On the rank of powers of a non-degenerate quadratic form

• Cosimo Flavi ^[1]
  1. [1] University of Bologna

     University of Bologna

     Bolonia, Italia

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 83-86
• Idioma: inglés
• Enlaces
  • Texto Completo Libro
• Resumen

  • A decomposition of a homogeneous polynomial is a representation of that polynomial as a sum of powers of linear forms; in particular, the minimum number of addends in this sum is said to be the rank of the polynomial. We analyze a way to determine explicit decompositions of a polynomial corresponding to a power of a non-degenerate quadratic form. The main instrument used in this context is the Apolarity Lemma, which is a classic result relating the summands of a decomposition to its apolar ideal.