5,793 research outputs found
Computing the support of local cohomology modules
For a polynomial ring , we present a method to compute the
characteristic cycle of the localization for any nonzero polynomial that avoids a direct computation of as a -module. Based on this
approach, we develop an algorithm for computing the characteristic cycle of the
local cohomology modules for any ideal using the
\v{C}ech complex. The algorithm, in particular, is useful for answering
questions regarding vanishing of local cohomology modules and computing
Lyubeznik numbers. These applications are illustrated by examples of
computations using our implementation of the algorithm in Macaulay~2.Comment: 15 page
Discrete Morse theory for computing cellular sheaf cohomology
Sheaves and sheaf cohomology are powerful tools in computational topology,
greatly generalizing persistent homology. We develop an algorithm for
simplifying the computation of cellular sheaf cohomology via (discrete)
Morse-theoretic techniques. As a consequence, we derive efficient techniques
for distributed computation of (ordinary) cohomology of a cell complex.Comment: 19 pages, 1 Figure. Added Section 5.
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