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» On Coherence in Computer Algebra
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STOC
2005
ACM
115views Algorithms» more  STOC 2005»
16 years 4 months ago
Computing the first Betti number and the connected components of semi-algebraic sets
In this paper we describe the first singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. We also describe algorithms for obtaining semi...
Saugata Basu, Richard Pollack, Marie-Franço...
AB
2008
Springer
15 years 10 months ago
On the Computational Power of Biochemistry
We explore the computational power of biochemistry with respect to basic chemistry, identifying complexation as the basic mechanism that distinguishes the former from the latter. W...
Luca Cardelli, Gianluigi Zavattaro
DIS
2007
Springer
15 years 10 months ago
Computational Discovery in Pure Mathematics
Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated th...
Simon Colton
ISSAC
2007
Springer
111views Mathematics» more  ISSAC 2007»
15 years 10 months ago
Numerical optimization in hybrid symbolic-numeric computation
Approximate symbolic computation problems can be formulated as constrained or unconstrained optimization problems, for example: GCD [3, 8, 12, 13, 23], factorization [5, 10], and ...
Lihong Zhi
CORR
2007
Springer
82views Education» more  CORR 2007»
15 years 4 months ago
Programs as polygraphs: computability and complexity
Abstract – This study presents Albert Burroni’s polygraphs as an algebraic and graphical description of first-order functional programs, where functions can have many outputs....
Guillaume Bonfante, Yves Guiraud