The Divide function is a placeholder for the division of the polynomial a by b . It is used in conjunction with mod, modp1, or evala as described below.

The call Divide(a,b,'q') mod p determines whether b divides a modulo p, a prime integer. It returns true if the division succeeds and assigns the quotient to q, such that a=b*q; otherwise it returns false. The polynomials a and b must be multivariate polynomials over the rationals or over a finite field specified by RootOfs.

The call modp1(Divide(a,b,'q'),p) does likewise for a and b polynomials in the $\mathrm{modp1}$ representation, p a prime integer.

The call evala(Divide(a,b,'q')) does likewise for a and b, multivariate polynomials defined over an algebraic number or function field specified by RootOf or radicals. See evala/Divide for more information.

$\mathrm{Divide}\left(x^3+x^2+2x+3\,x+2\,'q'\right)\mathbf{mod}5$

$\mathrm{true}$

$q$

$x^2+4x+4$

$a≔x^2+x-2-\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)\:$

$b≔x-\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)\:$

$\mathrm{evala}\left(\mathrm{Divide}\left(a\,b\,'\mathrm{q1}'\right)\right)$

$\mathrm{true}$

$\mathrm{q1}$

$x+1+\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)$

$\mathrm{evala}\left(\mathrm{Divide}\left(x^2-z\,x-\mathrm{sqrt}\left(z\right)\,'\mathrm{q2}'\right)\right)$

$\mathrm{true}$

$\mathrm{q2}$

$x+\sqrt{z}$