TOPICS
Search

Number Field Signature

The number field signature is the ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex conjugate pairs of imaginary embeddings. The extension field degree of the number field is s+2t.

For the number field Q(a) generated by an algebraic number a, the Wolfram Language function NumberFieldSignature[a] returns its signature as the list {s,t}.

See also

Field Embedding, Fundamental Unit, Imaginary Embedding, Number Field, Real Embedding, Unit

Portions of this entry contributed by Kevin O'Bryant

Explore with Wolfram|Alpha

References

Cohen, H. A Course in Computational Algebraic Number Theory, 3rd. corr. ed. New York: Springer-Verlag, 1996.

Referenced on Wolfram|Alpha

Number Field Signature

Cite this as:

Weisstein, Eric W., with contributions by Kevin O'Bryant. "Number Field Signature." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NumberFieldSignature.html

Subject classifications