2013/4/18 Simon King <simon.k...@uni-jena.de> > A symbolic expression is something fairly general---so general that many > methods won't make sense in this generality. A symbolic expression may > contain all "strange" stuff like sin(x^2), exp(pi), x^x, etc. >
> From computer science point of view, the mathematical algorithms are > implemented in methods of certain (base) classes. The polynomials we want > to consider here belong to classes that provide a quo_rem method. But > general symbolic expressions belong to a different class, and a quo_rem > method would make no sense for them. > Ok, I did get what was the problem about the instances of different classes, but now I have an idea of why from a mathematical POV. ;) > This line is a shortcut for > P = PolynomialRing(f,'x') > x = P.gen() > > It is syntactical sugar: P.<x>=f[] is not valid in Python, but it is a > convenient notation well known from the Magma computer algebra system. > Hence, the Sage developers wanted to make this notation available, by > means of a pre-processor. > > > x = P.gen() > > As I mentioned above, a polynomial ring knows its base ring and it > generator(s). Here, we have the base ring f, which you could check by > sage: P.base_ring() is f > True > > And P.gen() returns the generator (i.e., the "variable") of this > polynomial ring. Note that this "variable" is by no means the same as a > symbolic variable of the same name: > Thank you, now my ideas are more clear! Best regards, -- *Andrea Lazzarotto* — http://andrealazzarotto.com — http://lazza.dk* * -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
