Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68229220181226A new algorithm for computing SAGBI bases up to an arbitrary degree215221353010.22075/ijnaa.2017.1718.1640ENShahnaz FakouriDepartment of Mathematics and Computer Sciences, Damghan University, Damghan, IranAbdolali BasiriDepartment of Mathematics and Computer Sciences, Damghan University, Damghan, IranSajjad RahmaniDepartment of Mathematics and Computer Sciences, Damghan University, Damghan, IranJournal Article20170925We 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>.http://ijnaa.semnan.ac.ir/article_3530_27f14ecaa26f792a3f495500263a548b.pdf