On inverse systems and squarefree decomposition of zero-dimensional polynomial ideals

• Autores: Ulrich Oberst, F. Pauer, Werner Heiß
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 3, 2006, págs. 261-284
• Idioma: inglés
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• Resumen

  • Let I be a zero-dimensional ideal in a polynomial ring F[s]:=F[s1,¿,sn] over an arbitrary field F. We show how to compute an F-basis of the inverse system I of I. We describe the F[s]-module I by generators and relations and characterise the minimal length of a system of F[s]-generators of I. If the primary decomposition of I is known, such a system can be computed. Finally we generalise the well-known notion of squarefree decomposition of a univariate polynomial to the case of zero-dimensional ideals in F[s] and present an algorithm to compute this decomposition.