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Fixes sheaf cohomology printing, adds check that coefficient ring is …
…a field (oscar-system#3087) * docu sheaf cohomology * correction * fixes sheaf coh table printing * adjusts docu, checks that coefficient ring is a field * fix getindex and docu * fixes tests --------- Co-authored-by: Wolfram Decker <[email protected]> Co-authored-by: Rafael Mohr <[email protected]>
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docs/src/AlgebraicGeometry/SheafCohomology/sheaf_cohomology.md
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```@meta | ||
CurrentModule = Oscar | ||
DocTestSetup = quote | ||
using Oscar | ||
end | ||
``` | ||
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# Sheaves on Projective Space | ||
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We present two algorithms for computing sheaf cohomology over projective $n$-space. | ||
The algorithms are based on Tate resolutions via the **B**ernstein-**G**elfand-**G**elfand-correspondence | ||
as introduced in [EFS03](@cite) and on local cohomology (see [Eis98](@cite)), respectively. While the first | ||
algorithm makes use of syzygy computations over the exterior algebra, the second algorithm is based on | ||
syzygy computations over the symmetric algebra (see [DE02](@cite) for a tutorial). Thus, in most examples, | ||
the first algorithm is much faster. | ||
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```@docs | ||
sheaf_cohomology(M::ModuleFP{T}, l::Int, h::Int; algorithm::Symbol = :bgg) where {T <: MPolyDecRingElem} | ||
``` | ||
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