Gröbner bases and primary decomposition of polynomial ideals. (English) Zbl 0667.13008

Gianni, Patrizia; Trager, Barry; Zacharias, Gail

J. Symb. Comput. 6, No. 2-3, 149-167 (1988).

An algorithm to compute the primary decomposition of ideals in a polynomial ring over a “factorially closed algorithmic principal ideal domain” (see the paper for the technical definition) is given. The construction is based on the Gröbner basis algorithm. Induction over the dimension is used and localization at principal primes lowers the dimension. In the zero-dimensional case Gröbner bases are again used for decomposing. Finally it is showed how the reduction process can be applied to computing radicals and testing for primality.

Reviewer: R.Fröberg

MSC:

13F20	Polynomial rings and ideals; rings of integer-valued polynomials
13-04	Software, source code, etc. for problems pertaining to commutative algebra
68W30	Symbolic computation and algebraic computation
13A15	Ideals and multiplicative ideal theory in commutative rings

Keywords:

primary decomposition of ideals; factorially closed algorithmic principal ideal domain; Gröbner basis; computing radicals; testing for primality

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