Here is a list (in-progress) of the things needs to get Sage to build (and pass most tests) on Cygwin:

== Cygwin Prerequisites ==

These Cygwin packages need to be installed in order for the Sage build to complete.

* file, liblapack, liblapack0, liblapack-devel

* Prebuilt sage binaries for cygwin are here:  http://sage.math.washington.edu/home/wstein/binaries/cygwin/


== Doctest Tickets ==

 * #9162 -- pynac.pyx use double precision special functions instead of long double (REVISITED)

 * #9163 -- output of a subtle test in expect.py differs slightly on cygwin

 * #9165 -- lcalc does not work for elliptic curves on cygwin

 * #9166 -- sympow does not work on cygwin

 * #9167 -- importing sage.libs.ecl yields a "no such process" error

 * #9168 --  ratpoints does not work correctly

 * #9169 -- a cachefunc.py doctest hangs seemingly forever

 * #9170 -- get_memory_usage isn't implemented, e.g., because there's no top

 * #9171 -- some test failures in sagedoc.py

 * #9172 -- numerical noise in sage/rings/integer.pyx

 * #9173 -- BSD.py tests behave differently on cygwin, so need to be written to reflect that

 * #9174 -- robert miller's 2-descent is completely broken on cygwin

 * #9176 -- various heegner_index errors involving interval arithmetic on cygwin



== Build Tickets ==

 * #9154 -- BoehmGC again!

 * #9146 -- cygwin: gd doesn't correctly link in libpng with sage-4.4.3.

 * #8257: gd needs a better version of expr

 * #7319: gdmodule fails

 * #7321: numpy fails to build on cygwin due to not using the correct fortran compiler

 * #8780: Add cephes spkg for Cygwin (provides complex.h amongst other things)

 * #8192: PolyBoRi needs png12 and z to build on Cygwin.

 * #8782: pari does not work under Cygwin

 * #8907: Python should be build with enable-shared

 * #8278 / #6456: cvxopt does not work in Cygwin

 * #9050: libntl.dll should be libntl.dll.a

 * #8542 / #8903: Pynac needs to use a function pointer table.

 * #7337: PolyBoRi fails to build on cygwin
 
 * libflint.dll needs to be libflint.so, or polynomial_integer_dense_flint.pyx needs to know to use the .dll (maybe not a real issue, let's wait an see on this one).

 * Use ECL from #8951 and Maxima from #8731

 * #8642: port detection for the notebook does not work in Cygwin

 * #8855: sage-env needs to be updated for Cygwin

 * #8853: fix M_PI_4 in complex_double on Cygwin

 * #8852: minor doctest fix in fast_eval.pyx for Cygwin

 * #8850: Cython should link against BLAS instead of ATLAS on Cygwin

 * #8849: the palp interface throws a (harmless?) OSError on Cygwin

 * #8848, #8847, #8846, #8845, #8844, #8843

 * #9067: boehm_gc (still) fails to build on Cygwin


== Possible issue with Python 2.6 ==

http://groups.google.com/group/sage-windows/browse_thread/thread/88499b995a22ecc1

(I had no problems with that thus far in Vista Premium 32-bit -Alec Mihailovs)

(Alec - Win7 has a newer codebase, so this is not really a proof that we need not worry --- I think we really need to. Dmitrii)