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