Thanks for testing. Looking at ptestlong_Monterey.log, I see:

1) failures from run-time use of compilers like this:   
  RuntimeError: Command "gcc -bundle -undefined dynamic_lookup -isysroot 
/Library/Developer/CommandLineTools/SDKs/MacOSX12.sdk 
-L/Users/admin/SageMath/Git/sage/local/lib 
-Wl,-rpath,/Users/admin/SageMath/Git/sage/local/lib 
/Users/admin/.sage/temp/MBP16GMS/16939/spyx/_Users_admin__sage_temp_MBP16GMS_16939_tmp_6gfq9l9q_pyx/build/temp.macosx-12-arm64-3.9/Users/admin/.sage/temp/MBP16GMS/16939/spyx/_Users_admin__sage_temp_MBP16GMS_16939_tmp_6gfq9l9q_pyx/_Users_admin__sage_temp_MBP16GMS_16939_tmp_6gfq9l9q_pyx_0.o
 
-L/Users/admin/SageMath/Git/sage/local/lib 
-L/opt/homebrew/Cellar/openblas/0.3.19/lib -L///opt/homebrew/opt/ntl/lib 
-lmpfr -lgmp -lgmpxx -lpari -lm -lec -lgsl -lopenblas -lntl -o 
/Users/admin/.sage/temp/MBP16GMS/16939/spyx/_Users_admin__sage_temp_MBP16GMS_16939_tmp_6gfq9l9q_pyx/_Users_admin__sage_temp_MBP16GMS_16939_tmp_6gfq9l9q_pyx_0.cpython-39-darwin.so"
 
failed with exit status 1
    ld: library not found for -lmpfr

This is tracked in https://trac.sagemath.org/ticket/31348 and can likely be 
worked around by using ". .homebrew-build-env " before running the tests.

2) some numerical tolerances, including

sage -t --long --random-seed=56125665350235692256846696198278705067 
src/sage/functions/error.py
**********************************************************************
File "src/sage/functions/error.py", line 270, in 
sage.functions.error.Function_erf._evalf_
Failed example:
    RealBallField(128)(erf(5))
Expected:
    [0.99999999999846254020557196514981165651 +/- 7.33e-39]
Got:
    [0.99999999999846254020557196514981165651 +/- 6.25e-39]
**********************************************************************




On Thursday, January 20, 2022 at 8:03:10 PM UTC-8 [email protected] wrote:

>
> Here are the results of make ptestlong for an M1 Mac with macOS 12.1.
>
> ----------------------------------------------------------------------
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/sagedoc.py  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/tests/cmdline.py  # 4 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/sageinspect.py  # 35 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/graphs/connectivity.pyx  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/structure/element.pyx  # 43 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/cachefunc.pyx  # 54 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/repl/ipython_extension.py  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/cython.py  # 20 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/parallel/decorate.py  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/env.py  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/features/__init__.py  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/graphs/graph_decompositions/fast_digraph.pyx  # 5 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/rings/complex_arb.pyx  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/superseded.py  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/cpython/cython_metaclass.pyx  # 4 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/rings/polynomial/ore_polynomial_element.pyx  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/ext/memory_allocator.pxd  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/ext/memory_allocator.pyx  # 9 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/structure/factory.pyx  # 8 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/rings/tate_algebra_ideal.pyx  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/arith/long.pxd  # 14 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/cpython/getattr.pyx  # 4 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/lazy_attribute.pyx  # 3 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/docs/instancedoc.pyx  # 4 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/inherit_comparison.pyx  # 5 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/session.pyx  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/rings/integer_fake.pxd  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/misc/nested_class.pyx  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/repl/load.py  # 2 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/symbolic/pynac.pxi  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/cpython/wrapperdescr.pxd  # 6 doctests failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/cpython/string.pyx  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/functions/error.py  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/matrix/matrix_gf2e_dense.pyx  # 1 doctest failed
>
> sage -t --long --random-seed=197037298609633803429304901817476325006 
> src/sage/rings/real_arb.pyx  # 5 doctests failed
>
> ----------------------------------------------------------------------
>
> Total time for all tests: 784.5 seconds
>
>     cpu time: 5621.8 seconds
>
>     cumulative wall time: 6022.8 seconds
>
> Features detected for doctesting: 
> dvipng,ffmpeg,graphviz,imagemagick,pandoc,pdf2svg,sage.combinat,sage.geometry.polyhedron,sage.graphs,sage.plot,sage.rings.number_field,sage.rings.real_double,sage.symbolic,sagemath_doc_html,sphinx
>
> Pytest is not installed, skip checking tests that rely on it.
>
> make: *** [ptestlong] Error 1
>
> Guillermo
>
> On Fri, 21 Jan 2022 at 04:36, Matthias Köppe <[email protected]> wrote:
>
>> Thanks for testing! Glad it works now.
>>
>> On Thursday, January 20, 2022 at 7:25:01 PM UTC-8 [email protected] 
>> wrote:
>>
>>>
>>> You were right:  I had /usr/local/lib -> /opt/homebrew/lib (because I 
>>> tried to brew install apaffenholz/polymake/polymake, which fails in 
>>> Monterey).  After erasing it, ./configure --with-system-openblas followed 
>>> by make succeeds for 9.5.rc3 on an M1 Mac with macOS 12.1.
>>>
>>> Thanks again and sorry for the noise…
>>>
>>> Guillermo
>>>
>>> On Fri, 21 Jan 2022 at 03:51, Matthias Köppe <[email protected]> 
>>> wrote:
>>>
>>>> Might be worth checking if on this machine there is some stuff in 
>>>> /usr/local ...
>>>>
>>>> On Thursday, January 20, 2022 at 5:44:36 PM UTC-8 [email protected] 
>>>> wrote:
>>>>
>>>>>
>>>>> I just got access to an M1 Mac with macOS 12.1 (Monterey), so I tried 
>>>>> 9.5.rc3 with the results given below.
>>>>>
>>>>> I can confirm that on an M1 Mac with macOS 11.6.2 (Big Sur), after 
>>>>> ./configure 
>>>>> --with-system-openblas, make succeeds for 9.5.rc3.
>>>>>
>>>>> Sorry.
>>>>>
>>>>> Guillermo
>>>>>
>>>>> On Fri, 21 Jan 2022 at 02:26, Matthias Köppe <[email protected]> 
>>>>> wrote:
>>>>>
>>>>>> I thought we had solved the problems on M1 already in 
>>>>>> https://trac.sagemath.org/ticket/30592?
>>>>>>
>>>>>> On Thursday, January 20, 2022 at 4:50:29 PM UTC-8 [email protected] 
>>>>>> wrote:
>>>>>>
>>>>>>>
>>>>>>> About building on an M1 Mac with macOS 12.1.
>>>>>>>
>>>>>>> 1)
>>>>>>> After ./configure, make fails to install
>>>>>>>
>>>>>>> * package:         tachyon-0.98.9.p7
>>>>>>> * package:         libhomfly-1.02r6
>>>>>>> * package:         m4ri-20200115
>>>>>>> * package:         openblas-0.3.18
>>>>>>> No logs attached (already known).
>>>>>>>
>>>>>>> 2)
>>>>>>> After ./configure --with-system-openblas, make fails to install
>>>>>>>
>>>>>>> * package:         openblas-0.3.18
>>>>>>>
>>>>>>> * package:         singular-4.2.1p3
>>>>>>> Logs attached.
>>>>>>>
>>>>>>> Guillermo
>>>>>>>
>>>>>>> On Wed, 19 Jan 2022 at 01:05, Volker Braun <[email protected]> 
>>>>>>> wrote:
>>>>>>>
>>>>>>>> As always, you can get the latest beta version from the "develop" 
>>>>>>>> git branch. Alternatively, the self-contained source tarball is at 
>>>>>>>> http://www.sagemath.org/download-latest.html
>>>>>>>>
>>>>>>>> 8ea92d580a (tag: 9.5.rc3, trac/develop) Updated SageMath version to 
>>>>>>>> 9.5.rc3
>>>>>>>> ad7e1731c0 Trac #33200: trying to fix .zenodo.json
>>>>>>>> 809b80c433 Trac #33195: iml: Refresh build scripts with current 
>>>>>>>> autotools
>>>>>>>> 290af2b0c4 Trac #33191: tachyon, primecountpy, libhomfly, m4ri: Fix 
>>>>>>>> build errors on Apple Silicon with homebrew
>>>>>>>> 8e3116e243 Trac #33081: Segmentation fault with integers using musl 
>>>>>>>> libc 1.2.2
>>>>>>>> 33d12f2b66 Trac #32288: add CITATION.cff file for GitHub / zenodo 
>>>>>>>> integration and citation support
>>>>>>>> 8a05f2e79d Trac #29285: Unbreak the build when pyenv is present
>>>>>>>> f9b2db94f6 (tag: 9.5.rc2) Updated SageMath version to 9.5.rc2
>>>>>>>>
>>>>>>>  
>

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