### Abstract

We have formalized the Sturm–Tarski theorem (also referred as the Tarski theorem), which generalizes Sturm's theorem. Sturm's theorem is usually used as a way to count distinct real roots, while the Sturm-Tarksi theorem forms the basis for Tarski's classic quantifier elimination for real closed field.

### License

BSD License

### History

November 9, 2022
  Added theory file Tarski_Query_Impl to the entry proof session.

### Topics

- Mathematics/Analysis

### Session Sturm_Tarski

- PolyMisc
- Sturm_Tarski
- Pseudo_Remainder_Sequence
- Tarski_Query_Impl

### Depends on

- Polynomial Interpolation

### Used by

- The BKR Decision Procedure for Univariate Real Arithmetic
- The Budan–Fourier Theorem and Counting Real Roots with Multiplicity
- Count the Number of Complex Roots
- Evaluate Winding Numbers through Cauchy Indices

## Cite

×

Sturm_Tarski-AFP

    @article{Sturm_Tarski-AFP,
      author  = {Wenda Li},
      title   = {The Sturm–Tarski Theorem},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2014},
      note    = {\url{https://isa-afp.org/entries/Sturm_Tarski.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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