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

Document Type : Research Paper


Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran


We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra 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 subalgebras.