An algorithm to compute minimal Sullivan algebras

Abstract

In this note, we give an algorithm that starting with a Sullivan algebra gives us its minimal model. This algorithm is a kind of modified AT-model algorithm used to compute in the past other kinds of topology information such as (co)homology, cup products on cohomology and persistent homology. Taking as input a (non-minimal) Sullivan algebra A with an ordered finite set of generators preserving the filtration defined on A, we obtain as output a minimal Sullivan algebra with the same rational cohomology as A.