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, Iran0000-0003-4454-4379Sajjad 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>.https://ijnaa.semnan.ac.ir/article_3530_27f14ecaa26f792a3f495500263a548b.pdf