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**How lower and upper complexity bounds meet in elimination theory.**
*(English)*
Zbl 0899.68054

Cohen, GĂ©rard (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 11th international symposium, AAECC-11, Paris, France, July 17-22, 1995. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 948, 33-69 (1995).

Summary: Computer algebra is a research field that combines two main subjects that were separated for years: algebra and computer science. A short characterization would be: computer algebra deals with the symbolic manipulation of algebraic entities. Thus computer algebra seems to split in so many domains as algebra does, whereas every domain has its own approach to the subject.

These pages are mainly concerned with just one of these domains: elimination over algebraically closed fields. In other words, we discuss some basic problems whose origins come from algebraic geometry and commutative algebra. Because of the obvious limitations of a talk like this we are obliged to omit some related and relevant research domains as elimination over real closed fields or computational number theory.

For the entire collection see [Zbl 0847.00060].

These pages are mainly concerned with just one of these domains: elimination over algebraically closed fields. In other words, we discuss some basic problems whose origins come from algebraic geometry and commutative algebra. Because of the obvious limitations of a talk like this we are obliged to omit some related and relevant research domains as elimination over real closed fields or computational number theory.

For the entire collection see [Zbl 0847.00060].

### MSC:

68W30 | Symbolic computation and algebraic computation |

68Q25 | Analysis of algorithms and problem complexity |

14Q99 | Computational aspects in algebraic geometry |