Tensor product of modules slow?
topic: commutative algebra
Here is the ideal sheaf of a surface represented by a graded module:
`S = bordiga()`
`I = defining_ideal(S)`
`M = ideal_as_module(I)`
Now I wish to compute the pluri-genera of the surface:
`function pluri_genus(M::ModuleFP, n::Int)`
` V = repeat([M], outer = n)`
` T = tensor_product(V)`
` tbl = sheaf_cohomology(M, -4, 0)`
` return tbl[0, 0]`
`end`
I get, for example, as expected for a rational surface:
`julia> pluri_genus(M, 2)`
`0`
To implement the Enriques-Kodaira classification, for more difficult surfaces, I need to compute these numbers up to `n = 6`. But that seems to be out of reach.
The bottleneck in the function in `.julia/dev/Oscar/src/Modules/UngradedModules/Tensor.jl:120` is this line:
`result, pr_res = quo(tot[0], I)`
@HechtiDerLachs Any ideas?
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