Displaying similar documents to “Algebraic systems of quadratic forms of number fields and function fields.”

Algorithms for quadratic forms over real function fields

Konrad Jałowiecki, Przemysław Koprowski (2016)

Banach Center Publications

Similarity:

This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.

Some quartic number fields containing an imaginary quadratic subfield

Stéphane R. Louboutin (2011)

Colloquium Mathematicae

Similarity:

Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.