Because you divided by x in your computation, the polynomial f was coerced into the fraction field. In the fraction field, quotient is always possible without reminder:
sage: f.parent() Fraction Field of Multivariate Polynomial Ring in x, N, p, r, m, l over Rational Field You want to convert f back into the polynomial ring: sage: f = R(f) sage: f.parent() Multivariate Polynomial Ring in x, N, p, r, m, l over Rational Field sage: f.quo_rem(psi) # works now On Sunday, April 22, 2012 4:23:53 PM UTC-4, Michael Beeson wrote: > > Sage version 4.6.1 (I know it's old, new one is downloading now, but I > don't think this is a version problem.) > Given: polynomial f in x with some letters for the coefficients, and > polynomial psi of lower degree in x with constant coefficients. > Wanted: remainder of f on division by psi as polynomials in x, with > coefficients involving the letters in f. > Problem: Sage treats f as a polynomial in many variables and I can't > convince it to treat it as a polynomial in x only and perform the division > (or pseudo division). > Example: > > sage: R.<x,N,p,r,m,l> = PolynomialRing(QQ,6) > sage: a = x - x^-1 > sage: b = x^4-x^-4 > sage: c = x^9 - x^-9 > sage: f = N*a*b*c - (p*a+r*c)*(m*a + l *c) > sage: t = x^2 - x^-2 > sage: f = x^20*(N*a*b*c - (p*a+r*c)*(m*a + l *c)*t) > sage: f > -x^40*r*l + x^36*r*l + x^34*N - x^32*r*m - x^32*p*l - x^32*N > + x^30*r*m + x^30*p*l + x^28*r*m + x^28*p*l - x^26*r*m - x^26*p*l > - x^26*N - x^24*p*m + x^24*N + 2*x^22*p*m + 2*x^22*r*l - 2*x^18*p*m > - 2*x^18*r*l + x^16*p*m - x^16*N + x^14*r*m + x^14*p*l + x^14*N > - x^12*r*m - x^12*p*l - x^10*r*m - x^10*p*l + x^8*r*m + x^8*p*l > + x^8*N - x^6*N - x^4*r*l + r*l > > Now psi should be the 28-th cyclotomic polynomial x^12-x^10+x^8...; so > in a multivariate polynomial I can't compute that directly, > first sign of trouble. So I typed it in, and then f.quo_rem(psi) does > not yield the desired answer, because as polynomials in 6 variables, psi > does not divide f. > > -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
