Algorithms in algebraic topology and homological algebra: the problem of complexity (Q5959714)

The authors analyze the complexity of three algorithms to perform computations in algebraic topology. These algorithms were introduced by \textit{V. Álvarez, J. A. Armario, P. Real}, and \textit{B. Silva} [Int. conf. secondary calculus and cohomological physics, Moscow (1997; Zbl 0977.16003)], \textit{V. Álvarez, J. A. Armario}, and \textit{P. Real} [Proc. 1st meeting on geometry and topology, Braga 15--29 (1997; Zbl 0941.55007)], and \textit{P. Real} [Ann. Univ. Ferrara, Nuova Ser., Sez. VII 42, 57--63 (1996; Zbl 0936.55009)]. Their algorithms are to compute the homology of a commutative differential graded algebra, the homology of principal twisted Cartesian products of Eilenberg-MacLane spaces and Steenrod squares from a cochain level. They show that in the first two cases the complexity of the algorithms greatly simplify and in the last case it seems useful in low dimensions although a further analysis is suggested.