Details and Options
- The norm of a is defined to be the product of the roots of its minimal polynomial.
- AlgebraicNumberNorm[a,Extension->θ] finds the norm of a over the field .
Examplesopen allclose all
Basic Examples (1)
Norms of algebraic numbers:
Norm of over :
is irreducible in :
Since AlgebraicNumberNorm is multiplicative, having a prime norm implies the original number is prime:
Properties & Relations (3)
AlgebraicNumberNorm is multiplicative:
Units in a number field have norm :
Compute the smallest field that includes , i.e. :
Compute the norm in that field:
Neat Examples (1)
Plot of norms of elements in :