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  Cucker, Felipe Add to Alert Profile  
 
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  1 - 3 of 3 reviews    
  Computing the homology of basic semialgebraic sets in weak exponential time
Bürgisser P., Cucker F., Lairez P. Journal of the ACM 66(1): 1-30, 2019.  Type: Article

A semialgebraic set is a subset of a finite-dimensional Euclidean space defined by a finite list of polynomial equalities and inequalities. These sets can be weird, so it desirable to be able to describe their topological shape, in par...
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Mar 26 2019  
  Condition: the geometry of numerical algorithms
Bürgisser P., Cucker F., Springer Publishing Company, Incorporated, New York, NY, 2013. 583 pp.  Type: Book (978-3-642388-95-8)

Implementing numerical algorithms may require the approximation of numerical quantities, given that computers have only a finite number of bits and real numbers cannot be encoded with a finite number of bits. Growth in computational po...
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Nov 26 2013  
  A polynomial time algorithm for diophantine equations in one variable
Cucker F., Koiran P., Smale S. Journal of Symbolic Computation 27(1): 21-29, 1999.  Type: Article

An algorithm for computing the integer roots of a polynomial in onevariable with integer coefficients is presented. The goal of the paperis the proof of the following theorem: “There is a polynomial timealgorithm which given ...
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May 1 1999  

   
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