diff --git a/Makefile b/Makefile
index 414398ddf0d..257e3517bb1 100644
--- a/Makefile
+++ b/Makefile
@@ -80,42 +80,6 @@ download:
 dist: build/make/Makefile
 	./sage --sdist
 
-pypi-sdists: sage_setup
-	./sage --sh build/pkgs/sage_conf/spkg-src
-	./sage --sh build/pkgs/sage_sws2rst/spkg-src
-	./sage --sh build/pkgs/sage_docbuild/spkg-src
-	./sage --sh build/pkgs/sage_setup/spkg-src
-	./sage --sh build/pkgs/sagelib/spkg-src
-	./sage --sh build/pkgs/sagemath_objects/spkg-src
-	./sage --sh build/pkgs/sagemath_categories/spkg-src
-	./sage --sh build/pkgs/sagemath_environment/spkg-src
-	./sage --sh build/pkgs/sagemath_repl/spkg-src
-	@echo "Built sdists are in upstream/"
-
-# Ensuring wheels are present, even for packages that may have been installed
-# as editable. Until we have better uninstallation of script packages, we
-# just remove the timestamps, which will lead to rebuilds of the packages.
-PYPI_WHEEL_PACKAGES = sage_sws2rst sage_setup sagemath_environment sagemath_objects sagemath_repl sagemath_categories
-pypi-wheels:
-	for a in $(PYPI_WHEEL_PACKAGES); do \
-	    rm -f venv/var/lib/sage/installed/$$a-*; \
-	done
-	for a in $(PYPI_WHEEL_PACKAGES); do \
-	    $(MAKE) SAGE_EDITABLE=no SAGE_WHEELS=yes $$a; \
-	done
-	@echo "Built wheels are in venv/var/lib/sage/wheels/"
-
-# sage_docbuild is here, not in PYPI_WHEEL_PACKAGES, because it depends on sagelib
-WHEEL_PACKAGES = $(PYPI_WHEEL_PACKAGES) sage_conf sagelib sage_docbuild
-wheels:
-	for a in $(WHEEL_PACKAGES); do \
-	    rm -f venv/var/lib/sage/installed/$$a-*; \
-	done
-	for a in $(WHEEL_PACKAGES); do \
-	    $(MAKE) SAGE_EDITABLE=no SAGE_WHEELS=yes $$a; \
-	done
-	@echo "Built wheels are in venv/var/lib/sage/wheels/"
-
 ###############################################################################
 # Cleaning up
 ###############################################################################
@@ -380,7 +344,6 @@ list:
 	@$(MAKE) --silent -f build/make/Makefile SAGE_PKGCONFIG=dummy $@
 
 .PHONY: default build dist install micro_release \
-	pypi-sdists pypi-wheels wheels \
 	misc-clean bdist-clean distclean bootstrap-clean maintainer-clean \
 	test check testoptional testall testlong testoptionallong testallong \
 	ptest ptestoptional ptestall ptestlong ptestoptionallong ptestallong \
diff --git a/build/make/Makefile.in b/build/make/Makefile.in
index e971def2416..e4957c4d481 100644
--- a/build/make/Makefile.in
+++ b/build/make/Makefile.in
@@ -128,7 +128,23 @@ PIP_PACKAGES = @SAGE_PIP_PACKAGES@
 # Packages that use the 'script' package build rules
 SCRIPT_PACKAGES = @SAGE_SCRIPT_PACKAGES@
 
-
+# Packages for which we build wheels for PyPI
+PYPI_WHEEL_PACKAGES =				\
+	sage_sws2rst				\
+	sage_setup				\
+	sagemath_environment			\
+	sagemath_objects			\
+	sagemath_repl				\
+	sagemath_categories
+
+# sage_docbuild is here, not in PYPI_WHEEL_PACKAGES, because it depends on sagelib
+WHEEL_PACKAGES = $(PYPI_WHEEL_PACKAGES)		\
+	sage_conf				\
+	sagelib					\
+	sage_docbuild
+
+# Packages for which build sdists for PyPI
+PYPI_SDIST_PACKAGES = $(WHEEL_PACKAGES)
 
 # Generate the actual inst_<pkgname> variables; for each package that is
 # actually built this generates a line like:
@@ -198,6 +214,7 @@ SAGE_I_TARGETS = sagelib doc
 # Tell make not to look for files with these names:
 .PHONY: all all-sage all-toolchain all-build all-sageruntime \
 	all-start build-start base toolchain toolchain-deps base-toolchain \
+	pypi-sdists pypi-wheels wheels \
 	sagelib \
 	doc doc-html doc-html-jsmath doc-html-mathjax doc-pdf \
 	doc-uninstall \
@@ -418,6 +435,26 @@ list-broken-packages: auditwheel_or_delocate
 	    echo >&2 "$$fix_broken_packages"; \
 	fi
 
+pypi-sdists: $(PYPI_SDIST_PACKAGES:%=%-sdist)
+	@echo "Built sdists are in upstream/"
+
+# Ensuring wheels are present, even for packages that may have been installed
+# as editable. Until we have better uninstallation of script packages, we
+# just remove the timestamps, which will lead to rebuilds of the packages.
+PYPI_WHEEL_PACKAGES = sage_sws2rst sage_setup sagemath_environment sagemath_objects sagemath_repl sagemath_categories
+pypi-wheels:
+	for a in $(PYPI_WHEEL_PACKAGES); do \
+	    rm -f venv/var/lib/sage/installed/$$a-*; \
+	done
+	$(MAKE_REC) SAGE_EDITABLE=no SAGE_WHEELS=yes $(PYPI_WHEEL_PACKAGES)
+	@echo "Built wheels are in venv/var/lib/sage/wheels/"
+
+wheels:
+	for a in $(WHEEL_PACKAGES); do \
+	    rm -f venv/var/lib/sage/installed/$$a-*; \
+	done
+	$(MAKE_REC) SAGE_EDITABLE=no SAGE_WHEELS=yes $(WHEEL_PACKAGES)
+	@echo "Built wheels are in venv/var/lib/sage/wheels/"
 
 #==============================================================================
 # Setting SAGE_CHECK... variables
@@ -711,6 +748,13 @@ $(1)-uninstall: $(1)-$(4)-uninstall
 
 $(1)-clean: $(1)-uninstall
 
+$(1)-sdist: FORCE python_build sage_setup cython
+	$(AM_V_at) cd '$$(SAGE_ROOT)' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-src-env-config' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-env-config' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-env' && \
+		'$$(SAGE_ROOT)/build/pkgs/$(1)/spkg-src'
+
 # Recursive tox invocation (note - we do not set the environment here).
 # Setting SAGE_SPKG_WHEELS is for the benefit of sagelib's tox.ini
 $(1)-tox-%: FORCE
diff --git a/build/pkgs/sage_conf/spkg-src b/build/pkgs/sage_conf/spkg-src
index af6e8b16342..c2fa51df092 100755
--- a/build/pkgs/sage_conf/spkg-src
+++ b/build/pkgs/sage_conf/spkg-src
@@ -16,4 +16,7 @@ fi
 set -e
 
 cd pkgs/sage-conf_pypi
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sage_docbuild/spkg-src b/build/pkgs/sage_docbuild/spkg-src
index dc1ba829b3a..b21f8f015c8 100755
--- a/build/pkgs/sage_docbuild/spkg-src
+++ b/build/pkgs/sage_docbuild/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sage_docbuild
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sage_setup/spkg-src b/build/pkgs/sage_setup/spkg-src
index e1bcbdaabdb..1b137206a5c 100755
--- a/build/pkgs/sage_setup/spkg-src
+++ b/build/pkgs/sage_setup/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sage_setup
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sage_sws2rst/spkg-src b/build/pkgs/sage_sws2rst/spkg-src
index 0da7d0cd24c..5a2a6d464dd 100755
--- a/build/pkgs/sage_sws2rst/spkg-src
+++ b/build/pkgs/sage_sws2rst/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sage_sws2rst
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sagelib/spkg-src b/build/pkgs/sagelib/spkg-src
index db4e2682ba1..aa97a393b0b 100755
--- a/build/pkgs/sagelib/spkg-src
+++ b/build/pkgs/sagelib/spkg-src
@@ -4,7 +4,7 @@
 # This script is not used during build.
 #
 # HOW TO MAKE THE TARBALL:
-# ./sage --sh build/pkgs/sagelib/spkg-src
+# make python_build && ./sage --sh build/pkgs/sagelib/spkg-src
 
 if [ -z "$SAGE_ROOT" ] ; then
     echo >&2 "Error - SAGE_ROOT undefined ... exiting"
@@ -18,4 +18,8 @@ set -e
 cd "$SAGE_ROOT"/build/pkgs/sagelib
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sagemath_categories/spkg-src b/build/pkgs/sagemath_categories/spkg-src
index 327d51651b9..e7c48e54193 100755
--- a/build/pkgs/sagemath_categories/spkg-src
+++ b/build/pkgs/sagemath_categories/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sagemath_categories
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sagemath_environment/spkg-src b/build/pkgs/sagemath_environment/spkg-src
index 4e2b7503da2..2d5b3aafde7 100755
--- a/build/pkgs/sagemath_environment/spkg-src
+++ b/build/pkgs/sagemath_environment/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sagemath_environment
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sagemath_objects/spkg-src b/build/pkgs/sagemath_objects/spkg-src
index 68719fae1b6..f46ddc2bd3b 100755
--- a/build/pkgs/sagemath_objects/spkg-src
+++ b/build/pkgs/sagemath_objects/spkg-src
@@ -18,4 +18,8 @@ set -e
 cd build/pkgs/sagemath_objects
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/build/pkgs/sagemath_repl/spkg-src b/build/pkgs/sagemath_repl/spkg-src
index b20ea463784..2ef7b673696 100755
--- a/build/pkgs/sagemath_repl/spkg-src
+++ b/build/pkgs/sagemath_repl/spkg-src
@@ -18,4 +18,7 @@ set -e
 cd build/pkgs/sagemath_repl
 
 cd src
-python3 -u setup.py --no-user-cfg sdist --dist-dir "$SAGE_DISTFILES"
+# Get rid of old *.egg-info/SOURCES.txt
+rm -Rf *.egg-info
+
+python3 -m build --sdist --no-isolation --skip-dependency-check --outdir "$SAGE_DISTFILES"
diff --git a/pkgs/sagemath-objects/setup.py b/pkgs/sagemath-objects/setup.py
index 907cabef839..ad114fa0de1 100644
--- a/pkgs/sagemath-objects/setup.py
+++ b/pkgs/sagemath-objects/setup.py
@@ -14,41 +14,28 @@
 import sys
 sys.path.insert(0, os.path.dirname(__file__))
 
-if len(sys.argv) > 1 and (sys.argv[1] == "sdist" or sys.argv[1] == "egg_info"):
-    sdist = True
-else:
-    sdist = False
-
-if sdist:
-    cmdclass = {}
-else:
-    from sage_setup.excepthook import excepthook
-    sys.excepthook = excepthook
-
-    from sage_setup.setenv import setenv
-    setenv()
-
-    import sage.env
-    sage.env.default_required_modules = sage.env.default_optional_modules = ()
-
-    from sage_setup.command.sage_build_cython import sage_build_cython
-    from sage_setup.command.sage_build_ext import sage_build_ext
-
-    cmdclass = dict(build_cython=sage_build_cython,
-                    build_ext=sage_build_ext)
-
-if sdist:
-    python_packages = []
-    python_modules = []
-    cython_modules = []
-else:
-    from sage_setup.find import find_python_sources
-    python_packages, python_modules, cython_modules = find_python_sources(
-        '.', ['sage'])   # for now, we do the filtering using MANIFEST
-
-    log.warn('python_packages = {0}'.format(python_packages))
-    log.warn('python_modules = {0}'.format(python_modules))
-    log.warn('cython_modules = {0}'.format(cython_modules))
+from sage_setup.excepthook import excepthook
+sys.excepthook = excepthook
+
+from sage_setup.setenv import setenv
+setenv()
+
+import sage.env
+sage.env.default_required_modules = sage.env.default_optional_modules = ()
+
+from sage_setup.command.sage_build_cython import sage_build_cython
+from sage_setup.command.sage_build_ext import sage_build_ext
+
+cmdclass = dict(build_cython=sage_build_cython,
+                build_ext=sage_build_ext)
+
+from sage_setup.find import find_python_sources
+python_packages, python_modules, cython_modules = find_python_sources(
+    '.', ['sage'])   # for now, we do the filtering using MANIFEST
+
+log.warn('python_packages = {0}'.format(python_packages))
+log.warn('python_modules = {0}'.format(python_modules))
+log.warn('cython_modules = {0}'.format(cython_modules))
 
 setup(
     cmdclass = cmdclass,
diff --git a/pkgs/sagemath-standard/setup.py b/pkgs/sagemath-standard/setup.py
index d03b63400f6..975f89b5905 100755
--- a/pkgs/sagemath-standard/setup.py
+++ b/pkgs/sagemath-standard/setup.py
@@ -39,28 +39,20 @@
 ### Configuration
 #########################################################
 
-if len(sys.argv) > 1 and (sys.argv[1] in ["sdist", "egg_info", "dist_info"]):
-    sdist = True
-else:
-    sdist = False
+from sage_setup.excepthook import excepthook
+sys.excepthook = excepthook
 
-if sdist:
-    cmdclass = {}
-else:
-    from sage_setup.excepthook import excepthook
-    sys.excepthook = excepthook
+from sage_setup.setenv import setenv
+setenv()
 
-    from sage_setup.setenv import setenv
-    setenv()
+from sage_setup.command.sage_build_cython import sage_build_cython
+from sage_setup.command.sage_build_ext import sage_build_ext
+from sage_setup.command.sage_install import sage_develop, sage_install_and_clean
 
-    from sage_setup.command.sage_build_cython import sage_build_cython
-    from sage_setup.command.sage_build_ext import sage_build_ext
-    from sage_setup.command.sage_install import sage_develop, sage_install_and_clean
-
-    cmdclass = dict(build_cython=sage_build_cython,
-                    build_ext=sage_build_ext,
-                    develop=sage_develop,
-                    install=sage_install_and_clean)
+cmdclass = dict(build_cython=sage_build_cython,
+                build_ext=sage_build_ext,
+                develop=sage_develop,
+                install=sage_install_and_clean)
 
 #########################################################
 ### Testing related stuff
@@ -75,41 +67,39 @@
 ### Discovering Sources
 #########################################################
 
-if sdist:
-    # No need to compute distributions.  This avoids a dependency on Cython
-    # just to make an sdist.
-    distributions = None
-    python_packages = []
-    python_modules = []
-    cython_modules = []
-else:
+if any(x in sys.argv
+       for x in ['build', 'bdist_wheel', 'install']):
     log.info("Generating auto-generated sources")
     from sage_setup.autogen import autogen_all
     autogen_all()
 
-    # TODO: This should be quiet by default
-    print("Discovering Python/Cython source code....")
-    t = time.time()
-    from sage.misc.package import is_package_installed_and_updated
-    distributions = ['']
-    optional_packages_with_extensions = ['mcqd', 'bliss', 'tdlib',
-                                         'coxeter3', 'sirocco', 'meataxe']
-    distributions += ['sagemath-{}'.format(pkg)
-                      for pkg in optional_packages_with_extensions
-                      if is_package_installed_and_updated(pkg)]
-    log.warn('distributions = {0}'.format(distributions))
-    from sage_setup.find import find_python_sources
-    python_packages, python_modules, cython_modules = find_python_sources(
-        SAGE_SRC, ['sage'], distributions=distributions)
-
-    log.debug('python_packages = {0}'.format(python_packages))
-    print("Discovered Python/Cython sources, time: %.2f seconds." % (time.time() - t))
+# TODO: This should be quiet by default
+print("Discovering Python/Cython source code....")
+t = time.time()
+distributions = ['']
+from sage.misc.package import is_package_installed_and_updated
+optional_packages_with_extensions = ['mcqd', 'bliss', 'tdlib',
+                                     'coxeter3', 'sirocco', 'meataxe']
+distributions += ['sagemath-{}'.format(pkg)
+                  for pkg in optional_packages_with_extensions
+                  if is_package_installed_and_updated(pkg)]
+log.warn('distributions = {0}'.format(distributions))
+from sage_setup.find import find_python_sources, find_extra_files
+python_packages, python_modules, cython_modules = find_python_sources(
+    SAGE_SRC, ['sage'], distributions=distributions)
+
+log.debug('python_packages = {0}'.format(python_packages))
+log.debug('python_modules = {0}'.format(python_modules))
+log.debug('cython_modules = {0}'.format(cython_modules))
+
+print("Discovered Python/Cython sources, time: %.2f seconds." % (time.time() - t))
 
 #########################################################
 ### Distutils
 #########################################################
 
 code = setup(
-      packages = python_packages,
-      cmdclass = cmdclass,
-      ext_modules = cython_modules)
+      packages=python_packages,
+      cmdclass=cmdclass,
+      ext_modules=cython_modules,
+)
diff --git a/src/MANIFEST.in b/src/MANIFEST.in
index 3a63d07fc32..cf90162a5ef 100644
--- a/src/MANIFEST.in
+++ b/src/MANIFEST.in
@@ -1,3 +1,7 @@
+include VERSION.txt
+
+global-include *.pxi *.pxd *.h *.hpp
+
 prune sage/ext/interpreters   # In particular, __init__.py must not be present in the distribution; or sage_setup.autogen.interpreters.rebuild will not generate the code
 prune sage_setup
 prune sage_docbuild
@@ -36,6 +40,10 @@ include sage/stats/distributions/dgs_bern.c
 include sage/stats/distributions/dgs_gauss_dp.c
 include sage/stats/distributions/dgs_gauss_mp.c
 include sage/symbolic/ginac/*.cpp
+# Also actual C++ source files.
+include sage/geometry/triangulation/triangulations.cc
+include sage/geometry/triangulation/data.cc
+include sage/geometry/triangulation/functions.cc
 
 global-exclude __pycache__
 global-exclude *.py[co]
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index b1f5b45fe4a..76fb791abe0 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -52,7 +52,6 @@ class initialization directly.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from typing_extensions import final
 from sage.arith.misc import is_prime
 from sage.misc.lazy_import import lazy_import
 lazy_import('sage.calculus.functions', 'jacobian')