There is a algorithm for pseudoremainder in the rational function package,
used by various GCD algorithms, the PRS based reduced and subresultant
version.
This would work on polynomials with integer coefficients only, but that is
because that
is all that is necessary. The denominator, an integer, would be stored
somewhere else.
The GB package presumably has another idea of division though;
division by several polynomials, depending on ordering.
Multiplying a polynomial through by the LCM of coefficients should be easy:
just let rat do it.
p:rat(thepoly);
then use ratnumer(p).
The GB package is probably much slower than it should be, unless someone has
taken the effort to introduce the optimizations that have been described
recently (say, since 1984).
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Barton Willis
> Sent: Friday, October 27, 2006 6:57 AM
> To: maxima at math.utexas.edu
> Subject: poly_pseudo_divide
>
>
> In the Grobner package, there is a function
> poly_pseudo_divide for multivariable polynomial division. It
> seems that poly_pseudo_divide requires polynomials with
> *integer* (not rational) coefficients:
>
> (%i87) poly_pseudo_divide(x*y + x + 1,[x+y, x+5] , [x,y]);
> (%o87) [[y+1,0],-y^2-y+1,1,2] <--- OK
>
> (%i88) poly_pseudo_divide(x*y/ 2 + x + 1,[x+y, x+5] , [x,y]);
> (Maxima seems to hang)
>
> Questions:
>
> (1) Is there an option variable that allows
> poly_pseudo_divide to work for polynomials with rational coefficients?
>
> (2) If not, does somebody have Maxima code for multivariable
> polynomial division that works for polynomials with rational
> coefficients? Preferably (for speed), this code work entirely
> with CRE expressions.
>
> Notes:
>
> (a) I copied this note to the author of the Maxima Grobner package.
>
> (b) I wrote a pre-processor for poly_pseudo_divide that multiplies
> all the polynomials by a constant to transform all coefficients to
> integers. I think it works OK, but it's not ideal.
>
> Barton
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