/usr/lib/x86_64-linux-gnu/libsingular-polys.so is in libsingular4-dev 1:4.0.3-p3+ds-5.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libsingular-polys-4.0.3.so
/usr/lib/x86_64-linux-gnu/libsingular-polys-4.0.3.so