal Sarkar wrote: > > > > > Ok, I'll just add to this thread whatever I come across. > > > For the moment I think I found a small bug in hilbert_class_field. > > R.<X> = PolynomialRing(QQ) > > K.<u> = NumberField(X^2 + 5) > > L.<v> = K.hilbert_class_field() > > causes an error. > > However, when I create K explicitly as a quadratic field: > > K.<u> = QuadraticField(-5) > > L.<v> = K.hilbert_class_field() > > everything is ok. > > I'm not sure this is a bug: the two functions are not quite the same, > even though they have the same name. > > Try "K.hilbert_class_field?" in each case to see what is expected. > > There's an expression regarding consistency that I keep forgetting... > > Justin > > -- > Justin C. Walker, Curmudgeon at Large > Institute for the Absorption of Federal Funds > ----------- > My wife 'n kids 'n dogs are gone, > I can't get Jesus on the phone, > But Ol' Milwaukee's Best is my best friend. > ----------- --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
