Quantifier Elimination for Quartics

  • Lu Yang
  • Bican Xia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4120)


Concerning quartics, two particular quantifier elimination (QE) problems of historical interests and practical values are studied. We solve the problems by the theory of complete discrimination systems and negative root discriminant sequences for polynomials that provide a method for real (positive/negative) and complex root classification for polynomials. The equivalent quantifier-free formulas are obtained mainly be hand and are simpler than those obtained automatically by previous methods or QE tools. Also, applications of the results to program verification and determination of positivity of symmetric polynomials are showed.


Real Zero Positive Zero Counting Multiplicity Sign List Cylindrical Algebraic Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lu Yang
    • 1
  • Bican Xia
    • 2
  1. 1.Guangzhou UniversityGuangzhouChina
  2. 2.School of Mathematical SciencesPeking UniversityChina

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