Robert, Okay, I see the difference: a polynomial generator "over" the ring means something that will generate a ring over the given ring, not a polynomial generator "of" the ring.
thanks john perry On Dec 6, 12:31 pm, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > I think you are misinterpreting polygen. Polygen takes as input a > ring, and creates a new polynomial ring over that rings, and returns > the generator of that new ring (not the generator of the original > ring). Also, since you didn't provide a name to the polygen function, > it defaults to "x." > > Rather than type, the parent() function is often more informative. > > sage: R = GF(101)['y'] > sage: y = polygen(R) > sage: parent(y) > Univariate Polynomial Ring in x over Univariate Polynomial Ring in y > over Finite Field of size 101 > sage: y > x > > Type polygen? to see the documentation. > > - Robert > > On Dec 6, 2008, at 8:08 AM, john_perry_usm wrote: > > > > > Sorry, I didn't expect that. Here are two examples: > > > sage: R = GF(101)['y'] > > sage: y = polygen(R) > > sage: type(y) > > <type > > 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense'> > > sage: y^3/y^2 > > x^3/x^2 > > sage: simplify(y^3/y^2) > > x^3/x^2 > > sage: R.inject_variables() > > Defining y > > sage: type(y) > > <type > > 'sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_ > > p'\ > > > sage: y^3/y^2 > > y > > > This is what the student did: > > sage: R = PolynomialRing(QQ,'x') > > sage: x = polygen(R) > > sage: type(x) > > <type > > 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense'> > > sage: x^3/x^2 > > x^3/x^2 > > sage: R.inject_variables() > > Defining x > > sage: x^3/x^2 > > x > > > Let me know if you need more info. > > > john > > > On Dec 5, 6:53 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > >> On Fri, Dec 5, 2008 at 4:31 PM, john_perry_usm > >> <[EMAIL PROTECTED]> wrote: > > >>> Hi, > > >>> x = polygen(<ring>) returns an object of type > >>> Polynomial_generic_dense, while <ring>.inject_variables() injects > >>> x of > >>> type Polynomial_rational_dense. > > >>> Why the difference? > > >> Since I see no difference at all with the same ring, can you > >> make your question more precise? Thanks: > > >> sage: type(polygen(QQ)) > >> <class > >> 'sage.rings.polynomial.polynomial_element_generic.Polynomial_rational > >> _dense'> > >> sage: QQ['x'].inject_variables() > >> Defining x > >> sage: type(x) > >> <class > >> 'sage.rings.polynomial.polynomial_element_generic.Polynomial_rational > >> _dense'> > >> sage: > > >>> This was a problem for a student today, who was using polygen(), > >>> whose > >>> returnee will not simplify x^3/x^2, whereas inject_variables() did. > > >>> regards > >>> john perry > > >> -- > >> William Stein > >> Associate Professor of Mathematics > >> University of Washingtonhttp://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
