Carl, Burcin, thank you very much for your support.
Burcin, I'm sorry for the trivial mistake. Thank you for pointing it out. Unfortunately, I don't understand this: " The theory only works over characteristic 0, i.e., your fields should contain QQ. Also note that, sage: P.<x,z> = GF(5)[] sage: (x+x^5).derivative(x) 1 What is the integral of 1 w.r.t x in this case? " Could you be clearer? As I told, I'm not familiar with rings. I don't even know the meaning of the argument of GF (I took the number 5 from an example I see in sage-support group, I think). Do you think that QQ [] could fit in this case? Moreover, what's the difference between QQ and QQbar? About this: " You can get this information from the factorization you compute above. " It seems that factorization over GF(p) is broken (see http://groups.google.com/group/sage-devel/tree/browse_frm/thread/527e426dbfa04eda/2641f1509d1295db?rnum=1&_done=%2Fgroup%2Fsage-devel%2Fbrowse_frm%2Fthread%2F527e426dbfa04eda%3F#doc_2641f1509d1295db ), does it work for QQ? I don't seriously need factor, as long as I need the root finding next. Now let's go to Carl's help... > Taking a quick look at that page, it looks like they want the exact > roots in CC of a polynomial with algebraic coefficients. In Sage, we > can get this with QQbar: > > sage: K.<x> = QQbar[] > sage: (x^5-x-1).roots(ring=QQbar) > First problem with QQbar: it seems that resultant() doesn't like it, because it is not able to convert it to a Singular ring (this is the error, I'm not attaching all the output, tell me if you need it) TypeError: no conversion of this ring to a Singular ring defined On the contrary, QQ[] seems to work fine with resultant (but it doesn't have roots() ) Moreover, it seems that QQbar roots() is not working for multivariate polynomials ring... is it true or am I just missing something else? In that case, is possible to let it work in multivariate polynomials? As you can imagine, I would like to think about this as a method of solving integrals, so it is very likely to have a symbolic expression with more than just a single symbolic variable. > [(1.167303978261419?, 1), > (-0.7648844336005847? - 0.3524715460317263?*I, 1), > (-0.7648844336005847? + 0.3524715460317263?*I, 1), > (0.1812324444698754? - 1.083954101317711?*I, 1), > (0.1812324444698754? + 1.083954101317711?*I, 1)] > > (AFAIK, maxima can't do this; I don't think maxima can handle general > algebraic numbers. Since Sage's solve() is implemented using maxima, > solve() won't work for this problem.) > > Carl Apart from this, is there another way to solve an equation (with more than a single symbolic variable) obtaining exact roots? It seems that maxima would do the work (with algebraic numbers...), is it possible that it is the only symbolic equation solver within SAGE? What about SymPy or anything else? Finally, I still would like to know which is the best way to translate the output of a calculation with polynomial rings into a symbolic expression, that can be carried on with maxima or pynac. Can you help me? Thank you very much Regards Maurizio --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
