The regulator of a number field 
is a positive number associated with 
. 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 
as the determinant of an 
matrix, where 
has 
real embeddings and 
imaginary embeddings and 
.
The regulator is implemented in the Wolfram Language for example as NumberFieldRegulator[Sqrt[d]].
