A constructive characterization of standard bases. (English) Zbl 0619.13010

Mora, Ferdinando

Boll. Unione Mat. Ital., VI. Ser., D, Algebra Geom. 2, 41-50 (1983).

A basis \(f_ 1,...,f_ m\) of an ideal I in the ring of polynomials of n variables over a field is named standard if the initial forms (i.e. the forms of lowest degree) of the polynomials \(f_ 1,...,f_ m\) generate the ideal of the initial forms of the ideal I. It is given a sufficient condition for the standardness of a basis, and also an algorithm for the construction of a standard basis analogue to the known Buchberger algorithm for the Gröbner basis.

MSC:

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

Keywords:

polynomial ideal; algorithm; standard basis; Gröbner basis