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This paper presents a method for computing persistent homology of filtered d-dimensional simplicial complexes, establishing that it corresponds to the standard homology of a graded module over a polynomial ring. The authors provide a general algorithm applicable to any field, extending previous work that was limited to specific cases. Additionally, they discuss the complexities of classification over non-fields and offer an algorithm for computing individual persistent homology groups in such scenarios.

Author

ahmed oufqir

Language

EN