• python (does not work on cygwin32/64)
• normaliz (works on cygwin32/64, ONLY normaliz version 2.7 is compatible with current libraries)
• 4ti2 (works on cygwin32/64, tested with 4ti2 1.6)
• gfan (works on cygwin32/64)
• polymake (does not support cygwin)
• surf/surfer/surfex (not tested yet on cygwin)
• TOPCOM (works on cygwin64, not tested yet on cygwin32, however there's a bug in oldpolymake.lib::triangulations)
• FLINT (works on cygwin32, does not work on cygwin64 due to failing mpir 2.6.0)
• NTL (works on cygwin32/cygwin64, tested with 6.0.0)

ps: 3rd party software used by Singular and Preface