Multipersistence homology modules were introduced by G.Carlsson and A.Zomorodian (1) which gave, together with G.Singh (4), an algo- rithm to compute their Grobner bases. Although their algorithm has polynomial complexity when the chain modules are free, i.e. in the one-critical case, it might be exponential in general. We give a new presentation of multipersistence homology modules, which allows us to design an algorithm to compute their Grobner bases always in polyno- mial time by avoiding the mapping telescope.
['Antonio Patriarca', 'Martina Scolamiero', 'Francesco Vaccarino']
A presentation of general multipersistence modules computable in polynomial time