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## A Note on Sturm Theorem

XIE Lie-jun(Faculty of Science,Ningbo University,Ningbo Zhejiang 315211,China)
Classical Sturm theorem is used to tell the number of distinct roots of polynomials in arbitrary interval.Yet it fails to give more information such as multiplicities of roots.We define the generalized Sturm sequence,and a necessary and sufficient condition for all the roots of polynomials of any degree in given interval have even or odd multiplicity is presented.Also,we discuss the problem of the non-negative and non-positivity of polynomials as application.
【Fund】： 宁波大学重点科研基金(XK200453)
【CateGory Index】： O156
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 【Co-references】
 Chinese Journal Full-text Database 10 Hits
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