On Tue, Jan 5, 2010 at 12:37 AM, Michael Beeson <[email protected]> wrote: > Thanks, that's a start, but my polynomials have some parameters > a,b,c,... > in the coefficients. In Mathematica you say PolyomialRemainder[f,g,x] > where the > last 'x' names the polynomial variable, so all other variables are > parameters. When > I tried to modify your code by inserting a=var('a') and then > f=a*x^10, it didn't work, > because now f only belongs to sage.symbolic.expression.Expression, and > not > to P. Well, obviously, because I didn't specify that a belongs to > QQ. Is there > a way to do that so that I can work with parameters in the > coefficients of a polynomial? > Various guesses as to what might be the way to do that didn't work. > > If there's an easy way that I should have been able to look this up > for myself I would like to know that even more than the specific > answer. > > On another subject: > The documentation mentions the "ring" of symbolic expressions. To be > a ring one needs to know when two symbolic expressions are equal. Is > 1/0 a symbolic expression and if so is it equal to oo ?
1/0 is an error. sage: 1/0 Traceback (most recent call last): ... ZeroDivisionError: Rational division by zero > How about x- > x and 0? sage: bool(x-x == 0) True > x/x and 1? sage: bool(x/x == 1) True > More generally has anything been written > about the or "a" semantics for Sage? Maybe in the ginac documentation... > > Michael > > > On Jan 3, 12:42 pm, bump <[email protected]> wrote: >> On Jan 3, 10:59 am, Michael Beeson <[email protected]> wrote: >> >> > I am just learning Sage. I tried to define a polynomial and then >> > find the polynomial remainder upon division by the >> > cyclotomic_polynomial(18), which is 1-x^3+x^6. This is easily >> > accomplished in Mathematica using the PolynomialRemainder function. >> > But I could not find the analog of that function in the Sage >> > documentation. >> > What is the right way to do this in Sage? >> >> I think this is what you are trying to do: >> >> sage: P.<x> = PolynomialRing(QQ) >> sage: f = x^10+2*x^8+3*x+1 >> sage: f in P >> True >> sage: g = cyclotomic_polynomial(18); g >> x^6 - x^3 + 1 >> sage: f.quo_rem(g) >> (x^4 + 2*x^2 + x, 2*x^5 - 2*x^2 + 2*x + 1) >> >> The first term is the quotient and the second is the remainder. See >> sage: f.quo_rem? >> >> for the description of the method. >> >> Daniel Bump > > -- > 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 > URL: http://www.sagemath.org > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org -- 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 URL: http://www.sagemath.org
