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Apolarity and Canonical Forms for Homogeneous Polynomials

✍ Scribed by Richard Ehrenborg; Gian-Carlo Rota

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
702 KB
Volume
14
Category
Article
ISSN
0195-6698

No coin nor oath required. For personal study only.

✦ Synopsis

Käre Bernt Lindström, Gratulerar på Din sextioårs dag. Vi hoppas att denna artikel kommer falla Dig i smaken. Vi börjar med en kort studie i algebraiska matroider, och fortsätter med att bevisa relationen mellan Jacobianen av en mängd algebraiska funktioner och deras algebraiska oberoende. Med detta resulat bevisar vi de två huvudsatserna, som behandlar kanoniska former. Dessa satser reducerar frågan om en form är kanonisk för homogena polynom i (q) variabler och av grad (p) till att undersöka om ett homogent linjärt ekvations system har bata den triviala lösningen. Genom att använda apolaritet kan detta linjära system enkelt beskrivas. Till sist ger vi en mångfald av exempel av kanoniska former för homogena polynom.

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