You can probably eliminate some of the doctest errors with the following 
hack, which may not be the right way to proceed, but at least for me it 
allows doctesting to complete. Some of your other errors may be caused by 
using Python 3.9, and people are working on fixing those.

diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py
index 4e1a6b32e4..bfb7f36940 100644
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -40,6 +40,7 @@ optional_regex = re.compile(r'(arb216|arb218|py2|py3|long 
time|not implemented|n
 # which has not been patched, we need to ignore that message.
 # See :trac:`29317`.
 glpk_simplex_warning_regex = re.compile(r'(Long-step dual simplex will be 
used)')
+big_sur_warning_regex = re.compile(r'ld: warning: dylib.*was built for 
newer macOS version .* than being linked.*')
 find_sage_prompt = re.compile(r"^(\s*)sage: ", re.M)
 find_sage_continuation = re.compile(r"^(\s*)\.\.\.\.:", re.M)
 find_python_continuation = re.compile(r"^(\s*)\.\.\.([^\.])", re.M)
@@ -1087,6 +1088,7 @@ class SageOutputChecker(doctest.OutputChecker):
         """
         got = self.human_readable_escape_sequences(got)
         got = glpk_simplex_warning_regex.sub('', got)
+        got = big_sur_warning_regex.sub('', got)
         if isinstance(want, MarkedOutput):
             if want.random:
                 return True


On Tuesday, November 17, 2020 at 1:33:26 AM UTC-8 Andrew wrote:

> Just to confirm, I was able to compile 9.3.beta1 on macosx 10.0.1 running 
> xcode 12.2 with homebrew.
>
> The following doctests failed with `make ptestlong`:
>
> sage -t --long --random-seed=0 src/sage/misc/sagedoc.py  # 1 doctest failed
> sage -t --long --random-seed=0 src/sage/tests/cmdline.py  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/structure/element.pyx  # 8 
> doctests failed
> sage -t --long --random-seed=0 src/sage/misc/sageinspect.py  # 11 doctests 
> failed
> sage -t --long --random-seed=0 src/sage/functions/other.py  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/misc/cachefunc.pyx  # 6 doctests 
> failed
> sage -t --long --random-seed=0 src/sage/misc/cython.py  # 10 doctests 
> failed
> sage -t --long --random-seed=0 src/sage/graphs/connectivity.pyx  # 2 
> doctests failed
> sage -t --long --random-seed=0 src/sage/repl/ipython_extension.py  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/parallel/decorate.py  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/ext/memory_allocator.pxd  # 3 
> doctests failed
> sage -t --long --random-seed=0 src/sage/ext/memory_allocator.pyx  # 3 
> doctests failed
> sage -t --long --random-seed=0 src/sage/arith/long.pxd  # 2 doctests failed
> sage -t --long --random-seed=0 src/sage/cpython/cython_metaclass.pyx  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/misc/superseded.py  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/cpython/getattr.pyx  # 2 doctests 
> failed
> sage -t --long --random-seed=0 src/sage/structure/factory.pyx  # 2 
> doctests failed
> sage -t --long --random-seed=0 src/sage/misc/lazy_attribute.pyx  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/misc/inherit_comparison.pyx  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/rings/integer_fake.pxd  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/misc/session.pyx  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/docs/instancedoc.pyx  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/repl/preparse.py  # 12 doctests 
> failed
> sage -t --long --random-seed=0 src/sage/cpython/wrapperdescr.pxd  # 1 
> doctest failed
> sage -t --long --random-seed=0 src/sage/misc/nested_class.pyx  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/cpython/string.pyx  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/misc/gperftools.py  # 1 doctest 
> failed
> sage -t --long --random-seed=0 src/sage/rings/tate_algebra_ideal.pyx  # 2 
> doctests failed
>
> but the most amusing failure was at the end:
>
> Doctests interrupted: 2791/4216 files tested
> ----------------------------------------------------------------------
> Total time for all tests: 4482.7 seconds
>     cpu time: 10717.5 seconds
>     cumulative wall time: 13159.6 seconds
> Traceback (most recent call last):
> ...
> OSError: [Errno 24] Too many open files
> make: *** [ptestlong] Error 1
>
> That sage is compiling with the just released version of macosx and the 
> latest xcode I think that this is a win.
> On Tuesday, 17 November 2020 at 5:11:16 pm UTC+11 Andrew wrote:
>
>> Thanks very much for this Matthias. This is almost certainly my problem 
>> -- and I have to confess to user error as this was a hack I put in at one 
>> point to get around problems with an xcode update. I have deleted a bunch 
>> of spurious links like these and am now recompiling. It has already gotten 
>> much further than before. Ih particular, givaro now compiles. So I am 
>> optimistic that it will finish now.
>>
>> Thank you again -- and DIma and John -- for your help!
>> Andrew
>>
>> On Tuesday, 17 November 2020 at 4:16:35 pm UTC+11 Matthias Koeppe wrote:
>>
>>> According to your log, you seem to have /usr/local/include/stdlib.h 
>>> and /usr/local/include/math.h -- which seem to be breaking your giac build. 
>>> This seems nonstandard.
>>>
>>>
>>>
>>> On Sunday, November 15, 2020 at 9:23:40 PM UTC-8 Andrew wrote:
>>>
>>>> Thanks for this John. Did you do anything special to compile sage with 
>>>> big sur? I just tried:
>>>>
>>>> make distclean && source .homebrew-build-env && ./configure 
>>>> --with-system-gfortran=no --with-system-openblas=no --with-system-gmp=no 
>>>> && 
>>>> make
>>>>
>>>> but the build fails with:
>>>>
>>>> Error building Sage.
>>>>
>>>> The following package(s) may have failed to build (not necessarily
>>>> during this run of 'make all-start'):
>>>>
>>>> * package:         givaro-4.1.1
>>>>   last build time: 16 Nov 14:19
>>>>   log file:        /usr/local/src/sage/logs/pkgs/givaro-4.1.1.log
>>>>   build directory: 
>>>> /usr/local/src/sage/local/var/tmp/sage/build/givaro-4.1.1
>>>>
>>>> This is probably not related to 9.3.beta1 as sage has been failing to 
>>>> build, with givaro giving an error, on this laptop since 9.1. If anyone 
>>>> has 
>>>> any ideas as to how I might fix this I'd be grateful. I have tried 
>>>> deleting 
>>>> all of the homebrew packages and reinstalling. completely removing xcode 
>>>> and reinstalling, playing with the compilation switches, ... 
>>>>
>>>> In case anyone has time to look at this, here is my install.log.gz 
>>>> <https://www.maths.usyd.edu.au/u/mathas/install.log.gz> file . Here is 
>>>> my list of brew packages:
>>>> adns eigen gmp libdvdcss libvpx openexr r tkdiff
>>>> alluxio ffmpeg gnu-getopt libevent libyaml openjpeg rav1e unbound
>>>> aom fish      gnu-sed libffi little-cms2 openssl@1.1 readline unrar
>>>> arb        flac gnupg libgcrypt lua opus rsync vtk
>>>> aspell flint gnutls libgpg-error lz4 p11-kit rtmpdump webkit2png
>>>> autoconf fontconfig gobject-introspection libheif lzo p7zip rubberband 
>>>> webp
>>>> automake freetype gpatch libidn2 macvim pandoc ruby wget
>>>> bash frei0r graphite2 libksba make pari sass x264
>>>> bash-completion fribidi gsl liblqr metis pcre sdl2 x265
>>>> bdw-gc gawk guile libmpc mpfi pcre2 shared-mime-info xmlto
>>>> boost gcc harfbuzz libogg mpfr perl sip xvid
>>>> cairo gd hdf5 libomp netcdf pinentry snappy xxhash
>>>> ceres-solver gdbm icu4c libpng nettle pixman speex xz
>>>> cimg gettext ilmbase libsamplerate ninja pkg-config sqlite yarn
>>>> cmake gflags imagemagick libsndfile node poppler srt yasm
>>>> coreutils ghostscript isl libsoxr npth popt suite-sparse zeromq
>>>> cscope giflib jpeg libtasn1 nspr ppl swig zlib
>>>> dart git lame libtiff nss protobuf szip zstd
>>>> dav1d git-extras leptonica libtool ntl pyqt tbb
>>>> djvu2pdf git-lfs libass libunistring numpy python@3.8 tesseract
>>>> djvulibre glib libassuan libusb openblas python@3.9 texinfo
>>>> docbook glog libbluray libvidstab opencore-amr qpdf the_silver_searcher
>>>> docbook-xsl glpk libde265 libvorbis opencv qt theora
>>>> font-firacode-nerd-font                             gimp                
>>>>                                 gitup                                      
>>>>          pdf-images
>>>>
>>>> Andrew
>>>>
>>>

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