Results 281 to 290 of about 281,620 (316)

Differential forms in algebraic geometry

, 2011
Before considering more general spaces we shall first discuss (1) the r-dimensional projective space Π r . In this space we shall consider a homogeneous coordinate system (Z0, Z1, ... , Z r ). Let U α be that part of Π r in which Z α ≠ 0. In U α we may then introduce non-homogeneous coordinates zαi = Zι/Zα (ι≠α).
W. Hodge
semanticscholar   +3 more sources

Numerical Algebraic Geometry and Differential Equations

, 2014
In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.
Wenrui Hao, Bei Hu, A. Sommese
semanticscholar   +2 more sources

Differential forms in computational algebraic geometry

Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007
We 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 ...
Peter Bürgisser, Peter Scheiblechner
semanticscholar   +2 more sources

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