The Norm function is a placeholder for representing the norm of an algebraic number (or function), that is the product of its conjugates. It is used in conjunction with evala.

The call evala(Norm(a, L, K)) computes the norm of a over the algebraic number (or function) field represented by K. In case K is not specified and a is an algebraic number, the norm over the rational is computed. In case K is not specified and a is an algebraic function, the smallest possible algebraic extension of the rational numbers is chosen. The expression a is viewed as an element of the smallest field containing a and the RootOfs in L.

The RootOfs in K must form a subset of the RootOfs occurring in L and in a. In other words, K must be a 'syntactic' subfield of the field generated by L and the RootOfs in a.

$\mathrm{alias}\left(\mathrm{sqrt2}=\mathrm{RootOf}\left(x^2-2\right)\right)\:$

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

$\mathrm{evala}\left(\mathrm{Norm}\left(\mathrm{\alpha }\right)\right)$

$x^2-2$

$\mathrm{evala}\left(\mathrm{Norm}\left(\mathrm{\alpha }\,\varnothing \,\mathrm{sqrt2}\right)\right)$

$\mathrm{sqrt2}-x$

$\mathrm{evala}\left(\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$

$z^4-2x{z}^2+x^2-2$

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$\mathrm{evala}\left(\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$

Error, (in Norm) expects its 1st argument, A, to be of type {Matrix, Vector}, but received z-RootOf(_Z^2-x+RootOf(_Z^2-2))

$\mathrm{evala}\left(:-\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$

$z^4-2x{z}^2+x^2-2$