ИСТИНА

In the last decade, signature-based algorithms for computing Groebner bases (F5, F5C, G2V, GVW, SGB and other mo dications) are actively develop ed. We b egin with a discussion of the matrix version of F5. We point out the implicit link of this algorithm with involutive ideas, and also consider classical Buchberger algorithm in the context of matrix F5. Then we turn to SGB algorithm proposed by Sun, Wang, Ma and Zhang in 2012. We generalize it in a symmetric form such that the distinction between signatures and leading monomials disapp ears.