On Sun, 29 Oct 2006 19:50:16 -0800, Nils Bruin <[EMAIL PROTECTED]> wrote: >> One possibility, which I haven't quite thought through, is to allow the >> user to get away with: >> >> R=PolynomialRing(ZZ) >> > In principle, the only reason why one *has* to give the indeterminates > a name, is to make sure that polynomials can print in a sensible way. > However, in the absence of variable names, there are still sensible > ways of printing polynomials. To give some ideas:
But mathematically one never ever thinks about polynomial rings in n variables without some choice of names, e.g., x_1, ..., x_n. > sage: R=PolynomialRing(ZZ) > sage: f=R.0^2+2 > sage: f > Polynomial over Integers() with coefficient vector [2,0,1] It is confusing to have the same things print in such different ways. > Or, perhaps for multivariate poly's > > sage: R=PolynomialRing(ZZ,3) > sage: f= R.0*R.1+3*R.1^2 > Multivariate polynomial over Integers() given by > [(1,(1,1)),(3,(0,1))] > > (i.e., specify a sparse polynomial by a list of pairs of coefficient > and exponent vector) > > As a related example: When I define > > VectorSpace(Rationals(),5) > > I shouldn't be required to specify names for the basis vectors either, > should I? No. > Would you like to extend your binding injection to get > > sage: VectorSpace(Rationals(),5,'b') > sage: b0,b1,b2 > (1 0 0 0 0) (0 1 0 0 0) (0 0 1 0 0) No, definitely not. That's different in a number of ways. > I would be strongly in favour of not making it mandatory to specify > indeterminate names. > Is it acceptable to allow name assignment later anyway? Or would the > violation of the immutability of rings be unacceptable. This would violate ring immutability, which would cause a lot of problems. William --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
