Resultant - Maple Help

Resultant

inert resultant function

 Calling Sequence Resultant(a, b, x)

Parameters

 a, b - polynomials x - name

Description

 • The Resultant function is a placeholder for representing the resultant of the polynomials a and b with respect to the main variable x. It is used in conjunction with either mod or evala which define the coefficient domain as described below.
 • The call Resultant(a, b, x) mod p computes the resultant of a and b with respect to the main variable x modulo p, a prime integer. The argument a must be a (multivariate) polynomial over the rationals or over a finite field specified by RootOfs.
 • The call evala(Resultant(a, b, x)) does likewise for a and b (multivariate) polynomials with algebraic number (or function) coefficients defined by RootOfs.
 • The call modp1(Resultant(a, b), p) computes the resultant of a and b modulo p a prime integer where a and b are in the modp1 representation.

Examples

 > $\mathrm{Resultant}\left(2x+1,3x+4,x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}7$
 ${5}$ (1)
 > $r≔x+\mathrm{RootOf}\left({\mathrm{_Z}}^{2}-2\right):$
 > $s≔\mathrm{RootOf}\left({\mathrm{_Z}}^{2}-2\right)x+1:$
 > $\mathrm{evala}\left(\mathrm{Resultant}\left(r,s,x\right)\right)$
 ${-1}$ (2)
 > $\mathrm{evala}\left(\mathrm{Resultant}\left(2{x}^{2}+xy+x+y+3,3xy+{y}^{2},x\right)\right)$
 ${-}{{y}}^{{2}}{}\left({{y}}^{{2}}{-}{6}{}{y}{-}{27}\right)$ (3)