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05/03/2023
Factorization and root-finding for polynomials over division quaternion algebras
Polynomial factorization and root finding are among the most standard th...
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02/04/2023
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Pourchet proved in 1971 that every nonnegative univariate polynomial wit...
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01/02/2023
Computing square roots in quaternion algebras
We present an explicit algorithmic method for computing square roots in ...
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11/16/2021
Isotropic vectors over global fields
We present a complete suite of algorithms for finding isotropic vectors ...
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11/16/2021
Solving sums of squares in global fields
The problem of writing a totally positive element as a sum of squares ha...
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08/24/2020
Computing singular elements modulo squares
The group of singular elements was first introduced by Helmut Hasse and ...
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03/17/2017
Roots multiplicity without companion matrices
We show a method for constructing a polynomial interpolating roots' mult...
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11/20/2016