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Resultants of slice regular polynomials in two quaternionic variables

Anna Gori, Giulia Sarfatti, Fabio Vlacci

Computer Aided Geometric Design（2024）

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Abstract
We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant. We use this tool to investigate the existence of common zeros and common factors of slice regular polynomials and give a kinematic interpretation of our results.
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Key words
Quaternionic slice regular polynomials,vanishing sets,non-commutative resultant
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