##  [Sturm Sequence](/sturm-sequence) 

  ##  [Sturm Sequence](https://algebra.quantumdictionary.io/sturm-sequence-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sequence of polynomials obtained by applying the Euclidean algorithm to a real univariate polynomial and its derivative (or using a signed remainder sequence) whose sign variations evaluated at interval endpoints count the number of distinct real roots inside that interval (Sturm's theorem).