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Algorithme isobarique

Ernest Cesàro (1884)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Algorithms for quadratic forms over real function fields

Konrad Jałowiecki, Przemysław Koprowski (2016)

Banach Center Publications

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.

All Liouville Numbers are Transcendental

Artur Korniłowicz, Adam Naumowicz, Adam Grabowski (2017)

Formalized Mathematics

In this Mizar article, we complete the formalization of one of the items from Abad and Abad’s challenge list of “Top 100 Theorems” about Liouville numbers and the existence of transcendental numbers. It is item #18 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. Liouville numbers were introduced by Joseph Liouville in 1844 [15] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real...

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