Divide - Maple Help

Divide

inert divide function

 Calling Sequence Divide(a, b, 'q')

Parameters

 a, b - multivariate polynomials q - (optional) unevaluated name

Description

 • 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.

Examples

 > $\mathrm{Divide}\left({x}^{3}+{x}^{2}+2x+3,x+2,'q'\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}5$
 ${\mathrm{true}}$ (1)
 > $q$
 ${{x}}^{{2}}{+}{4}{}{x}{+}{4}$ (2)
 > $a≔{x}^{2}+x-2-\mathrm{RootOf}\left({\mathrm{_Z}}^{2}-2\right):$
 > $b≔x-\mathrm{RootOf}\left({\mathrm{_Z}}^{2}-2\right):$
 > $\mathrm{evala}\left(\mathrm{Divide}\left(a,b,'\mathrm{q1}'\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{q1}$
 ${x}{+}{1}{+}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{2}\right)$ (4)
 > $\mathrm{evala}\left(\mathrm{Divide}\left({x}^{2}-z,x-\mathrm{sqrt}\left(z\right),'\mathrm{q2}'\right)\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{q2}$
 ${x}{+}\sqrt{{z}}$ (6)