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Differential forms in computational algebraic geometry
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007We give a uniform method for the two problems #CCC and #ICC of counting connected and irreducible components of complex algebraic varieties, respectively. Our algorithms are purely algebraic, i.e., they use only the field structure of C. They work efficiently in parallel and can be implemented by algebraic circuits of polynomial depth, i.e., in ...
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Completeness in Partial Differential Algebraic Geometry
This paper studies various aspects of complete differential algebraic varieties. The setting is the following, introduced by Kolchin. If \(F\) is a field of characteristic \(0\) equipped with \(m\) commuting derivations, then one has the notion of \textit{differential algebraic varieties} over \(F\). For simplicity, we fix a \textit{universal domain} \(
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