Complexity theory aims at the understanding of the inherent hardness of computational problems. This book studies the complexity of the most basic counting problems in algebraic geometry within an algebraic framework of computation. The author gives an efficient parallel method for the two problems of counting the connected and irreducible components of complex algebraic varieties. On the other hand, it is shown that deciding connectedness of varieties is PSPACE-hard. This result is also extend to higher Betti numbers. Furthermore, the problem of counting irreducible components for a fixed number of equations is reduced to a fixed number of variables. The consequences are a polynomial time algorithm in the BSS-model, and a randomised parallel polylogarithmic time algolrithm in the Turing model. The book is intended for mathematicians interested in computational complexity, and for computer scientists interested in algebraic geometry. The required prerequisites are completely presented, so the text should be accessable to graduate students.
Produktkennzeichnungen
EAN
9783836498449
ISBN
9783836498449
ISBN-10
3836498448
ISBN-13
9783836498449
eBay Product ID (ePID)
70097450
Produkt Hauptmerkmale
Produktart
Lehrbuch
Sprache
Englisch
Anzahl der Seiten
160 Seiten
Verlag
Vdm Verlag, Vdm
Publikationsname
Complexity of Counting Components of Algebraic Varieties
Autor
Peter Scheiblechner
Format
Taschenbuch
Erscheinungsjahr
2008
Maße
Gewicht
230g
Zusätzliche Produkteigenschaften
Hörbuch
No
Inhaltsbeschreibung
Paperback
Item Length
22cm
Item Height
10mm
Item Width
15cm
Sprachausgabe
Englisch
Seiten
156 Seiten
Item Weight
255g
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