Make computation of LU decomposition of matrix over GF(2^e) interruptible

[user202729]

As in the title. Before this change, the test fails.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit e7000e9; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[vneiger]

Looks good to me. Thanks!

[vbraun]

I'm getting

[sagelib-10.8.beta2] [spkg-install]   FAILED: src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/meson-generated_src_sage_matrix_matrix_gf2e_dense.pyx.c.o
[sagelib-10.8.beta2] [spkg-install]   gcc -Isrc/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p -Isrc/sage/matrix -I../../src/sage/matrix -Isrc/sage/cpython -I../../src/sage/cpython -Isrc/sage/ext -I../../src/sage/ext -Isrc/sage/libs/flint -I../../src/sage/libs/flint -Isrc/sage/libs/ntl -I../../src/sage/libs/ntl -Isrc/sage/rings -I../../src/sage/rings -Isrc/sage/rings/finite_rings -I../../src/sage/rings/finite_rings -I../../local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/cysignals -I/home/release/Sage/local/var/lib/sage/venv-python3.12.5/include/python3.12 -I/home/release/Sage/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/numpy/_core/include -I/usr/include/libpng16 -fvisibility=hidden -fdiagnostics-color=always -DNDEBUG -D_FILE_OFFSET_BITS=64 -Wall -Winvalid-pch -std=c17 -O3 -g -O2 -fPIC -DWITH_GZFILEOP -MD -MQ src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/meson-generated_src_sage_matrix_matrix_gf2e_dense.pyx.c.o -MF src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/meson-generated_src_sage_matrix_matrix_gf2e_dense.pyx.c.o.d -o src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/meson-generated_src_sage_matrix_matrix_gf2e_dense.pyx.c.o -c src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/src/sage/matrix/matrix_gf2e_dense.pyx.c
[sagelib-10.8.beta2] [spkg-install]   src/sage/matrix/matrix_gf2e_dense.cpython-312-x86_64-linux-gnu.so.p/src/sage/matrix/matrix_gf2e_dense.pyx.c:1127:10: fatal error: ios: No such file or directory
[sagelib-10.8.beta2] [spkg-install]    1127 | #include "ios"
[sagelib-10.8.beta2] [spkg-install]         |          ^~~~~
[sagelib-10.8.beta2] [spkg-install]   compilation terminated.

[user202729]

the reason is likely missing "must compile with C++" marker somewhere. That error is indicator of C++ requirement cython/cython#1910 .

Still, I suspect the reason why this builds in test-long CI but fails in @vbraun 's build is #39030 (?) any idea why test-long CI doesn't fail?

[user202729]

I fix the immediate issue, but not the full issue. See #40802 for more discussion.

[user202729]

turns out the cause is just that it builds before the commit 3a956e4 , but not after it.

Either way, should be fixed now.