Add is_nilpotent(::MatrixElem)
#1783
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| is_zero(A) && return true | ||
| while i < n | ||
| i *= 2 | ||
| A = mul!(A, A, A) |
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It might or might not be faster to compute the minimal or characteristic polynomial (if there are dedicated optimized methods for this and the given matrix type
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yeah that's true. but for that one would need to know which specialized methods exist in which cases, which I honestly don't
| A = deepcopy(A) | ||
| i = 1 | ||
| is_zero(A) && return true | ||
| while i < n |
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Actually, is this algorithm even correct when A contains zero divisors? I normally think about matrices over integral domains, and then of course A is nilpotent iff A^n=0. But over a ring with zero-divisors, we could have a triangularizable matrix with nilpotent eigenvalues where
Admittedly this is somewhat fringe, but we should still handle it right? For starters we could add is_domain_type(T) || error("Only supported over integral domains") ? (AFAIK there is no is_domain / is_integral_domain which for e.g.
Then if someone needs this over non-domains, they at least get a helpful error and can provide an implementation for their use case.
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Good catch! Thanks for mentioning this. I added the suggested error
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The HeckeCI failures are thofma/Hecke.jl#1600. |
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The OscarCI job fails due to the same problem in the Hecke doctests (why do they even run in this job? I thought that's why we have the HeckeCI job). |
I reported the issue with the OscarCI job running the Hecke doctests in oscar-system/OscarDevTools.jl#38. |
I need something for checking nilpotency of a matrix in OSCAR. If you have good ideas for speed improvements, please let me know. Otherwise, I would be happy to get this merged soonish, and performance things can be adapted later anyway.