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AlgebraicNumberNorm

AlgebraicNumberNorm[a]
gives the norm of the algebraic number a.
  • The norm of a is defined to be the product of the roots of its minimal polynomial.
Norms of algebraic numbers:
Norms of algebraic numbers:
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Integers and rational numbers:
Radical expressions:
Root and AlgebraicNumber objects:
AlgebraicNumberNorm automatically threads over lists:
Norm of over :
is irreducible in :
Since AlgebraicNumberNorm is multiplicative, having a prime norm implies the original number is prime:
AlgebraicNumberNorm is multiplicative:
Units in a number field have norm :
Compute the smallest field that includes , i.e. :
Compute the norm in that field:
Plot of norms of elements in :
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