A new algorithm for computing SAGBI bases up to an arbitrary degree

Abstract

We present a new algorithm for computing a <span>SAGBI</span> basis up to an arbitrary degree for a <span>subalgebra</span> generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in <span>subalgebras</span>.