/usr/include/singular/singular/polys/ is in libsingular4-dev-common 1:4.0.3-p3+ds-5.
This file is owned by root:root, with mode 0o755.
..
/usr/include/singular/singular/polys/PolyEnumerator.h
/usr/include/singular/singular/polys/clapconv.h
/usr/include/singular/singular/polys/clapsing.h
/usr/include/singular/singular/polys/coeffrings.h
/usr/include/singular/singular/polys/ext_fields/
/usr/include/singular/singular/polys/ext_fields/algext.h
/usr/include/singular/singular/polys/ext_fields/transext.h
/usr/include/singular/singular/polys/flintconv.h
/usr/include/singular/singular/polys/kbuckets.h
/usr/include/singular/singular/polys/matpol.h
/usr/include/singular/singular/polys/mod_raw.h
/usr/include/singular/singular/polys/monomials/
/usr/include/singular/singular/polys/monomials/maps.h
/usr/include/singular/singular/polys/monomials/monomials.h
/usr/include/singular/singular/polys/monomials/p_polys.h
/usr/include/singular/singular/polys/monomials/ring.h
/usr/include/singular/singular/polys/nc/
/usr/include/singular/singular/polys/nc/gb_hack.h
/usr/include/singular/singular/polys/nc/nc.h
/usr/include/singular/singular/polys/nc/ncSACache.h
/usr/include/singular/singular/polys/nc/ncSAFormula.h
/usr/include/singular/singular/polys/nc/ncSAMult.h
/usr/include/singular/singular/polys/nc/sca.h
/usr/include/singular/singular/polys/nc/summator.h
/usr/include/singular/singular/polys/operations/
/usr/include/singular/singular/polys/operations/pShallowCopyDelete.h
/usr/include/singular/singular/polys/prCopy.h
/usr/include/singular/singular/polys/sbuckets.h
/usr/include/singular/singular/polys/simpleideals.h
/usr/include/singular/singular/polys/sparsmat.h
/usr/include/singular/singular/polys/templates/
/usr/include/singular/singular/polys/templates/p_MemAdd.h
/usr/include/singular/singular/polys/templates/p_MemCmp.h
/usr/include/singular/singular/polys/templates/p_Procs.h
/usr/include/singular/singular/polys/weight.h