The process of substituting variables in a polynomial with other polynomials is dubbed polynomial composition.The behaviour of Gröbner bases and Sagbi bases under composition is well known.In this paper,the autho...The process of substituting variables in a polynomial with other polynomials is dubbed polynomial composition.The behaviour of Gröbner bases and Sagbi bases under composition is well known.In this paper,the authors provide a sufficient and necessary condition on a setΘof polynomials under which the Sagbi-Gröbner basis computation commutes with composition.This has natural applications to the computations of Sagbi-Gröbner bases for subsets of composed polynomials of subalgebra.展开更多
文摘The process of substituting variables in a polynomial with other polynomials is dubbed polynomial composition.The behaviour of Gröbner bases and Sagbi bases under composition is well known.In this paper,the authors provide a sufficient and necessary condition on a setΘof polynomials under which the Sagbi-Gröbner basis computation commutes with composition.This has natural applications to the computations of Sagbi-Gröbner bases for subsets of composed polynomials of subalgebra.
