On the Real and Imaginary Roots of Algebraical Equations
James Joseph Sylvester
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James Joseph Sylvester
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J. Cohn (1977)
Acta Arithmetica
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Kostov, Vladimir (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 12D10. We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realized by real polynomials.
Jindřich Spal (1970)
Kybernetika
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P. H. Diananda (1964)
Annales Polonici Mathematici
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Jindřich Spal (1979)
Kybernetika
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Olivier Carton, Christian Choffrut (2010)
RAIRO - Theoretical Informatics and Applications
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This contribution extends the notions of roots and periodicity to strings of transfinite lengths. It shows that given a transfinite string, either it possesses a unique root or the set of its roots are equivalent in a strong way.