The Expand function is a placeholder for representing the expand function. It is used in conjunction with mod, or evala, which define the coefficient domain as described below.

The call evala(Expand(a)) expands products in a where a may contain algebraic numbers and functions defined by RootOfs or radicals. See evala/Expand for more information.

The call Expand(a) mod p expands products in a over the integers mod p where a may contain RootOfs or radicals representing algebraic extensions.

$\mathrm{Expand}\left({\left(x+2\right)}^2\left(x-2\right)\right)\mathbf{mod}3$

$x^3+2x^2+2x+1$

$\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left(x^2-2\right)\right)\:$

$\mathrm{evala}\left(\mathrm{Expand}\left({\left(x+\mathrm{\alpha }\right)}^2\left(x-\mathrm{\alpha }\right)\right)\right)$

$\mathrm{\alpha }{x}^2+x^3-2\mathrm{\alpha }-2x$

$\mathrm{alias}\left(\mathrm{\beta }=\mathrm{RootOf}\left(x^2+x+1\right)\right)\:$

$\mathrm{Expand}\left({\left(x+\mathrm{\beta }\right)}^2\left(x-\mathrm{\beta }\right)\right)\mathbf{mod}2$

$\mathrm{\beta }{x}^2+x^3+x\mathrm{\beta }+x+1$