Fix precompilation on Julia 1.13 (Hessenberg method overwrites)

[ChrisRackauckas-Claude]

Summary

• Stop defining LinearAlgebra.eigencopy_oftype(::UpperHessenberg, ...) on Julia ≥ 1.13 (already in LinearAlgebra; backported from 1.14).
• Stop defining LinearAlgebra.eigvals!(::UpperHessenberg, ...) on Julia ≥ 1.13 (generic fallback still present because JuliaLang/LinearAlgebra.jl#1602 was not backported; overwriting it fails precompilation).
• Bump to 0.4.1 for registration.

Root cause

Precompiling GenericLinearAlgebra 0.4.0 on Julia 1.13 fails with:

WARNING: Method definition eigencopy_oftype(...UpperHessenberg...) in LinearAlgebra overwritten in GenericLinearAlgebra
ERROR: Method overwriting is not permitted during Module precompilation.

and, after guarding only eigencopy_oftype, the same error for eigvals!(::UpperHessenberg).

Related: #180, #181 (partial fix for eigencopy_oftype only; Julia-pre CI still fails on the eigvals! overwrite).

Notes

• On Julia 1.13+, BlasFloat UpperHessenberg eigensolves go through LinearAlgebra's LAPACK methods.
• Full generic-UpperHessenberg support on 1.13 still needs a LinearAlgebra #1602 backport (or Julia 1.14).
• This unblocks packages such as ExponentialUtilities whose Julia-pre CI fails solely because GenericLinearAlgebra cannot precompile.

Test plan

• Diff reviewed against fix precompilation on 1.13 #181; adds the missing eigvals! guard
• CI on this PR (especially Julia pre)

Made with Cursor

[codecov]

Codecov Report

❌ Patch coverage is 50.00000% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 95.73%. Comparing base (2f53d98) to head (bd8139e).

Files with missing lines	Patch %	Lines
src/eigenGeneral.jl	50.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #182   +/-   ##
=======================================
  Coverage   95.73%   95.73%           
=======================================
  Files          11       11           
  Lines        1524     1524           
=======================================
  Hits         1459     1459           
  Misses         65       65           

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[ChrisRackauckas-Claude]

Pushed a follow-up: the julia-pre failure was because v\"1.13.0-DEV\" < v\"1.13\" is true, so the guards never fired on nightlies. Switched both bounds to v\"1.13.0-\".

[ChrisRackauckas-Claude]

Yes — on 1.13.0-rc* the LinearAlgebra densifying fallback is still present (#1602 is on `LinearAlgebra` `release-1.13` but not in the Julia rc pin yet), so `eigvals(::UpperHessenberg{BigFloat})` becomes `eigvals!(triu!(H.data); permute, scale)` and hits our `StridedMatrix` pirate.

Pushed a fix: `_schur!(::UpperHessenberg)` now accepts/ignores `permute`/`scale` (and other kwargs), matching the old comment that these should be absorbed.

[andreasnoack]

I think these changes are redundant. See the top post in #180

[ChrisRackauckas]

Oh that's probably better.