There's an open pull request for polynomial division in Polynomial.jl: 
https://github.com/vtjnash/Polynomial.jl/pull/4

Maybe you could coordinate with the author of that pull request and the 
package maintainer to get some version of this into the package.

On Sunday, January 19, 2014 8:38:58 PM UTC-8, Marcus Urban wrote:
>
> If anyone is interested, I posted a Gist for polynomial division at 
> https://gist.github.com/mathpup/8514578. The code using the existing 
> polynomial module Polynomial.jl.
>
> My code includes a few utility functions and promotion rules. Since the 
> division process repeatedly applies polynomial operations, the division 
> function divrem() performs the type promotion once at the beginning to 
> avoid repeatedly promoting types inside the main loop. By default, the 
> standard div() operator (/) is used. For polynomials with integer 
> coefficients, the result will be a polynomial with floating point 
> coefficients. I provided the ability to specify // instead of the default 
> division operator as a clever way to provide a result with rational 
> coefficients for integer polynomials, but I'm not sure how expensive this 
> is (since it's done in the main loop). In the grand scheme, I don't know 
> how much difference it makes or whether it would ever be an issue.
>
>

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