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.

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