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Media type:
E-Book
Title:
Algorithms of intrinsic complexity for point searching in compact real singular hypersurfaces
:
dedicated to Tomás Recio on the occasion of his 60th birthday
Description:
For a real squarefree multivariate polynomial F , we treat the general problem of finding real solutions of the equation F = 0 , provided that the real solution set {F = 0}R is compact. We admit that the equation F = 0 may have singular real solutions. We are going to decide whether this equation has a non-singular real solution and, if this is the case, we exibit one for each generically smooth connected component of {F = 0}R . We design a family of elimination algorithms of intrinsic complexity which solves this problem. In worst case the complexity of our algorithms does not exceed the already known extrinsic complexity bound of (nd)O(n) for the elimination problem under consideration, where n is the number of indeterminates of F and d its (positive) degree. In the case that the real variety defined by F is smooth, there exist already algorithms of intrinsic