Mora, Ferdinando A constructive characterization of standard bases. (English) Zbl 0619.13010 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. Cited in 5 Documents 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 PDF BibTeX XML Cite \textit{F. Mora}, Boll. Unione Mat. Ital., VI. Ser., D, Algebra Geom. 2, No. 1, 41--50 (1983; Zbl 0619.13010)