Regulator

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or totally imaginary cubic field is the natural logarithm of the field's fundamental unit, i.e.,

There is also a more complicated definition for a general number field K as the determinant of an r×r matrix, where K has r_1 real embeddings and 2r_2 imaginary embeddings and r=r_1+r_2-1.

The regulator is implemented in the Wolfram Language for example as NumberFieldRegulator [Sqrt[d]].

See also

This entry contributed by David Terr

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Terr, David. "Regulator." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Regulator.html

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