/usr/include/singular/singular/kernel/ is in libsingular4-dev-common 1:4.1.0-p3+ds-2build1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/singular/singular/kernel/GBEngine/
/usr/include/singular/singular/kernel/GBEngine/f5c.h
/usr/include/singular/singular/kernel/GBEngine/f5data.h
/usr/include/singular/singular/kernel/GBEngine/f5gb.h
/usr/include/singular/singular/kernel/GBEngine/f5lists.h
/usr/include/singular/singular/kernel/GBEngine/janet.h
/usr/include/singular/singular/kernel/GBEngine/kInline.h
/usr/include/singular/singular/kernel/GBEngine/khstd.h
/usr/include/singular/singular/kernel/GBEngine/kstd1.h
/usr/include/singular/singular/kernel/GBEngine/kstdfac.h
/usr/include/singular/singular/kernel/GBEngine/kutil.h
/usr/include/singular/singular/kernel/GBEngine/nc.h
/usr/include/singular/singular/kernel/GBEngine/ratgring.h
/usr/include/singular/singular/kernel/GBEngine/ringgb.h
/usr/include/singular/singular/kernel/GBEngine/shiftgb.h
/usr/include/singular/singular/kernel/GBEngine/syz.h
/usr/include/singular/singular/kernel/GBEngine/tgb.h
/usr/include/singular/singular/kernel/GBEngine/tgb_internal.h
/usr/include/singular/singular/kernel/GBEngine/tgbgauss.h
/usr/include/singular/singular/kernel/GBEngine/units.h
/usr/include/singular/singular/kernel/combinatorics/
/usr/include/singular/singular/kernel/combinatorics/hilb.h
/usr/include/singular/singular/kernel/combinatorics/hutil.h
/usr/include/singular/singular/kernel/combinatorics/stairc.h
/usr/include/singular/singular/kernel/digitech.h
/usr/include/singular/singular/kernel/fast_mult.h
/usr/include/singular/singular/kernel/fglm/
/usr/include/singular/singular/kernel/fglm/fglm.h
/usr/include/singular/singular/kernel/fglm/fglmgauss.h
/usr/include/singular/singular/kernel/fglm/fglmvec.h
/usr/include/singular/singular/kernel/groebner_walk/
/usr/include/singular/singular/kernel/groebner_walk/walkMain.h
/usr/include/singular/singular/kernel/groebner_walk/walkProc.h
/usr/include/singular/singular/kernel/groebner_walk/walkSupport.h
/usr/include/singular/singular/kernel/ideals.h
/usr/include/singular/singular/kernel/linear_algebra/
/usr/include/singular/singular/kernel/linear_algebra/Cache.h
/usr/include/singular/singular/kernel/linear_algebra/CacheImplementation.h
/usr/include/singular/singular/kernel/linear_algebra/Minor.h
/usr/include/singular/singular/kernel/linear_algebra/MinorInterface.h
/usr/include/singular/singular/kernel/linear_algebra/MinorProcessor.h
/usr/include/singular/singular/kernel/linear_algebra/eigenval.h
/usr/include/singular/singular/kernel/linear_algebra/interpolation.h
/usr/include/singular/singular/kernel/linear_algebra/linearAlgebra.h
/usr/include/singular/singular/kernel/linear_algebra/minpoly.h
/usr/include/singular/singular/kernel/maps/
/usr/include/singular/singular/kernel/maps/fast_maps.h
/usr/include/singular/singular/kernel/maps/find_perm.h
/usr/include/singular/singular/kernel/maps/gen_maps.h
/usr/include/singular/singular/kernel/mod2.h
/usr/include/singular/singular/kernel/numeric/
/usr/include/singular/singular/kernel/numeric/mpr_base.h
/usr/include/singular/singular/kernel/numeric/mpr_inout.h
/usr/include/singular/singular/kernel/numeric/mpr_numeric.h
/usr/include/singular/singular/kernel/oswrapper/
/usr/include/singular/singular/kernel/oswrapper/feread.h
/usr/include/singular/singular/kernel/oswrapper/rlimit.h
/usr/include/singular/singular/kernel/oswrapper/timer.h
/usr/include/singular/singular/kernel/polys.h
/usr/include/singular/singular/kernel/preimage.h
/usr/include/singular/singular/kernel/spectrum/
/usr/include/singular/singular/kernel/spectrum/GMPrat.h
/usr/include/singular/singular/kernel/spectrum/kmatrix.h
/usr/include/singular/singular/kernel/spectrum/multicnt.h
/usr/include/singular/singular/kernel/spectrum/npolygon.h
/usr/include/singular/singular/kernel/spectrum/semic.h
/usr/include/singular/singular/kernel/spectrum/spectrum.h
/usr/include/singular/singular/kernel/spectrum/splist.h
/usr/include/singular/singular/kernel/structs.h