This function returns true if the polynomial Q divides P and false otherwise. The coefficients of P and Q must be algebraic functions or algebraic numbers.

Algebraic functions and algebraic numbers may be represented by radicals or with the RootOf notation (see type,algnum, type,algfun, type,radnum, type,radfun).

When Q divides P, the optional argument p is assigned the quotient P/Q.

The division property is meant in the domain $K_x$ where:

x is the set of names in P and Q which do not appear inside a RootOf or a radical,

K is a field generated over the rational numbers by the coefficients of P and Q.

The arguments P and Q must be polynomials in x.

Algebraic numbers and functions occurring in the results are reduced modulo their minimal polynomial (see Normal).

If a or b contains functions, their arguments are normalized recursively and the functions are frozen before the computation proceeds.

Other objects are frozen and considered as variables.

$\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left(x^3+x+1\right)\right)$

$\mathrm{\alpha }$

$\mathrm{evala}\left(\mathrm{Divide}\left(x^3+x+1\,x-\mathrm{\alpha }\,'\mathrm{a1}'\right)\right)$

$\mathrm{true}$

$\mathrm{a1}$

${\mathrm{\alpha }}^2+\mathrm{\alpha }x+x^2+1$

$\mathrm{evala}\left(\mathrm{Divide}\left(x^3+x+1\,x-\mathrm{\alpha }+1\,'\mathrm{a2}'\right)\right)$

$\mathrm{false}$

$\mathrm{a2}$

$\mathrm{a2}$

$\mathrm{P1}≔\mathrm{expand}\left(\left(x-\mathrm{sqrt}\left(t\right)y\right){\left(\mathrm{sqrt}\left(t\right)x+1\right)}^2\right)$

$\mathrm{P1}≔t{x}^3+2\sqrt{t}{x}^2+x-t^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}y{x}^2-2tyx-\sqrt{t}y$

$\mathrm{Q1}≔ty-\mathrm{sqrt}\left(t\right)x$

$\mathrm{Q1}≔ty-\sqrt{t}x$

$\mathrm{evala}\left(\mathrm{Divide}\left(\mathrm{P1}\,\mathrm{Q1}\,'\mathrm{a3}'\right)\right)$

$\mathrm{true}$

$\mathrm{a3}$

$-\sqrt{t}{x}^2-2x-\frac{1}{\sqrt{t}}$

$\mathrm{evala}\left(\mathrm{Divide}\left(\mathrm{P1}\,\mathrm{Q1}+\frac{1}{x}\,'\mathrm{a3}'\right)\right)$

Error, (in `evala/Divide/preproc0`) invalid arguments