2 citations · 3 across the 10 of their papers we have counts for
17 papers
Polynomials assuming only local prime powers
Przemysław Koprowski
We study the class of polynomials that map a local field (i.e., the completion of a number field at a non-Archimedean place) into the subset of its -th powers, where is the…
Factorization and root-finding for polynomials over division quaternion algebras
Przemysław Koprowski
Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras,…
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Victor Magron, Przemysław Koprowski, Tristan Vaccon
Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for co…
Computing square roots in quaternion algebras
Przemysław Koprowski
We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.
Solving sums of squares in global fields
Przemysław Koprowski
The problem of writing a totally positive element as a sum of squares has a long history in mathematics, going back to Bachet and Lagrange. While for some specific rings (like inte…
Isotropic vectors over global fields
Przemysław Koprowski
We present a complete suite of algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic different from 2. Thi…