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
 * #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 ==

 * #8278 / #6456: cvxopt does not work in Cygwin
 * #11119: ECL 11.1.1 fails on Cygwin
 * #9154: BoehmGC again! (needs review)
 * #10247: Sage 4.6 has PARI problems on Cygwin
 * #10240: pari-2.4.3.svn-12577.p9 incorrectly checks for the shared library on Cygwin
 * libblas.dll.a is not copied to $SAGE_LOCAL/lib when ATLAS is "installed"
 * gmp and pari are linked in the wrong order in c_lib
 * Add "#include <time.h> needs to be added to sage/combinat/partitions_c.cc
 * Add "#include <time.h>" to src/Singular/Minor.h the in the Singular spkg
 * Add gmp to the libaries for sage/combinat/combinat_cython.pyx and sage/geometry/toric_lattice_element.pyx


== Closed ==

 * #9845: lcalc doesn't build on cygwin due to missing time.h include
 * #9776: Cygwin: GLPK extension module needs to be more explicit in its linking (positive review)
 * #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
 * #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).
 * #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
 * #9166 -- sympow does not work on cygwin (This should be fixed by the patches made for Solaris x86 - see #9703)

== 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)