Merge tag '9.7.beta3' into t/28925/modify_find_python_sources__clean_…

…stale_files_to_support_modularization_of_sagelib_by_native_namespace_packages__pep_420_ SageMath version 9.7.beta3, Release Date: 2022-06-19
sagemath · Jun 25, 2022 · dd2c525 · dd2c525
2 parents 81237e1 + f8df808
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diff --git a/.github/workflows/tox-experimental.yml b/.github/workflows/tox-experimental.yml
@@ -38,10 +38,7 @@ jobs:
       fail-fast: false
       max-parallel: 6
       matrix:
-        # This list is different from the one in tox.yml:
-        # Trac #31526 switches gcc 4.x-based distributions to using the gcc_spkg configuration factor
-        # Trac #32281 removes gcc 4.x-based distributions whose binutils are unusable
-        tox_system_factor: [ubuntu-xenial, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy, debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-18, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2. linuxmint-20.3, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36,  centos-7-gcc_spkg, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, slackware-14.2, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386-gcc_spkg]
+        tox_system_factor: [gitpod, ubuntu-trusty-toolchain-gcc_9, ubuntu-xenial-toolchain-gcc_9, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy, ubuntu-kinetic, debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2, linuxmint-20.3, linuxmint-21, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36, fedora-37, centos-7-devtoolset-gcc_11, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386-devtoolset-gcc_11]
         tox_packages_factor: [maximal]
         targets_pattern: [0-g, h-o, p, q-z]
     env:

diff --git a/.github/workflows/tox-optional.yml b/.github/workflows/tox-optional.yml
@@ -38,10 +38,7 @@ jobs:
       fail-fast: false
       max-parallel: 6
       matrix:
-        # This list is different from the one in tox.yml:
-        # Trac #31526 switches gcc 4.x-based distributions to using the gcc_spkg configuration factor
-        # Trac #32281 removes gcc 4.x-based distributions whose binutils are unusable
-        tox_system_factor: [ubuntu-xenial, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy, debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-18, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2. linuxmint-20.3, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36,  centos-7-gcc_spkg, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, slackware-14.2, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386-gcc_spkg]
+        tox_system_factor: [gitpod, ubuntu-trusty-toolchain-gcc_9, ubuntu-xenial-toolchain-gcc_9, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy, ubuntu-kinetic, debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2, linuxmint-20.3, linuxmint-21, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36, fedora-37, centos-7-devtoolset-gcc_11, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386-devtoolset-gcc_11]
         tox_packages_factor: [maximal]
         targets_pattern: [0-g, h-o, p, q-z]
     env:

diff --git a/.github/workflows/tox.yml b/.github/workflows/tox.yml
@@ -38,7 +38,7 @@ jobs:
       fail-fast: false
       max-parallel: 20
       matrix:
-        tox_system_factor: [ubuntu-trusty, ubuntu-xenial, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy,  debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-17, linuxmint-18, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2, linuxmint-20.3, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36, centos-7, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, slackware-14.2, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386]
+        tox_system_factor: [ubuntu-trusty-toolchain-gcc_9, ubuntu-xenial-toolchain-gcc_9, ubuntu-bionic, ubuntu-focal, ubuntu-hirsute, ubuntu-impish, ubuntu-jammy, ubuntu-kinetic, debian-stretch, debian-buster, debian-bullseye, debian-bookworm, debian-sid, linuxmint-19, linuxmint-19.3, linuxmint-20.1, linuxmint-20.2, linuxmint-20.3, linuxmint-21, fedora-26, fedora-27, fedora-28, fedora-29, fedora-30, fedora-31, fedora-32, fedora-33, fedora-34, fedora-35, fedora-36, fedora-37, centos-7-devtoolset-gcc_11, centos-stream-8, gentoo-python3.9, gentoo-python3.10, archlinux-latest, opensuse-15.3, opensuse-tumbleweed, conda-forge, ubuntu-bionic-i386, manylinux-2_24-i686, debian-buster-i386, centos-7-i386-devtoolset-gcc_11]
         tox_packages_factor: [minimal, standard]
     env:
       TOX_ENV: docker-${{ matrix.tox_system_factor }}-${{ matrix.tox_packages_factor }}

diff --git a/.gitignore b/.gitignore
@@ -187,6 +187,7 @@ build/bin/sage-build-env-config
 
 # Generated by docbuild
 /src/doc/en/reference/*/sage
+/src/doc/en/reference/*/sage_docbuild
 /src/doc/en/reference/sage
 /src/doc/en/reference/spkg/*.rst
 /src/doc/output

diff --git a/.zenodo.json b/.zenodo.json
@@ -1,10 +1,10 @@
 {
     "description": "Mirror of the Sage https://sagemath.org/ source tree", 
     "license": "other-open", 
-    "title": "sagemath/sage: 9.7.beta2", 
-    "version": "9.7.beta2", 
+    "title": "sagemath/sage: 9.7.beta3", 
+    "version": "9.7.beta3", 
     "upload_type": "software", 
-    "publication_date": "2022-06-12", 
+    "publication_date": "2022-06-19", 
     "creators": [
         {
             "affiliation": "SageMath.org", 
@@ -15,7 +15,7 @@
     "related_identifiers": [
         {
             "scheme": "url", 
-            "identifier": "https://github.com/sagemath/sage/tree/9.7.beta2", 
+            "identifier": "https://github.com/sagemath/sage/tree/9.7.beta3", 
             "relation": "isSupplementTo"
         }, 
         {

diff --git a/README.md b/README.md
@@ -243,8 +243,8 @@ in the Installation Guide.
 
 3.  [Linux, Cygwin] Install the required minimal build prerequisites.
 
-    - Compilers: `gcc`, `gfortran`, `g++` (a recent enough matching
-      set of these three will avoid building Sage-specific compilers).
+    - Compilers: `gcc`, `gfortran`, `g++` (GCC 6.3 to 12.x and recent
+      versions of Clang (LLVM) are supported).
       See the Installation Manual for a discussion of suitable compilers.
 
     - Build tools: GNU `make`, GNU `m4`, `perl` (including

diff --git a/VERSION.txt b/VERSION.txt
@@ -1 +1 @@
-SageMath version 9.7.beta2, Release Date: 2022-06-12
+SageMath version 9.7.beta3, Release Date: 2022-06-19
diff --git a/build/bin/write-dockerfile.sh b/build/bin/write-dockerfile.sh
@@ -13,7 +13,7 @@ EXTRA_SAGE_PACKAGES="${5:-_bootstrap}"
 STRIP_COMMENTS="sed s/#.*//;"
 SAGE_ROOT=.
 export PATH="$SAGE_ROOT"/build/bin:$PATH
-SYSTEM_PACKAGES=
+SYSTEM_PACKAGES=$EXTRA_SYSTEM_PACKAGES
 CONFIGURE_ARGS="--enable-option-checking "
 for PKG_BASE in $($SAGE_ROOT/sage -package list --has-file=distros/$SYSTEM.txt $SAGE_PACKAGE_LIST_ARGS) $EXTRA_SAGE_PACKAGES; do
     PKG_SCRIPTS="$SAGE_ROOT"/build/pkgs/$PKG_BASE
@@ -60,6 +60,9 @@ RUN $UPDATE $INSTALL software-properties-common && ($INSTALL gpg gpg-agent || ec
 RUN $SUDO add-apt-repository $EXTRA_REPOSITORY
 EOF
         fi
+        if [ -n "$EXTRA_PATH" ]; then
+            RUN="RUN export PATH=$EXTRA_PATH:\$PATH && "
+        fi
         ;;
     fedora*|redhat*|centos*)
         cat <<EOF

diff --git a/build/pkgs/configure/checksums.ini b/build/pkgs/configure/checksums.ini
@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=fee64e7ae45bcfd9bfa1c55605a579f49b19057e
-md5=42d9e4a2308a8c01f4e68f3915c3b856
-cksum=3408158874
+sha1=b6a462ba966439bb0cbd460d2bd1cb02d3343fba
+md5=95d6ce767184d6ee956feaf65494b4e8
+cksum=2637324690
diff --git a/build/pkgs/configure/package-version.txt b/build/pkgs/configure/package-version.txt
@@ -1 +1 @@
-b95c1659af1d26926ddf421d28b2d1f76dbc4810
+b466c8ae02c04d287d28d2d669e1d111df3724ff
diff --git a/build/pkgs/gcc/spkg-configure.m4 b/build/pkgs/gcc/spkg-configure.m4
@@ -161,20 +161,16 @@ SAGE_SPKG_CONFIGURE_BASE([gcc], [
             # Add the .0 because Debian/Ubuntu gives version numbers like
             # 4.6 instead of 4.6.4 (Trac #18885)
             AS_CASE(["$GXX_VERSION.0"],
-                [[[0-3]].*|4.[[0-7]].*|4.9.*], [
-                    # Install our own GCC if the system-provided one is older than gcc-4.8 or is 4.9.x
+                [[[0-5]].*|6.[[0-2]].*], [
+                    # Install our own GCC if the system-provided one is older than gcc-6.3
                     SAGE_SHOULD_INSTALL_GCC([you have $CXX version $GXX_VERSION, which is quite old])
                 ],
                 [1[[3-9]].*], [
                     # Install our own GCC if the system-provided one is newer than 12.x.
                     # See https://trac.sagemath.org/ticket/29456
                     SAGE_SHOULD_INSTALL_GCC([$CXX is g++ version $GXX_VERSION, which is too recent for this version of Sage])
-                ],
-                [4.[[8-9]].*|5.[[0-1]].*], [
-                    # GCC less than 5.1 is not ready for AVX512.
-                    sage_use_march_native=no
                 ])
-        fi
+            fi
 
         # The following tests check that the version of the compilers
         # are all the same.

diff --git a/build/pkgs/memory_allocator/checksums.ini b/build/pkgs/memory_allocator/checksums.ini
@@ -1,5 +1,5 @@
 tarball=memory_allocator-VERSION.tar.gz
-sha1=7721219be84207f6112e118fc79af0c2729fca34
-md5=868753a09c44194cba303db89cca4396
-cksum=16627262
+sha1=1a874de2674a1948797de109adfd1f56193e153a
+md5=c3a5d0f5acf896eec84266964a8aec0e
+cksum=3431157422
 upstream_url=https://pypi.io/packages/source/m/memory_allocator/memory_allocator-VERSION.tar.gz
diff --git a/build/pkgs/memory_allocator/package-version.txt b/build/pkgs/memory_allocator/package-version.txt
@@ -1 +1 @@
-0.1.1
+0.1.3
diff --git a/build/pkgs/sage_setup/dependencies b/build/pkgs/sage_setup/dependencies
@@ -1,4 +1,4 @@
-$(PYTHON) cython pkgconfig $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/*.py $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/command/*.py $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/autogen/interpreters/specs/*.py | $(PYTHON_TOOLCHAIN)
+$(PYTHON) cython pkgconfig jinja2 $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/*.py $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/autogen/interpreters/specs/*.py $(SAGE_ROOT)/pkgs/sage-setup/sage_setup/command/*.py | $(PYTHON_TOOLCHAIN)
 
 ----------
 All lines of this file are ignored except the first.
diff --git a/build/pkgs/singular/spkg-configure.m4 b/build/pkgs/singular/spkg-configure.m4
@@ -48,8 +48,8 @@ SAGE_SPKG_CONFIGURE([singular], [
                            ], [
                             AC_MSG_RESULT(no)
                             sage_spkg_install_singular=yes
-                          ])
-                        ])
+                          ], [AC_MSG_RESULT(yes)])
+                        ], [AC_MSG_RESULT(yes)])
 
                       AC_LANG_POP()
                       LIBS="${ORIG_LIBS}"

diff --git a/pkgs/sage-conf/VERSION.txt b/pkgs/sage-conf/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sage-conf_pypi/VERSION.txt b/pkgs/sage-conf_pypi/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sage-docbuild/VERSION.txt b/pkgs/sage-docbuild/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sage-setup/VERSION.txt b/pkgs/sage-setup/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sage-setup/requirements.txt b/pkgs/sage-setup/requirements.txt
@@ -1,2 +1,3 @@
 Cython
 pkgconfig
+jinja2
diff --git a/pkgs/sage-setup/setup.cfg b/pkgs/sage-setup/setup.cfg
@@ -35,3 +35,4 @@ python_requires = >=3.8, <3.11
 
 install_requires =
     pkgconfig
+    jinja2
diff --git a/pkgs/sage-sws2rst/VERSION.txt b/pkgs/sage-sws2rst/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sagemath-categories/VERSION.txt b/pkgs/sagemath-categories/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sagemath-environment/VERSION.txt b/pkgs/sagemath-environment/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sagemath-objects/VERSION.txt b/pkgs/sagemath-objects/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/pkgs/sagemath-repl/VERSION.txt b/pkgs/sagemath-repl/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/src/VERSION.txt b/src/VERSION.txt
@@ -1 +1 @@
-9.7.beta2
+9.7.beta3
diff --git a/src/bin/sage-preparse b/src/bin/sage-preparse
@@ -278,8 +278,7 @@ def do_load_and_attach(G, file, files_before):
             files = z.group('files').split()
             lws = z.group('lws')
             for w in files:
-                name = w.replace(',','').replace('"','').replace("'","")
-                #print "'%s'"%name, files_before
+                name = w.replace(',', '').replace('"', '').replace("'", "")
                 if name in files_before:
                    print("WARNING: not loading {} (in {}) again since would cause circular loop"
                         .format(name, file))

diff --git a/src/bin/sage-runtests b/src/bin/sage-runtests
@@ -43,13 +43,15 @@ if __name__ == "__main__":
     # By default, include all tests marked 'sagemath_doc_html' -- see
     # https://trac.sagemath.org/ticket/25345 and
     # https://trac.sagemath.org/ticket/26110:
-    parser.add_argument("--optional", metavar="PKGS", default=_get_optional_defaults(),
-        help='only run tests including one of the "# optional" tags listed in PKGS; '
+    parser.add_argument("--optional", metavar="FEATURES", default=_get_optional_defaults(),
+        help='only run tests including one of the "# optional" tags listed in FEATURES (separated by commas); '
              'if "sage" is listed, will also run the standard doctests; '
              'if "sagemath_doc_html" is listed, will also run the tests relying on the HTML documentation; '
-             'if "optional" is listed, will also run tests for installed optional (new-style) packages; '
+             'if "optional" is listed, will also run tests for installed optional packages or detected features; '
              'if "external" is listed, will also run tests for available external software; '
-             'if set to "all", then all tests will be run')
+             'if set to "all", then all tests will be run; '
+             'use "!FEATURE" to disable tests marked "# optional - FEATURE". '
+             'Note that "!" needs to be quoted or escaped in the shell.')
     parser.add_argument("--randorder", type=int, metavar="SEED", help="randomize order of tests")
     parser.add_argument("--random-seed", dest="random_seed", type=int, metavar="SEED", help="random seed (integer) for fuzzing doctests",
                         default=os.environ.get("SAGE_DOCTEST_RANDOM_SEED"))

diff --git a/src/bin/sage-version.sh b/src/bin/sage-version.sh
@@ -1,5 +1,5 @@
 # Sage version information for shell scripts
 # This file is auto-generated by the sage-update-version script, do not edit!
-SAGE_VERSION='9.7.beta2'
-SAGE_RELEASE_DATE='2022-06-12'
-SAGE_VERSION_BANNER='SageMath version 9.7.beta2, Release Date: 2022-06-12'
+SAGE_VERSION='9.7.beta3'
+SAGE_RELEASE_DATE='2022-06-19'
+SAGE_VERSION_BANNER='SageMath version 9.7.beta3, Release Date: 2022-06-19'
diff --git a/src/doc/en/developer/coding_basics.rst b/src/doc/en/developer/coding_basics.rst
@@ -728,10 +728,9 @@ there is not one already. That is, you can do the following:
 LaTeX Typesetting
 -----------------
 
-In Sage's documentation LaTeX code is allowed and is marked with **backticks or
-dollar signs**:
+In Sage's documentation LaTeX code is allowed and is marked with **backticks**:
 
-    ```x^2 + y^2 = 1``` and ``$x^2 + y^2 = 1$`` both yield `x^2 + y^2 = 1`.
+    ```x^2 + y^2 = 1``` yields `x^2 + y^2 = 1`.
 
 **Backslashes:** For LaTeX commands containing backslashes, either use double
 backslashes or begin the docstring with a ``r"""`` instead of ``"""``. Both of
@@ -744,7 +743,7 @@ the following are valid::
 
     def sin(x):
         r"""
-        Return $\sin(x)$.
+        Return `\sin(x)`.
         """
 
 **MATH block:** This is similar to the LaTeX syntax ``\[<math expression>\]``

diff --git a/src/doc/en/installation/source.rst b/src/doc/en/installation/source.rst
@@ -58,11 +58,8 @@ and the :wikipedia:`bash <Bash_(Unix_shell)>` shell,
 the following standard command-line development tools must be installed on your
 computer:
 
-- A **C/C++ compiler**: Since SageMath builds its own GCC if needed,
-  a wide variety of C/C++ compilers is supported.
-  Many GCC versions work,
-  from as old as version 4.8 (but we recommend at least 5.1) to the most recent release.
-  Clang also works.
+- A **C/C++ compiler**: GCC versions 6.3 to 12.x are supported.
+  Clang (LLVM) is also supported.
   See also `Using alternative compilers`_.
 - **make**: GNU make, version 3.80 or later. Version 3.82 or later is recommended.
 - **m4**: GNU m4 1.4.2 or later (non-GNU or older versions might also work).

diff --git a/src/doc/en/reference/combinat/module_list.rst b/src/doc/en/reference/combinat/module_list.rst
@@ -164,6 +164,8 @@ Comprehensive Module List
     sage/combinat/ncsym/ncsym
     sage/combinat/necklace
     sage/combinat/non_decreasing_parking_function
+    sage/combinat/nu_dyck_word
+    sage/combinat/nu_tamari_lattice
     sage/combinat/ordered_tree
     sage/combinat/output
     sage/combinat/parallelogram_polyomino

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
@@ -998,6 +998,9 @@ REFERENCES:
               lacunas of the Thue-Morse word*, Proc. GASCOM 2008 (June
               16-20 2008, Bibbiena, Arezzo-Italia), 53--67.
 
+.. [BMFPR] \M. Bousquet-Melou, E. Fusy, L.-F. Preville Ratelle.
+           *The number of intervals in the m-Tamari lattices*. :arxiv:`1106.1498`
+
 .. [BMS2006] Bugeaud, Mignotte, and Siksek. "Classical and modular
              approaches to exponential Diophantine
              equations: I. Fibonacci and Lucas perfect powers." Annals
@@ -4786,6 +4789,10 @@ REFERENCES:
              *PICARO - a block cipher allowing efficient higher-order side-channel
              resistance*; in ACNS, (2012), pp. 311-328.
 
+.. [PRV2017] \L.-F. Préville-Ratelle and X. Viennot,
+             *The enumeration of generalized Tamari intervals*.
+             Trans. Amer. Math. Soc. 369 (2017), pp 5219--5239
+
 .. [Prototype_pattern] Prototype pattern,
                        :wikipedia:`Prototype_pattern`
 

diff --git a/src/doc/en/website/templates/index.html b/src/doc/en/website/templates/index.html
@@ -33,7 +33,7 @@ <h1>{{ docstitle|e }}</h1>
 <p>
 This is documentation for Sage {{ release }}.
 Documentations in other languages are available <a href="../../index.html">here</a>.
-</p>.
+</p>
 {% block tables %}
 <h2>
   <strong>

diff --git a/src/sage/algebras/askey_wilson.py b/src/sage/algebras/askey_wilson.py
@@ -300,6 +300,7 @@ def _latex_term(self, t):
         """
         if sum(t) == 0:
             return '1'
+
         def exp(l, e):
             if e == 0:
                 return ''
@@ -338,6 +339,7 @@ def algebra_generators(self):
             [A, B, C, a, b, g]
         """
         A = self.variable_names()
+
         def build_monomial(g):
             exp = [0] * 6
             exp[A.index(g)] = 1

diff --git a/src/sage/algebras/clifford_algebra.py b/src/sage/algebras/clifford_algebra.py
@@ -1963,6 +1963,7 @@ def lifted_bilinear_form(self, M):
             back are implemented, check if this is faster.
         """
         R = self.base_ring()
+
         def lifted_form(x, y):
             result = R.zero()
             for mx, cx in x:

diff --git a/src/sage/algebras/commutative_dga.py b/src/sage/algebras/commutative_dga.py
@@ -2281,7 +2281,7 @@ def cohomology_generators(self, max_degree):
 
         ALGORITHM:
 
-        Reduce a basis of the `n`'th cohomology modulo all the degree $n$
+        Reduce a basis of the `n`'th cohomology modulo all the degree `n`
         products of the lower degree cohomologies.
 
         EXAMPLES::
@@ -2292,12 +2292,12 @@ def cohomology_generators(self, max_degree):
             {1: [a], 2: [x], 3: [a*y]}
 
         The previous example has infinitely generated cohomology:
-        $a y^n$ is a cohomology generator for each $n$::
+        `a y^n` is a cohomology generator for each `n`::
 
             sage: B.cohomology_generators(10)
             {1: [a], 2: [x], 3: [a*y], 5: [a*y^2], 7: [a*y^3], 9: [a*y^4]}
 
-        In contrast, the corresponding algebra in characteristic $p$
+        In contrast, the corresponding algebra in characteristic `p`
         has finitely generated cohomology::
 
             sage: A3.<a,x,y> = GradedCommutativeAlgebra(GF(3), degrees=(1,2,2))

diff --git a/src/sage/algebras/free_algebra.py b/src/sage/algebras/free_algebra.py
@@ -591,6 +591,7 @@ def _element_constructor_(self, x):
             if self.has_coerce_map_from(P): # letterplace versus generic
                 ngens = P.ngens()
                 M = self._indices
+
                 def exp_to_monomial(T):
                     out = []
                     for i in range(len(T)):

diff --git a/src/sage/algebras/free_algebra_element.py b/src/sage/algebras/free_algebra_element.py
@@ -150,7 +150,8 @@ def __call__(self, *x, **kwds):
 
         if kwds:
             p = self.parent()
-            def extract_from(kwds,g):
+
+            def extract_from(kwds, g):
                 for x in g:
                     try:
                         return kwds[x]

diff --git a/src/sage/algebras/hecke_algebras/ariki_koike_algebra.py b/src/sage/algebras/hecke_algebras/ariki_koike_algebra.py
@@ -1688,6 +1688,7 @@ def _product_TT(self, kp, a, k, b):
                     T[kp] = a + b
                     return self._from_dict({(tuple(T), self._one_perm): one},
                                            remove_zeros=False, coerce=False)
+
                 def key(exp):
                     if exp > 0 or kp == 0:
                         T = list(self._zero_tuple)
@@ -1715,6 +1716,7 @@ def key(exp):
             T[kp] = a
             ret = {(tuple(T), s1): one}
             zero = self.base_ring().zero()
+
             def T_index(exp, ind, i, indp):
                 T = list(self._zero_tuple)
                 T[ind] = exp