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Merge branch 'develop' into oriented_matroids
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thecaligarmo committed Oct 5, 2024
2 parents 69c0bbd + b0f09d9 commit 8b6ac18
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2 changes: 1 addition & 1 deletion .ci/retrofit-worktree.sh
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Expand Up @@ -43,4 +43,4 @@ git worktree add --detach $WORKTREE_NAME
rm -rf $WORKTREE_DIRECTORY/.git && mv $WORKTREE_NAME/.git $WORKTREE_DIRECTORY/
rm -rf $WORKTREE_NAME && ln -s $WORKTREE_DIRECTORY $WORKTREE_NAME
if [ ! -f $WORKTREE_NAME/.gitignore ]; then cp .gitignore $WORKTREE_NAME/; fi
(cd $WORKTREE_NAME && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git checkout new && git status)
(cd $WORKTREE_NAME && git add -A && git commit --quiet --allow-empty -m "old" -a && git tag -f old && git checkout -f new && git clean -fd && git status)
3 changes: 3 additions & 0 deletions .github/workflows/doc-build.yml
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Expand Up @@ -213,6 +213,9 @@ jobs:
(cd doc && mv .git ../git && mv .gitattributes ../gitattributes)
mv CHANGES.html doc
fi
# Create the robots.txt file to discourage web crawlers from indexing doc preview webpages
echo "User-agent: *" > doc/robots.txt
echo "Disallow: /" >> doc/robots.txt
# Zip everything for increased performance
zip -r doc.zip doc
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4 changes: 2 additions & 2 deletions CITATION.cff
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Expand Up @@ -4,8 +4,8 @@ title: SageMath
abstract: SageMath is a free open-source mathematics software system.
authors:
- name: "The SageMath Developers"
version: 10.5.beta5
version: 10.5.beta6
doi: 10.5281/zenodo.8042260
date-released: 2024-09-22
date-released: 2024-09-29
repository-code: "https://github.com/sagemath/sage"
url: "https://www.sagemath.org/"
2 changes: 1 addition & 1 deletion VERSION.txt
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@@ -1 +1 @@
SageMath version 10.5.beta5, Release Date: 2024-09-22
SageMath version 10.5.beta6, Release Date: 2024-09-29
4 changes: 2 additions & 2 deletions build/pkgs/configure/checksums.ini
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@@ -1,3 +1,3 @@
tarball=configure-VERSION.tar.gz
sha1=2cdffd348b8a4de62b51e1f6c37a7d414004c09e
sha256=273c37842eedefc3575e34bb14819ab3738a32c39ae634f2342bb50baa740c60
sha1=140d921780212198287a0d626b8c9655d4408f7a
sha256=4f82ec8bdb67c4dffd43daddd5160e8f9c624f6a5cf16c4128bfab2e5ddca459
2 changes: 1 addition & 1 deletion build/pkgs/configure/package-version.txt
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@@ -1 +1 @@
9b58ceaa68960b38142f27fdfc04373301da4e46
2b4fe39e420df022d34a67fbc820252618e15f83
4 changes: 2 additions & 2 deletions build/pkgs/fricas/checksums.ini
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@@ -1,4 +1,4 @@
tarball=fricas-VERSION-full.tar.bz2
sha1=2f1e1bbbad7e04a7114ffbd93eeedadc5db32272
sha256=fc2112ad45ba7b45ac423165f32bd5b244622107a1e4e1d56b9136f96746f2a0
sha1=c5104c92808ff01a02ecdd3f412d44da3b2c21fb
sha256=32b87461ef079659e97247ad0a771ec8cf0d5a0f934788d67d37fb7acf63f9c4
upstream_url=https://github.com/fricas/fricas/releases/download/VERSION/fricas-VERSION-full.tar.bz2
2 changes: 1 addition & 1 deletion build/pkgs/fricas/package-version.txt
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@@ -1 +1 @@
1.3.10
1.3.11
4 changes: 2 additions & 2 deletions build/pkgs/gc/checksums.ini
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@@ -1,4 +1,4 @@
tarball=gc-VERSION.tar.gz
sha1=3f543532c47e592a8f5ea6f7a529c8ed7465a5c7
sha256=b9183fe49d4c44c7327992f626f8eaa1d8b14de140f243edb1c9dcff7719a7fc
sha1=1c8d7bde86aa98df957563982f38c583c2c6707f
sha256=7649020621cb26325e1fb5c8742590d92fb48ce5c259b502faf7d9fb5dabb160
upstream_url=https://github.com/ivmai/bdwgc/releases/download/vVERSION/gc-VERSION.tar.gz
2 changes: 1 addition & 1 deletion build/pkgs/gc/package-version.txt
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@@ -1 +1 @@
8.2.6
8.2.8
4 changes: 2 additions & 2 deletions build/pkgs/maxima/checksums.ini
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@@ -1,4 +1,4 @@
tarball=maxima-VERSION.tar.gz
sha1=1010594e6d6082bbd8efaac1b7756ec1721a4ed5
sha256=7390f06b48da65c9033e8b2f629b978b90056454a54022db7de70e2225aa8b07
sha1=fff13f4c010e6daab65fbc8a6895c2bd79925177
sha256=9104021b24fd53e8c03a983509cb42e937a925e8c0c85c335d7709a14fd40f7a
upstream_url=https://sourceforge.net/projects/maxima/files/Maxima-source/VERSION-source/maxima-VERSION.tar.gz/download
2 changes: 1 addition & 1 deletion build/pkgs/maxima/package-version.txt
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@@ -1 +1 @@
5.46.0
5.47.0
2 changes: 1 addition & 1 deletion build/pkgs/mpmath/version_requirements.txt
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@@ -1 +1 @@
mpmath >=1.1.0
mpmath >=1.1.0, <1.4
4 changes: 2 additions & 2 deletions build/pkgs/openblas/checksums.ini
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@@ -1,4 +1,4 @@
tarball=openblas-VERSION.tar.gz
sha1=af6dce0e486e684be842053fcbd98eaf97e39749
sha256=4e6e4f5cb14c209262e33e6816d70221a2fe49eb69eaf0a06f065598ac602c68
sha1=f75172274a7ce69901605b8c759e2e0891c9b7f4
sha256=f1003466ad074e9b0c8d421a204121100b0751c96fc6fcf3d1456bd12f8a00a1
upstream_url=https://github.com/xianyi/OpenBLAS/archive/vVERSION.tar.gz
2 changes: 1 addition & 1 deletion build/pkgs/openblas/package-version.txt
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@@ -1 +1 @@
0.3.26
0.3.28
2 changes: 1 addition & 1 deletion build/pkgs/sage_conf/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sage-conf ~= 10.5b5
sage-conf ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sage_docbuild/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sage-docbuild ~= 10.5b5
sage-docbuild ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sage_setup/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sage-setup ~= 10.5b5
sage-setup ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sage_sws2rst/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sage-sws2rst ~= 10.5b5
sage-sws2rst ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagelib/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-standard ~= 10.5b5
sagemath-standard ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_bliss/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-bliss ~= 10.5b5
sagemath-bliss ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_categories/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-categories ~= 10.5b5
sagemath-categories ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_coxeter3/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-coxeter3 ~= 10.5b5
sagemath-coxeter3 ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_environment/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-environment ~= 10.5b5
sagemath-environment ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_mcqd/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-mcqd ~= 10.5b5
sagemath-mcqd ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_meataxe/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-meataxe ~= 10.5b5
sagemath-meataxe ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_objects/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-objects ~= 10.5b5
sagemath-objects ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_repl/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-repl ~= 10.5b5
sagemath-repl ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_sirocco/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-sirocco ~= 10.5b5
sagemath-sirocco ~= 10.5b6
2 changes: 1 addition & 1 deletion build/pkgs/sagemath_tdlib/version_requirements.txt
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@@ -1,2 +1,2 @@
# This file is updated on every release by the sage-update-version script
sagemath-tdlib ~= 10.5b5
sagemath-tdlib ~= 10.5b6
3 changes: 2 additions & 1 deletion build/pkgs/zlib/spkg-configure.m4
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@@ -1,7 +1,8 @@
SAGE_SPKG_CONFIGURE([zlib], [
PKG_CHECK_MODULES([zlib], [zlib >= 1.2.11], [zlib_cv_pc=yes], [zlib_cv_pc=no])
AC_CHECK_LIB([z], [inflateEnd], [zlib_cv_libz=yes], [zlib_cv_libz=no])
AC_CHECK_HEADER([zlib.h], [zlib_cv_zlib_h=yes], [zlib_cv_zlib_h=no])
if test "$zlib_cv_libz" = "yes" && test "$zlib_cv_zlib_h" = "yes"; then
if test "$zlib_cv_pc" = "yes" && test "$zlib_cv_libz" = "yes" && test "$zlib_cv_zlib_h" = "yes"; then
PKG_CHECK_MODULES([LIBPNG], [libpng >= 1.2], [], [
dnl inflateValidate is needed for Sage's libpng, newer than 1.2; this ensures
dnl we have the minimum required for building zlib version
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8 changes: 7 additions & 1 deletion configure.ac
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Expand Up @@ -450,7 +450,7 @@ AC_ARG_ENABLE([cvxopt],
AC_ARG_ENABLE([notebook],
AS_HELP_STRING([--disable-notebook],
[disable build of the Jupyter notebook and related packages]), [
for pkg in notebook nbconvert beautifulsoup4 sagenb_export nbformat nbclient terminado send2trash prometheus_client mistune pandocfilters bleach defusedxml jsonschema jupyter_jsmol argon2_cffi argon2_cffi_bindings webencodings tinycss2 ipympl soupsieve fastjsonschema anyio arrow async_lru fqdn isoduration json5 jsonpointer jsonschema_specifications jupyter_events jupyter_lsp jupyter_server jupyter_server_terminals jupyterlab jupyterlab_server jupyterlab_pygments jupyterlab_mathjax2 jupyter_sphinx notebook_shim overrides python_json_logger pyyaml referencing rfc3339_validator rfc3986_validator sniffio types_python_dateutil uri_template webcolors websocket_client; do
for pkg in notebook nbconvert beautifulsoup4 sagenb_export nbformat nbclient terminado send2trash prometheus_client mistune pandocfilters bleach defusedxml jsonschema jupyter_jsmol argon2_cffi argon2_cffi_bindings webencodings tinycss2 ipympl soupsieve fastjsonschema anyio arrow async_lru fqdn isoduration json5 jsonpointer jsonschema_specifications jupyter_events jupyter_lsp jupyter_server jupyter_server_terminals jupyterlab jupyterlab_server jupyterlab_pygments jupyterlab_mathjax2 jupyter_sphinx notebook_shim overrides python_json_logger pyyaml referencing rfc3339_validator rfc3986_validator sniffio types_python_dateutil uri_template webcolors websocket_client httpx httpcore h11; do
AS_VAR_SET([SAGE_ENABLE_$pkg], [$enableval])
done
])
Expand All @@ -463,6 +463,12 @@ AC_ARG_ENABLE([r],
done
])

AC_ARG_ENABLE([sagetex],
AS_HELP_STRING([--disable-sagetex],
[don't build SageTeX]), [
AS_VAR_SET([SAGE_ENABLE_sagetex], [$enableval])
])

AC_ARG_ENABLE([doc],
AS_HELP_STRING([--disable-doc],
[disable build of the Sage documentation and packages depending on it]), [
Expand Down
2 changes: 1 addition & 1 deletion pkgs/sage-conf/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sage-conf_conda/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sage-conf_pypi/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sage-docbuild/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sage-setup/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sage-sws2rst/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-bliss/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-categories/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-coxeter3/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-environment/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-mcqd/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-meataxe/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-objects/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-repl/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-sirocco/VERSION.txt
Original file line number Diff line number Diff line change
@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion pkgs/sagemath-tdlib/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
2 changes: 1 addition & 1 deletion src/VERSION.txt
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@@ -1 +1 @@
10.5.beta5
10.5.beta6
6 changes: 3 additions & 3 deletions src/bin/sage-version.sh
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Expand Up @@ -4,6 +4,6 @@
# which stops "setup.py develop" from rewriting it as a Python file.
:
# This file is auto-generated by the sage-update-version script, do not edit!
SAGE_VERSION='10.5.beta5'
SAGE_RELEASE_DATE='2024-09-22'
SAGE_VERSION_BANNER='SageMath version 10.5.beta5, Release Date: 2024-09-22'
SAGE_VERSION='10.5.beta6'
SAGE_RELEASE_DATE='2024-09-29'
SAGE_VERSION_BANNER='SageMath version 10.5.beta6, Release Date: 2024-09-29'
6 changes: 3 additions & 3 deletions src/doc/de/tutorial/interactive_shell.rst
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Expand Up @@ -356,9 +356,9 @@ dem man nachgehen sollte.
sage: time g = maple('1938^99484')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.11
sage: gap(0)
sage: libgap(0)
0
sage: time g = gap.eval('1938^99484;;')
sage: time g = libgap.eval('1938^99484;')
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 1.02

Expand Down Expand Up @@ -742,7 +742,7 @@ nicht erlaubt.
::

sage: a = gap(2)
sage: a = libgap(2)
sage: a.save('a')
sage: load('a')
Traceback (most recent call last):
Expand Down
52 changes: 23 additions & 29 deletions src/doc/en/constructions/groups.rst
Original file line number Diff line number Diff line change
Expand Up @@ -124,31 +124,25 @@ You can compute conjugacy classes of a finite group using "natively"::

You can use the Sage-GAP interface::

sage: gap.eval("G := Group((1,2)(3,4),(1,2,3))")
'Group([ (1,2)(3,4), (1,2,3) ])'
sage: gap.eval("CG := ConjugacyClasses(G)")
'[ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]'
sage: gap.eval("gamma := CG[3]")
'(2,4,3)^G'
sage: gap.eval("g := Representative(gamma)")
'(2,4,3)'
sage: libgap.eval("G := Group((1,2)(3,4),(1,2,3))")
Group([ (1,2)(3,4), (1,2,3) ])
sage: libgap.eval("CG := ConjugacyClasses(G)")
[ ()^G, (2,3,4)^G, (2,4,3)^G, (1,2)(3,4)^G ]
sage: libgap.eval("gamma := CG[3]")
(2,4,3)^G
sage: libgap.eval("g := Representative(gamma)")
(2,4,3)

Or, here's another (more "pythonic") way to do this type of computation::

sage: G = gap.Group('[(1,2,3), (1,2)(3,4), (1,7)]')
sage: G = libgap.eval("Group([(1,2,3), (1,2)(3,4), (1,7)])")
sage: CG = G.ConjugacyClasses()
sage: gamma = CG[2]
sage: g = gamma.Representative()
sage: CG; gamma; g
[ ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), () ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (4,7) ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (3,4,7) ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (2,3)(4,7) ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (2,3,4,7) ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (1,2)(3,4,7) ),
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (1,2,3,4,7) ) ]
ConjugacyClass( SymmetricGroup( [ 1, 2, 3, 4, 7 ] ), (4,7) )
(4,7)
[ ()^G, (4,7)^G, (3,4,7)^G, (2,3)(4,7)^G, (2,3,4,7)^G, (1,2)(3,4,7)^G, (1,2,3,4,7)^G ]
(3,4,7)^G
(3,4,7)

.. index::
pair: group; normal subgroups
Expand All @@ -162,29 +156,29 @@ If you want to find all the normal subgroups of a permutation group
:math:`G` (up to conjugacy), you can use Sage's interface to GAP::

sage: G = AlternatingGroup( 5 )
sage: gap(G).NormalSubgroups()
[ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
sage: libgap(G).NormalSubgroups()
[ Alt( [ 1 .. 5 ] ), Group(()) ]

or

::

sage: G = gap("AlternatingGroup( 5 )")
sage: G = libgap.AlternatingGroup( 5 )
sage: G.NormalSubgroups()
[ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
[ Alt( [ 1 .. 5 ] ), Group(()) ]

Here's another way, working more directly with GAP::

sage: print(gap.eval("G := AlternatingGroup( 5 )"))
sage: libgap.eval("G := AlternatingGroup( 5 )")
Alt( [ 1 .. 5 ] )
sage: print(gap.eval("normal := NormalSubgroups( G )"))
sage: libgap.eval("normal := NormalSubgroups( G )")
[ Alt( [ 1 .. 5 ] ), Group(()) ]
sage: G = gap.new("DihedralGroup( 10 )")
sage: G = libgap.eval("DihedralGroup( 10 )")
sage: G.NormalSubgroups().SortedList()
[ Group( <identity> of ... ), Group( [ f2 ] ), Group( [ f1, f2 ] ) ]
sage: print(gap.eval("G := SymmetricGroup( 4 )"))
[ Group([ ]), Group([ f2 ]), <pc group of size 10 with 2 generators> ]
sage: libgap.eval("G := SymmetricGroup( 4 )")
Sym( [ 1 .. 4 ] )
sage: print(gap.eval("normal := NormalSubgroups( G );"))
sage: libgap.eval("normal := NormalSubgroups( G );")
[ Sym( [ 1 .. 4 ] ), Alt( [ 1 .. 4 ] ), Group([ (1,4)(2,3), ... ]),
Group(()) ]

Expand All @@ -201,7 +195,7 @@ How do you compute the center of a group in Sage?
Although Sage calls GAP to do the computation of the group center,
``center`` is "wrapped" (i.e., Sage has a class PermutationGroup with
associated class method "center"), so the user does not need to use
the ``gap`` command. Here's an example::
the ``libgap`` command. Here's an example::

sage: G = PermutationGroup(['(1,2,3)(4,5)', '(3,4)'])
sage: G.center()
Expand Down
2 changes: 1 addition & 1 deletion src/doc/en/constructions/interface_issues.rst
Original file line number Diff line number Diff line change
Expand Up @@ -92,7 +92,7 @@ Sage and other computer algebra systems

If ``foo`` is a Pari, GAP ( without ending semicolon), Singular,
Maxima command, resp., enter ``gp("foo")`` for Pari,
``gap.eval("foo")}`` ``singular.eval("foo")``, ``maxima("foo")``, resp..
``libgap.eval("foo")}`` ``singular.eval("foo")``, ``maxima("foo")``, resp..
These programs merely send the command string to the external
program, execute it, and read the result back into Sage. Therefore,
these will not work if the external program is not installed and in
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6 changes: 3 additions & 3 deletions src/doc/en/constructions/linear_algebra.rst
Original file line number Diff line number Diff line change
Expand Up @@ -306,11 +306,11 @@ Finally, you can use Sage's GAP interface as well to compute

::

sage: print(gap.eval("A := [[1,2,3],[4,5,6],[7,8,9]]"))
sage: A = libgap([[1,2,3],[4,5,6],[7,8,9]]); A
[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
sage: print(gap.eval("v := Eigenvectors( Rationals,A)"))
sage: libgap(QQ).Eigenvectors(A)
[ [ 1, -2, 1 ] ]
sage: print(gap.eval("lambda := Eigenvalues( Rationals,A)"))
sage: libgap(QQ).Eigenvalues(A)
[ 0 ]

.. _section-rref:
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