论文信息 - Ideals Generated by Quadrics Exhibiting Double Exponential Degrees

Ideals Generated by Quadrics Exhibiting Double Exponential Degrees

Abstract We modify the example of Mayr and Meyer to give an example of a polynomial ideal generated by quadrics which exhibits double exponential growth for the ideal membership problem. We also show that the homogenization of this example gives a set of elements which has a minimal syzygy of double exponential degree.

Jee Koh | J. Koh

[1] David Masser,et al. Fields of large transcendence degree generated by values of elliptic functions , 1983 .

[2] Daniel Lazard,et al. A Note on Upper Bounds for Ideal-Theoretic Problems , 1992, J. Symb. Comput..

[3] Grete Hermann,et al. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale , 1926 .

[4] Michael Eugene Stillman,et al. On the Complexity of Computing Syzygies , 1988, J. Symb. Comput..

[5] A. Seidenberg. Constructions in algebra , 1974 .

[6] A. Meyer,et al. The complexity of the word problems for commutative semigroups and polynomial ideals , 1982 .

[7] Chee-Keng Yap,et al. A New Lower Bound Construction for Commutative Thue Systems with aApplications , 1991, J. Symb. Comput..