论文信息 - A Note on Testing the Resultant

A Note on Testing the Resultant

Shub (in "From Topology to Computation: Proceedings of the Smalefest." (M. Hirsch, J. Marsden, and M. Shub, Eds.), pp. 281-301, Springer-Verlag, New York/Berlin, 1993) proposes to attack the complex PC versus the NPC problem by focussing on lower bounds on testing the resultant of quadratic forms for zero. Taking up this question we show in the present paper a lower bound of order n3 for the resultant.

Thomas Lickteig | Klaus Meer

[1] S. Smale,et al. On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[2] Olga Taussky,et al. Moderne Algebra , 1933 .

[3] Joos Heintz,et al. On the Intrinsic Complexity of Elimination Theory , 1993, J. Complex..

[4] Thomas Lickteig,et al. Semi-algebraic decision complexity, the real spectrum, and degree , 1996 .

[5] Marek Karpinski,et al. On real Turing machines that toss coins , 1995, STOC '95.

[6] James Renegar,et al. On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I: Introduction. Preliminaries. The Geometry of Semi-Algebraic Sets. The Decision Problem for the Existential Theory of the Reals , 1992, J. Symb. Comput..

[7] Thomas Lickteig,et al. Test complexity of generic polynomials , 1992, J. Complex..

[8] V. Strassen. Die Berechnungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoeffizienten , 1973 .