Content and Primpart are placeholders for a content and primitive part of a polynomial over a coefficient domain. They are used in conjunction with mod and evala as described below.

The calls Content(a, x) mod p and Primpart(a, x) mod p compute the content and primitive part of a respectively modulo the prime integer p. The argument a must be a multivariate polynomial over the rationals or over a finite field specified by RootOfs. See content for more information.

The calls evala(Content(a,x)) and evala(Primpart(a,x)) compute a content and a primitive part of a respectively over a coefficient domain which may include algebraic numbers and algebraic functions.  The polynomial a must be a multivariate polynomial with algebraic number (or function) coefficients specified by RootOfs or radicals. See evala,Content for more information.

The optional arguments 'pp' and 'co' are assigned a/Content(a) and a/Primpart(a) respectively, computed over the appropriate coefficient domain.

$\mathrm{Content}\left(x\left(y+4\right)+y^2+4\,x\right)\mathbf{mod}5$

$y+4$

$\mathrm{Primpart}\left(x\left(y+4\right)+y^2+4\,x\right)\mathbf{mod}5$

$x+y+1$

$a≔5x^3+3y^2$

$a≔5x^3+3y^2$

$\mathrm{Content}\left(a\,x\right)\mathbf{mod}11$

$1$

$\mathrm{Primpart}\left(a\,x\,'\mathrm{c1}'\right)\mathbf{mod}11$

$x^3+5y^2$

$\mathrm{c1}$

$5$

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

$p≔t\sqrt{2}xy-tx+ty-\frac{t\sqrt{2}}{2}$

$\mathrm{evala}\left(\mathrm{Primpart}\left(p\,y\right)\right)$

$-1+\sqrt{2}y$

$r≔\mathrm{RootOf}\left(x^3+x+1\right)$

$r≔\mathrm{RootOf}\left({\mathrm{\_Z}}^3+\mathrm{\_Z}+1\right)$

$q≔\mathrm{evala}\left(\mathrm{Expand}\left(\left(y-r\right)\left(x+r^2+1\right)\right)\right)$

$q≔{\mathrm{RootOf}\left({\mathrm{\_Z}}^3+\mathrm{\_Z}+1\right)}^{2}y-\mathrm{RootOf}\left({\mathrm{\_Z}}^3+\mathrm{\_Z}+1\right)x+xy+y+1$

$\mathrm{evala}\left(\mathrm{Content}\left(q\,x\,'\mathrm{q1}'\right)\right)$

$y-\mathrm{RootOf}\left({\mathrm{\_Z}}^3+\mathrm{\_Z}+1\right)$

$\mathrm{q1}$

${\mathrm{RootOf}\left({\mathrm{\_Z}}^3+\mathrm{\_Z}+1\right)}^2+x+1$