norm of an algebraic number (or function) - Maple Help

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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

aliassqrt2=RootOfx22:

aliasα=RootOfy2x+RootOfx22,y:

evalaNormα

x22

(1)

evalaNormα,,sqrt2

sqrt2x

(2)

evalaNormzα

z42xz2+x22

(3)

The name Norm must be global.

withLinearAlgebra:

evalaNormzα

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))

evala:-Normzα

z42xz2+x22

(4)

See Also

evala, LinearAlgebra[Norm], mod, norm, Normal, product, RootOf, VectorCalculus[Norm]


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