Norm - Maple Help

evala/Norm

norm of an algebraic number (or function)

 Calling Sequence Norm(a, L, K)

Parameters

 a - any expression L - (optional) set of RootOfs K - (optional) set of RootOfs

Description

 • 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.

Examples

 > $\mathrm{alias}\left(\mathrm{sqrt2}=\mathrm{RootOf}\left({x}^{2}-2\right)\right):$
 > $\mathrm{alias}\left(\mathrm{\alpha }=\mathrm{RootOf}\left({y}^{2}-x+\mathrm{RootOf}\left({x}^{2}-2\right),y\right)\right):$
 > $\mathrm{evala}\left(\mathrm{Norm}\left(\mathrm{\alpha }\right)\right)$
 ${{x}}^{{2}}{-}{2}$ (1)
 > $\mathrm{evala}\left(\mathrm{Norm}\left(\mathrm{\alpha },\varnothing ,\mathrm{sqrt2}\right)\right)$
 ${\mathrm{sqrt2}}{-}{x}$ (2)
 > $\mathrm{evala}\left(\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$
 ${{z}}^{{4}}{-}{2}{}{x}{}{{z}}^{{2}}{+}{{x}}^{{2}}{-}{2}$ (3)

The name Norm must be global.

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $\mathrm{evala}\left(\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$
 > $\mathrm{evala}\left(:-\mathrm{Norm}\left(z-\mathrm{\alpha }\right)\right)$
 ${{z}}^{{4}}{-}{2}{}{x}{}{{z}}^{{2}}{+}{{x}}^{{2}}{-}{2}$ (4)