| Safe Haskell | None |
|---|---|
| Language | Haskell98 |
Math.NumberTheory.QuadraticField
Description
A module for arithmetic in quadratic number fields. A quadratic number field is a field of the form Q(sqrt d), where d is a square-free integer. For example, we can perform the following calculation in Q(sqrt 2):
(1 + sqrt 2) / (2 + sqrt 2)
It is also possible to mix different square roots in the same calculation. For example:
(1 + sqrt 2) * (1 + sqrt 3)
Square roots of negative numbers are also permitted. For example:
i * sqrt(-3)
Documentation
A basis for quadratic number fields Q(sqrt d), where d is a square-free integer.
sqrt :: Integer -> QNF Source #
Although this has the same name as the Prelude.sqrt function, it should be thought of as more like a constructor for creating elements of quadratic fields.
Note that for d positive, sqrt d means the positive square root, and sqrt (-d) should be interpreted as the square root with positive imaginary part, that is i * sqrt d. This has the consequence that for example, sqrt (-2) * sqrt (-3) = - sqrt 6.