diff --git a/gnu/local.mk b/gnu/local.mk
index cf1d733433b..149ef8dff9a 100644
--- a/gnu/local.mk
+++ b/gnu/local.mk
@@ -2223,7 +2223,6 @@ dist_patch_DATA =						\
   %D%/packages/patches/rw-igraph-0.10.patch			\
   %D%/packages/patches/rxvt-unicode-fix-cursor-position.patch	\
   %D%/packages/patches/s7-flint-3.patch                      	\
-  %D%/packages/patches/sage-update-pari-gp.patch               	\
   %D%/packages/patches/sajson-for-gemmi-numbers-as-strings.patch	\
   %D%/packages/patches/sajson-build-with-gcc10.patch		\
   %D%/packages/patches/sbc-fix-build-non-x86.patch		\
diff --git a/gnu/packages/patches/sage-update-pari-gp.patch b/gnu/packages/patches/sage-update-pari-gp.patch
deleted file mode 100644
index 741b9b14786..00000000000
--- a/gnu/packages/patches/sage-update-pari-gp.patch
+++ /dev/null
@@ -1,5020 +0,0 @@
-diff --git a/build/pkgs/cypari/checksums.ini b/build/pkgs/cypari/checksums.ini
-index 1ead9490d1a..3794d83334f 100644
---- a/build/pkgs/cypari/checksums.ini
-+++ b/build/pkgs/cypari/checksums.ini
-@@ -1,4 +1,4 @@
- tarball=cypari2-VERSION.tar.gz
--sha1=4e9f14d218bc1cea29e03a2ceec9bf3dfbfd5eb3
--sha256=817606bf661b71d33e1d012421907a4f8fb09dd81b7d3e3ae179b3978020bbf1
-+sha1=556d1a16818663ba6e6a3c9d2b14cc907a7eef4c
-+sha256=aaa017a6a280581902f73cf5ce1695712b6598a032be14cfab81f97c475f83b8
- upstream_url=https://files.pythonhosted.org/packages/source/c/cypari2/cypari2-VERSION.tar.gz
-diff --git a/build/pkgs/cypari/package-version.txt b/build/pkgs/cypari/package-version.txt
-index ccbccc3dc62..c043eea7767 100644
---- a/build/pkgs/cypari/package-version.txt
-+++ b/build/pkgs/cypari/package-version.txt
-@@ -1 +1 @@
--2.2.0
-+2.2.1
-diff --git a/build/pkgs/cysignals/checksums.ini b/build/pkgs/cysignals/checksums.ini
-index 8ba1030ffdf..9c6648af170 100644
---- a/build/pkgs/cysignals/checksums.ini
-+++ b/build/pkgs/cysignals/checksums.ini
-@@ -1,4 +1,4 @@
- tarball=cysignals-VERSION.tar.gz
--sha1=76db7aa59d55e867c83b329c017382555253af43
--sha256=0f1e321e55a07f901c86a36a1e4497f6ff9dfe700681d0130a38c36e4eb238c3
-+sha1=e285e209a3a5f9469cb5ade746c518cd3a600a9b
-+sha256=89f7626dbf29db5ab3d6eff15a89978f4eb5193c320e9099bcc157dacdefd1eb
- upstream_url=https://files.pythonhosted.org/packages/source/c/cysignals/cysignals-VERSION.tar.gz
-diff --git a/build/pkgs/cysignals/dependencies b/build/pkgs/cysignals/dependencies
-index cd45ae2076c..d42690aa7b1 100644
---- a/build/pkgs/cysignals/dependencies
-+++ b/build/pkgs/cysignals/dependencies
-@@ -1,4 +1,4 @@
-- cython pari | $(PYTHON_TOOLCHAIN) $(PYTHON)
-+ cython | $(PYTHON_TOOLCHAIN) meson_python $(PYTHON)
- 
- ----------
- All lines of this file are ignored except the first.
-diff --git a/build/pkgs/cysignals/package-version.txt b/build/pkgs/cysignals/package-version.txt
-index 3d0e62313ce..81f363239f5 100644
---- a/build/pkgs/cysignals/package-version.txt
-+++ b/build/pkgs/cysignals/package-version.txt
-@@ -1 +1 @@
--1.11.4
-+1.12.3
-diff --git a/build/pkgs/cysignals/spkg-install.in b/build/pkgs/cysignals/spkg-install.in
-index 0894611a27e..2e2a9691837 100644
---- a/build/pkgs/cysignals/spkg-install.in
-+++ b/build/pkgs/cysignals/spkg-install.in
-@@ -3,9 +3,4 @@ cd src
- # #29473: Override -Wp,-D_FORTIFY_SOURCE from Fedora's python3.
- export CPPFLAGS="$CPPFLAGS -Wp,-U_FORTIFY_SOURCE"
- 
--if [ "$SAGE_DEBUG" = yes ]; then
--    CYSIGNALS_CONFIGURE="--enable-debug $CYSIGNALS_CONFIGURE"
--fi
--
--sdh_configure $CYSIGNALS_CONFIGURE
- sdh_pip_install .
-diff --git a/build/pkgs/pari/checksums.ini b/build/pkgs/pari/checksums.ini
-index d56c437a2ee..cfb35617995 100644
---- a/build/pkgs/pari/checksums.ini
-+++ b/build/pkgs/pari/checksums.ini
-@@ -1,4 +1,4 @@
- tarball=pari-VERSION.tar.gz
--sha1=377593dfe72df13578ea0a517fcb0f81cc9758d4
--sha256=0efdda7515d9d954f63324c34b34c560e60f73a81c3924a71260a2cc91d5f981
--upstream_url=https://pari.math.u-bordeaux.fr/pub/pari/OLD/${VERSION_MAJOR}.${VERSION_MINOR}/pari-VERSION.tar.gz
-+sha1=f5f5656a68947ef6a4841d40dd09a72fe96762a5
-+sha256=67ba6f3071233725258541e4f174b5efbc64c65ae5115bade9edfc45f1fde5dc
-+upstream_url=https://pari.math.u-bordeaux.fr/pub/pari/unix/pari-VERSION.tar.gz
-diff --git a/build/pkgs/pari/package-version.txt b/build/pkgs/pari/package-version.txt
-index 7a561821071..3f8eb714d02 100644
---- a/build/pkgs/pari/package-version.txt
-+++ b/build/pkgs/pari/package-version.txt
-@@ -1 +1 @@
--2.15.5
-+2.17.1
-diff --git a/build/pkgs/pari/spkg-configure.m4 b/build/pkgs/pari/spkg-configure.m4
-index 207487119a6..d9d90e0d421 100644
---- a/build/pkgs/pari/spkg-configure.m4
-+++ b/build/pkgs/pari/spkg-configure.m4
-@@ -1,8 +1,7 @@
- SAGE_SPKG_CONFIGURE([pari], [
-   dnl See gp_version below on how the version is computed from MAJV.MINV.PATCHV
--  m4_pushdef([SAGE_PARI_MINVER],["134916"])dnl this version and higher allowed
--  dnl Do not allow Pari 2.17 or later, see #38769:
--  m4_pushdef([SAGE_PARI_MAXVER],["135424"])dnl this version and higher not allowed
-+  m4_pushdef([SAGE_PARI_MINVER],["135245"])dnl this version and higher allowed
-+  m4_pushdef([SAGE_PARI_MAXVER],["999999"])dnl this version and higher not allowed
-   SAGE_SPKG_DEPCHECK([gmp readline], [
-     AC_PATH_PROG([GP], [gp])
-     if test x$GP = x; then dnl GP test
-diff --git a/environment-3.11-linux-aarch64.yml b/environment-3.11-linux-aarch64.yml
-index c17c3395c99..a26cafa98db 100644
---- a/environment-3.11-linux-aarch64.yml
-+++ b/environment-3.11-linux-aarch64.yml
-@@ -1,7 +1,7 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: linux-aarch64
--# input_hash: 09e3b72a7aa5c065370cb8a339e14ed42ad43f0c89abc55b38713be2d4560fd9
-+# input_hash: 8682c27c6bd8b3e849271dd9881b907b660025227d849b37e5c7098a5a6a84ab
- 
- channels:
-   - conda-forge
-@@ -9,12 +9,12 @@ dependencies:
-   - _openmp_mutex=4.5=2_kmp_llvm
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - alsa-lib=1.2.13=h86ecc28_0
--  - arpack=3.9.1=nompi_hd363cd0_101
-+  - arpack=3.9.1=nompi_h6fc4d3a_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321h2148fe1_1
-   - automake=1.17=pl5321h8af1aa0_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=hd62202e_0
-+  - bdw-gc=8.2.8=h5ad3122_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - binutils=2.43=hf1166c9_2
-   - binutils_impl_linux-aarch64=2.43=h4c662bb_2
-@@ -28,33 +28,33 @@ dependencies:
-   - brotli-python=1.1.0=py311h89d996e_2
-   - bzip2=1.0.8=h68df207_7
-   - c-ares=1.34.4=h86ecc28_0
--  - c-compiler=1.8.0=h6561dab_1
-+  - c-compiler=1.9.0=h6561dab_0
-   - ca-certificates=2024.12.14=hcefe29a_0
-   - cairo=1.18.2=h83712da_1
-   - cddlib=1!0.94m=h719063d_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py311h14e8bb7_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-   - cliquer=1.22=h31becfc_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
-   - contourpy=1.3.1=py311hc07b1fb_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py311ha09ea12_0
-+  - coverage=7.6.10=py311ha09ea12_0
-   - cpython=3.11.11=py311hd8ed1ab_1
--  - cxx-compiler=1.8.0=heb6c788_1
-+  - cxx-compiler=1.9.0=heb6c788_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py311h5ab95f0_0
-+  - cypari2=2.2.1=py311hc8fbf20_0
-   - cyrus-sasl=2.1.27=hf6b2984_7
--  - cysignals=1.11.2=py311h644d908_3
-+  - cysignals=1.12.3=py311h89d996e_0
-   - cython=3.0.11=py311hac78f04_3
-   - dbus=1.13.6=h12b9eeb_3
--  - debugpy=1.8.11=py311h89d996e_0
-+  - debugpy=1.8.12=py311h89d996e_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - double-conversion=3.3.0=h2f0025b_0
-   - ecl=24.5.10=h5567cc5_0
--  - eclib=20231212=h154513d_1
-+  - eclib=20231212=h4705ef2_2
-   - ecm=7.0.5=ha2d0fc4_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -68,14 +68,14 @@ dependencies:
-   - fontconfig=2.15.0=h8dda3cd_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py311h58d527c_0
--  - fortran-compiler=1.8.0=h25a59a9_1
--  - fplll=5.4.5=hb3a790e_0
--  - fpylll=0.6.1=py311h5d3d69a_0
-+  - fonttools=4.55.6=py311h58d527c_0
-+  - fortran-compiler=1.9.0=h25a59a9_0
-+  - fplll=5.5.0=h45c7457_0
-+  - fpylll=0.6.2=py311h2dc1a0e_0
-   - freetype=2.12.1=hf0a5ef3_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h1754e88_1
--  - gap-defaults=4.14.0=h8af1aa0_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h1754e88_2
-+  - gap-defaults=4.14.0=h8af1aa0_2
-   - gcc=13.3.0=h8a56e6e_1
-   - gcc_impl_linux-aarch64=13.3.0=hcdea9b6_1
-   - gcc_linux-aarch64=13.3.0=h1cd514b_7
-@@ -84,7 +84,7 @@ dependencies:
-   - gfortran=13.3.0=h8a56e6e_1
-   - gfortran_impl_linux-aarch64=13.3.0=h174a3c4_1
-   - gfortran_linux-aarch64=13.3.0=h2809cf8_7
--  - giac=1.9.0.21=h04922a4_1
-+  - giac=1.9.0.21=h6e4ddb9_2
-   - givaro=4.2.0=h364d21b_0
-   - glpk=5.0=h66325d0_0
-   - gmp=6.3.0=h0a1ffab_2
-@@ -95,21 +95,21 @@ dependencies:
-   - gxx_impl_linux-aarch64=13.3.0=h1211b58_1
-   - gxx_linux-aarch64=13.3.0=h2864abd_7
-   - h2=4.1.0=pyhd8ed1ab_1
--  - harfbuzz=9.0.0=hbf49d6b_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - harfbuzz=10.2.0=h785c1aa_0
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=hf9b3779_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h207f3e5_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h15043fe_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh3099207_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-@@ -117,7 +117,7 @@ dependencies:
-   - keyutils=1.6.1=h4e544f5_0
-   - kiwisolver=1.4.7=py311h75754e6_0
-   - krb5=1.21.3=h50a48e9_0
--  - lcalc=2.0.5=he588f68_2
-+  - lcalc=2.0.5=h30a6b3d_3
-   - lcms2=2.16=h922389a_0
-   - ld_impl_linux-aarch64=2.43=h80caac9_2
-   - lerc=4.0.0=h4de3ea5_0
-@@ -131,27 +131,27 @@ dependencies:
-   - libbrotlidec=1.1.0=h86ecc28_2
-   - libbrotlienc=1.1.0=h86ecc28_2
-   - libcblas=3.9.0=26_linuxaarch64_openblas
--  - libclang-cpp19.1=19.1.6=default_he324ac1_0
--  - libclang13=19.1.6=default_h4390ef5_0
-+  - libclang-cpp19.1=19.1.7=default_he324ac1_0
-+  - libclang13=19.1.7=default_h4390ef5_0
-   - libcups=2.3.3=h405e4a8_4
-   - libcurl=8.11.1=h6702fde_0
-   - libdeflate=1.23=h5e3c512_0
-   - libdrm=2.4.124=h86ecc28_0
--  - libedit=3.1.20191231=he28a2e2_2
-+  - libedit=3.1.20240808=pl5321h976ea20_0
-   - libegl=1.7.0=hd24410f_2
-   - libev=4.33=h31becfc_2
-   - libexpat=2.6.4=h5ad3122_0
-   - libffi=3.4.2=h3557bc0_5
--  - libflint=3.1.2=h0433c20_101
-+  - libflint=3.1.3.1=hf9b8075_101
-   - libgcc=14.2.0=he277a41_1
-   - libgcc-devel_linux-aarch64=13.3.0=h0c07274_101
-   - libgcc-ng=14.2.0=he9431aa_1
--  - libgd=2.3.3=h6818b27_10
-+  - libgd=2.3.3=hc8d7b1d_11
-   - libgfortran=14.2.0=he9431aa_1
-   - libgfortran-ng=14.2.0=he9431aa_1
-   - libgfortran5=14.2.0=hb6113d0_1
-   - libgl=1.7.0=hd24410f_2
--  - libglib=2.82.2=hc486b8e_0
-+  - libglib=2.82.2=hc486b8e_1
-   - libglvnd=1.7.0=hd24410f_2
-   - libglx=1.7.0=hd24410f_2
-   - libgomp=14.2.0=he277a41_1
-@@ -160,7 +160,7 @@ dependencies:
-   - libjpeg-turbo=3.0.0=h31becfc_1
-   - liblapack=3.9.0=26_linuxaarch64_openblas
-   - liblapacke=3.9.0=26_linuxaarch64_openblas
--  - libllvm19=19.1.6=h2edbd07_0
-+  - libllvm19=19.1.7=h2edbd07_0
-   - liblzma=5.6.3=h86ecc28_1
-   - liblzma-devel=5.6.3=h86ecc28_1
-   - libnghttp2=1.64.0=hc8609a4_0
-@@ -169,18 +169,18 @@ dependencies:
-   - libopenblas=0.3.28=pthreads_h9d3fd7e_1
-   - libopengl=1.7.0=hd24410f_2
-   - libpciaccess=0.18=h31becfc_0
--  - libpng=1.6.44=hc4a20ef_0
-+  - libpng=1.6.45=hec79eb8_0
-   - libpq=17.2=hd56632b_1
-   - libsanitizer=13.3.0=ha58e236_1
-   - libsodium=1.0.20=h68df207_0
--  - libsqlite=3.47.2=h5eb1b54_0
-+  - libsqlite=3.48.0=h5eb1b54_1
-   - libssh2=1.11.1=ha41c0db_0
-   - libstdcxx=14.2.0=h3f4de04_1
-   - libstdcxx-devel_linux-aarch64=13.3.0=h0c07274_101
-   - libstdcxx-ng=14.2.0=hf1166c9_1
-   - libtiff=4.7.0=h88f7998_3
-   - libuuid=2.38.1=hb4cce97_0
--  - libwebp-base=1.4.0=h31becfc_0
-+  - libwebp-base=1.5.0=h0886dbf_0
-   - libxcb=1.17.0=h262b8f6_0
-   - libxcrypt=4.4.36=h31becfc_1
-   - libxkbcommon=1.7.0=h46f2afe_1
-@@ -188,7 +188,7 @@ dependencies:
-   - libxslt=1.1.39=h1cc9640_0
-   - libzlib=1.3.1=h86ecc28_2
-   - linbox=1.7.0=hf74d613_1
--  - llvm-openmp=19.1.6=h013ceaa_0
-+  - llvm-openmp=19.1.7=h013ceaa_0
-   - lrcalc=2.1=h5ad3122_7
-   - m4=1.4.18=h516909a_1001
-   - m4ri=20140914=hedfd65a_1006
-@@ -206,22 +206,22 @@ dependencies:
-   - mpfr=4.2.1=h2305555_3
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
--  - mysql-common=9.0.1=h3f5c77f_3
--  - mysql-libs=9.0.1=h11569fd_3
-+  - mysql-common=9.0.1=h3f5c77f_4
-+  - mysql-libs=9.0.1=h11569fd_4
-   - nauty=2.8.8=h31becfc_1
--  - ncurses=6.5=hcccb83c_1
-+  - ncurses=6.5=ha32ae93_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h70be974_0
-   - ntl=11.4.3=h0d7519b_1
--  - numpy=1.26.4=py311h69ead2a_0
-+  - numpy=2.2.2=py311h6c2b7b4_0
-   - openblas=0.3.28=pthreads_h3a8cbd8_1
-   - openjpeg=2.5.3=h3f56577_0
-   - openldap=2.6.9=h30c48ee_0
--  - openssl=3.4.0=h86ecc28_0
-+  - openssl=3.4.0=hd08dc88_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=hb9de7d4_0
--  - pari=2.15.5=h169c2a7_2_pthread
-+  - pari=2.17.1=h45cace7_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -231,7 +231,7 @@ dependencies:
-   - perl=5.32.1=7_h31becfc_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py311hb2a0dd2_0
-+  - pillow=11.1.0=py311ha4eaa5e_0
-   - pip=24.3.1=pyh8b19718_2
-   - pixman=0.44.2=h86a87f0_0
-   - pkg-config=0.29.2=hce167ba_1009
-@@ -240,18 +240,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h984aac9_1006
--  - pplpy=0.8.9=py311ha3770eb_1
--  - primecount=7.9=hd600fc2_0
--  - primecountpy=0.1.0=py311h098ece5_4
--  - primesieve=11.1=h2f0025b_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py311ha879c10_0
-+  - pplpy=0.8.9=py311h3d7cd5b_2
-+  - primecount=7.14=hfe4b40e_0
-+  - primecountpy=0.1.0=py311hc07b1fb_5
-+  - primesieve=12.4=h0a1ffab_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py311ha879c10_0
-   - pthread-stubs=0.4=h86ecc28_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pyside6=6.8.1=py311habb2604_0
-   - pysocks=1.7.1=pyha55dd90_7
-@@ -265,43 +265,43 @@ dependencies:
-   - pyzmq=26.2.0=py311h826da9f_3
-   - qd=2.3.22=h05efe27_1004
-   - qhull=2020.2=h70be974_5
--  - qt6-main=6.8.1=h0d3cc05_0
-+  - qt6-main=6.8.1=ha0a94ed_2
-   - readline=8.2=h8fc344f_1
-   - requests=2.32.3=pyhd8ed1ab_1
-   - rw=0.9=h31becfc_2
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py311h5912639_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py311h13dcf5b_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - singular=4.4.0=hee12f27_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h578a6b9_0
-+  - sqlite=3.48.0=h578a6b9_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hd600fc2_0
--  - sympow=2.023.6=h157afb5_3
--  - sympy=1.13.3=pyh2585a3b_104
--  - sysroot_linux-aarch64=2.17=h5b4a56d_18
-+  - sympow=2.023.6=h4d450c3_4
-+  - sympy=1.13.3=pyh2585a3b_105
-+  - sysroot_linux-aarch64=2.17=h68829e0_18
-   - tachyon=0.99b6=ha0bfc61_1002
-   - tk=8.6.13=h194ca79_0
-   - tomli=2.2.1=pyhd8ed1ab_1
-   - tornado=6.4.2=py311h5487e9b_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py311ha879c10_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py311ha879c10_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wayland=1.23.1=h698ed42_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-diff --git a/environment-3.11-linux.yml b/environment-3.11-linux.yml
-index 2d99c14d61c..18b21418a74 100644
---- a/environment-3.11-linux.yml
-+++ b/environment-3.11-linux.yml
-@@ -1,7 +1,7 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: linux-64
--# input_hash: 71d6929e3ba448868bcdf30d6cb1d190d88758e7272df5cf428554adbbf0ff6a
-+# input_hash: 45c87b39adab7299f4500096956e14d99327f4a9bb48bc2fc7ced5996c569943
- 
- channels:
-   - conda-forge
-@@ -10,12 +10,12 @@ dependencies:
-   - _openmp_mutex=4.5=2_kmp_llvm
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - alsa-lib=1.2.13=hb9d3cd8_0
--  - arpack=3.9.1=nompi_h77f6705_101
-+  - arpack=3.9.1=nompi_hf03ea27_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321h2b4cb7a_1
-   - automake=1.17=pl5321ha770c72_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=h4bd325d_0
-+  - bdw-gc=8.2.8=h5888daf_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - binutils=2.43=h4852527_2
-   - binutils_impl_linux-64=2.43=h4bf12b8_2
-@@ -29,33 +29,33 @@ dependencies:
-   - brotli-python=1.1.0=py311hfdbb021_2
-   - bzip2=1.0.8=h4bc722e_7
-   - c-ares=1.34.4=hb9d3cd8_0
--  - c-compiler=1.8.0=h2b85faf_1
-+  - c-compiler=1.9.0=h2b85faf_0
-   - ca-certificates=2024.12.14=hbcca054_0
-   - cairo=1.18.2=h3394656_1
-   - cddlib=1!0.94m=h9202a9a_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py311hf29c0ef_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-   - cliquer=1.22=hd590300_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
-   - contourpy=1.3.1=py311hd18a35c_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py311h2dc5d0c_0
-+  - coverage=7.6.10=py311h2dc5d0c_0
-   - cpython=3.11.11=py311hd8ed1ab_1
--  - cxx-compiler=1.8.0=h1a2810e_1
-+  - cxx-compiler=1.9.0=h1a2810e_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py311hd2352ae_0
-+  - cypari2=2.2.1=py311h8699650_0
-   - cyrus-sasl=2.1.27=h54b06d7_7
--  - cysignals=1.11.2=py311h82528dc_3
-+  - cysignals=1.12.3=py311hfdbb021_0
-   - cython=3.0.11=py311h55d416d_3
-   - dbus=1.13.6=h5008d03_3
--  - debugpy=1.8.11=py311hfdbb021_0
-+  - debugpy=1.8.12=py311hfdbb021_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - double-conversion=3.3.0=h59595ed_0
-   - ecl=24.5.10=h0f3afd4_0
--  - eclib=20231212=h43e5eba_1
-+  - eclib=20231212=h75fb491_2
-   - ecm=7.0.5=h9458935_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -69,14 +69,14 @@ dependencies:
-   - fontconfig=2.15.0=h7e30c49_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py311h2dc5d0c_0
--  - fortran-compiler=1.8.0=h36df796_1
--  - fplll=5.4.5=h384768b_0
--  - fpylll=0.6.1=py311hcfae7cf_0
-+  - fonttools=4.55.6=py311h2dc5d0c_0
-+  - fortran-compiler=1.9.0=h36df796_0
-+  - fplll=5.5.0=hd20a173_0
-+  - fpylll=0.6.2=py311hf0b6740_0
-   - freetype=2.12.1=h267a509_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h3b03731_1
--  - gap-defaults=4.14.0=ha770c72_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h3b03731_2
-+  - gap-defaults=4.14.0=ha770c72_2
-   - gcc=13.3.0=h9576a4e_1
-   - gcc_impl_linux-64=13.3.0=hfea6d02_1
-   - gcc_linux-64=13.3.0=hc28eda2_7
-@@ -85,7 +85,7 @@ dependencies:
-   - gfortran=13.3.0=h9576a4e_1
-   - gfortran_impl_linux-64=13.3.0=h10434e7_1
-   - gfortran_linux-64=13.3.0=hb919d3a_7
--  - giac=1.9.0.21=h673759e_1
-+  - giac=1.9.0.21=hca478b9_2
-   - givaro=4.2.0=hb789bce_0
-   - glpk=5.0=h445213a_0
-   - gmp=6.3.0=hac33072_2
-@@ -96,21 +96,21 @@ dependencies:
-   - gxx_impl_linux-64=13.3.0=hdbfa832_1
-   - gxx_linux-64=13.3.0=h6834431_7
-   - h2=4.1.0=pyhd8ed1ab_1
--  - harfbuzz=9.0.0=hda332d3_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - harfbuzz=10.2.0=h4bba637_0
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=he02047a_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=he44f51b_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h623f65a_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh3099207_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-@@ -118,7 +118,7 @@ dependencies:
-   - keyutils=1.6.1=h166bdaf_0
-   - kiwisolver=1.4.7=py311hd18a35c_0
-   - krb5=1.21.3=h659f571_0
--  - lcalc=2.0.5=h5aac1b6_2
-+  - lcalc=2.0.5=h9cf73fc_3
-   - lcms2=2.16=hb7c19ff_0
-   - ld_impl_linux-64=2.43=h712a8e2_2
-   - lerc=4.0.0=h27087fc_0
-@@ -132,27 +132,27 @@ dependencies:
-   - libbrotlidec=1.1.0=hb9d3cd8_2
-   - libbrotlienc=1.1.0=hb9d3cd8_2
-   - libcblas=3.9.0=26_linux64_openblas
--  - libclang-cpp19.1=19.1.6=default_hb5137d0_0
--  - libclang13=19.1.6=default_h9c6a7e4_0
-+  - libclang-cpp19.1=19.1.7=default_hb5137d0_0
-+  - libclang13=19.1.7=default_h9c6a7e4_0
-   - libcups=2.3.3=h4637d8d_4
-   - libcurl=8.11.1=h332b0f4_0
-   - libdeflate=1.23=h4ddbbb0_0
-   - libdrm=2.4.124=hb9d3cd8_0
--  - libedit=3.1.20191231=he28a2e2_2
-+  - libedit=3.1.20240808=pl5321h7949ede_0
-   - libegl=1.7.0=ha4b6fd6_2
-   - libev=4.33=hd590300_2
-   - libexpat=2.6.4=h5888daf_0
-   - libffi=3.4.2=h7f98852_5
--  - libflint=3.1.2=h6fb9888_101
-+  - libflint=3.1.3.1=h0aae882_101
-   - libgcc=14.2.0=h77fa898_1
-   - libgcc-devel_linux-64=13.3.0=h84ea5a7_101
-   - libgcc-ng=14.2.0=h69a702a_1
--  - libgd=2.3.3=hd3e95f3_10
-+  - libgd=2.3.3=h6f5c62b_11
-   - libgfortran=14.2.0=h69a702a_1
-   - libgfortran-ng=14.2.0=h69a702a_1
-   - libgfortran5=14.2.0=hd5240d6_1
-   - libgl=1.7.0=ha4b6fd6_2
--  - libglib=2.82.2=h2ff4ddf_0
-+  - libglib=2.82.2=h2ff4ddf_1
-   - libglvnd=1.7.0=ha4b6fd6_2
-   - libglx=1.7.0=ha4b6fd6_2
-   - libgomp=14.2.0=h77fa898_1
-@@ -161,27 +161,27 @@ dependencies:
-   - libjpeg-turbo=3.0.0=hd590300_1
-   - liblapack=3.9.0=26_linux64_openblas
-   - liblapacke=3.9.0=26_linux64_openblas
--  - libllvm19=19.1.6=ha7bfdaf_0
-+  - libllvm19=19.1.7=ha7bfdaf_0
-   - liblzma=5.6.3=hb9d3cd8_1
-   - liblzma-devel=5.6.3=hb9d3cd8_1
-   - libnghttp2=1.64.0=h161d5f1_0
-   - libnsl=2.0.1=hd590300_0
--  - libntlm=1.4=h7f98852_1002
-+  - libntlm=1.8=hb9d3cd8_0
-   - libopenblas=0.3.28=pthreads_h94d23a6_1
-   - libopengl=1.7.0=ha4b6fd6_2
-   - libpciaccess=0.18=hd590300_0
--  - libpng=1.6.44=hadc24fc_0
-+  - libpng=1.6.45=h943b412_0
-   - libpq=17.2=h3b95a9b_1
-   - libsanitizer=13.3.0=heb74ff8_1
-   - libsodium=1.0.20=h4ab18f5_0
--  - libsqlite=3.47.2=hee588c1_0
-+  - libsqlite=3.48.0=hee588c1_1
-   - libssh2=1.11.1=hf672d98_0
-   - libstdcxx=14.2.0=hc0a3c3a_1
-   - libstdcxx-devel_linux-64=13.3.0=h84ea5a7_101
-   - libstdcxx-ng=14.2.0=h4852527_1
-   - libtiff=4.7.0=hd9ff511_3
-   - libuuid=2.38.1=h0b41bf4_0
--  - libwebp-base=1.4.0=hd590300_0
-+  - libwebp-base=1.5.0=h851e524_0
-   - libxcb=1.17.0=h8a09558_0
-   - libxcrypt=4.4.36=hd590300_1
-   - libxkbcommon=1.7.0=h2c5496b_1
-@@ -189,7 +189,7 @@ dependencies:
-   - libxslt=1.1.39=h76b75d6_0
-   - libzlib=1.3.1=hb9d3cd8_2
-   - linbox=1.7.0=h7298d08_1
--  - llvm-openmp=19.1.6=h024ca30_0
-+  - llvm-openmp=19.1.7=h024ca30_0
-   - lrcalc=2.1=h5888daf_7
-   - m4=1.4.18=h516909a_1001
-   - m4ri=20140914=hae5d5c5_1006
-@@ -207,22 +207,22 @@ dependencies:
-   - mpfr=4.2.1=h90cbb55_3
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
--  - mysql-common=9.0.1=h266115a_3
--  - mysql-libs=9.0.1=he0572af_3
-+  - mysql-common=9.0.1=h266115a_4
-+  - mysql-libs=9.0.1=he0572af_4
-   - nauty=2.8.8=hd590300_1
--  - ncurses=6.5=he02047a_1
-+  - ncurses=6.5=h2d0b736_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h297d8ca_0
-   - ntl=11.4.3=hef3c4d3_1
--  - numpy=1.26.4=py311h64a7726_0
-+  - numpy=2.2.2=py311h5d046bc_0
-   - openblas=0.3.28=pthreads_h6ec200e_1
-   - openjpeg=2.5.3=h5fbd93e_0
-   - openldap=2.6.9=he970967_0
--  - openssl=3.4.0=hb9d3cd8_0
-+  - openssl=3.4.0=h7b32b05_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=h36c2ea0_0
--  - pari=2.15.5=h4d4ae9b_2_pthread
-+  - pari=2.17.1=ha40142e_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -232,7 +232,7 @@ dependencies:
-   - perl=5.32.1=7_hd590300_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py311h49e9ac3_0
-+  - pillow=11.1.0=py311h1322bbf_0
-   - pip=24.3.1=pyh8b19718_2
-   - pixman=0.44.2=h29eaf8c_0
-   - pkg-config=0.29.2=h4bc722e_1009
-@@ -241,18 +241,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h6ec01c2_1006
--  - pplpy=0.8.9=py311ha9f9f00_1
--  - primecount=7.9=hcb278e6_0
--  - primecountpy=0.1.0=py311h9547e67_4
--  - primesieve=11.1=h59595ed_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py311h9ecbd09_0
-+  - pplpy=0.8.9=py311h17071fb_2
-+  - primecount=7.14=h530483c_0
-+  - primecountpy=0.1.0=py311hd18a35c_5
-+  - primesieve=12.4=he02047a_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py311h9ecbd09_0
-   - pthread-stubs=0.4=hb9d3cd8_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pyside6=6.8.1=py311h9053184_0
-   - pysocks=1.7.1=pyha55dd90_7
-@@ -266,43 +266,43 @@ dependencies:
-   - pyzmq=26.2.0=py311h7deb3e3_3
-   - qd=2.3.22=h2cc385e_1004
-   - qhull=2020.2=h434a139_5
--  - qt6-main=6.8.1=h9d28a51_0
-+  - qt6-main=6.8.1=h588cce1_2
-   - readline=8.2=h8228510_1
-   - requests=2.32.3=pyhd8ed1ab_1
-   - rw=0.9=hd590300_2
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py311he9a78e4_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py311hc1ac118_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - singular=4.4.0=hc910cb2_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h9eae976_0
-+  - sqlite=3.48.0=h9eae976_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hcb278e6_0
--  - sympow=2.023.6=hc6ab17c_3
--  - sympy=1.13.3=pyh2585a3b_104
--  - sysroot_linux-64=2.17=h4a8ded7_18
-+  - sympow=2.023.6=h3028977_4
-+  - sympy=1.13.3=pyh2585a3b_105
-+  - sysroot_linux-64=2.17=h0157908_18
-   - tachyon=0.99b6=hba7d16a_1002
-   - tk=8.6.13=noxft_h4845f30_101
-   - tomli=2.2.1=pyhd8ed1ab_1
-   - tornado=6.4.2=py311h9ecbd09_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py311h9ecbd09_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py311h9ecbd09_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wayland=1.23.1=h3e06ad9_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-diff --git a/environment-3.11-macos-x86_64.yml b/environment-3.11-macos-x86_64.yml
-index fb34c25a567..b68c0feb98e 100644
---- a/environment-3.11-macos-x86_64.yml
-+++ b/environment-3.11-macos-x86_64.yml
-@@ -1,19 +1,19 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: osx-64
--# input_hash: 58971dc791eb5f5f7e12b0e44db07ecd9b2fc48def89f671effaabd2bd0720d6
-+# input_hash: 8fa3ecd8c3d833b875f3db11bdea6e4c970fe7eae9e991e45ec6979be4e7b00f
- 
- channels:
-   - conda-forge
- dependencies:
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - appnope=0.1.4=pyhd8ed1ab_1
--  - arpack=3.9.1=nompi_hf81eadf_101
-+  - arpack=3.9.1=nompi_hdfe9103_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321hed12c24_1
-   - automake=1.17=pl5321h694c41f_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=h940c156_0
-+  - bdw-gc=8.2.8=h240833e_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - blas=2.126=openblas
-   - blas-devel=3.9.0=26_osx64_openblas
-@@ -24,40 +24,40 @@ dependencies:
-   - brotli-python=1.1.0=py311hd89902b_2
-   - bzip2=1.0.8=hfdf4475_7
-   - c-ares=1.34.4=hf13058a_0
--  - c-compiler=1.8.0=hfc4bf79_1
-+  - c-compiler=1.9.0=h09a7c41_0
-   - ca-certificates=2024.12.14=h8857fd0_0
--  - cctools=1010.6=h5b2de21_2
--  - cctools_osx-64=1010.6=hea4301f_2
-+  - cctools=1010.6=hd3558d4_2
-+  - cctools_osx-64=1010.6=h00edd4c_2
-   - cddlib=1!0.94m=h0f52abe_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py311h137bacd_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
--  - clang=17.0.6=default_he371ed4_7
--  - clang-17=17.0.6=default_hb173f14_7
--  - clang_impl_osx-64=17.0.6=h1af8efd_23
--  - clang_osx-64=17.0.6=h7e5c614_23
--  - clangxx=17.0.6=default_he371ed4_7
--  - clangxx_impl_osx-64=17.0.6=hc3430b7_23
--  - clangxx_osx-64=17.0.6=h7e5c614_23
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-+  - clang=18.1.8=default_h179603d_5
-+  - clang-18=18.1.8=default_h0c94c6a_5
-+  - clang_impl_osx-64=18.1.8=h6a44ed1_23
-+  - clang_osx-64=18.1.8=h7e5c614_23
-+  - clangxx=18.1.8=default_h179603d_5
-+  - clangxx_impl_osx-64=18.1.8=h4b7810f_23
-+  - clangxx_osx-64=18.1.8=h7e5c614_23
-   - cliquer=1.22=h10d778d_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
--  - compiler-rt=17.0.6=h1020d70_2
--  - compiler-rt_osx-64=17.0.6=hf2b8a54_2
-+  - compiler-rt=18.1.8=h1020d70_1
-+  - compiler-rt_osx-64=18.1.8=hf2b8a54_1
-   - contourpy=1.3.1=py311h4e34fa0_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py311ha3cf9ac_0
-+  - coverage=7.6.10=py311ha3cf9ac_0
-   - cpython=3.11.11=py311hd8ed1ab_1
--  - cxx-compiler=1.8.0=h385f146_1
-+  - cxx-compiler=1.9.0=h20888b2_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py311h4fde0ae_0
--  - cysignals=1.11.2=py311h8a58447_3
-+  - cypari2=2.2.1=py311h29339b9_0
-+  - cysignals=1.12.3=py311hc356e98_0
-   - cython=3.0.11=py311h4cb39f0_3
--  - debugpy=1.8.11=py311hc356e98_0
-+  - debugpy=1.8.12=py311hc356e98_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - ecl=24.5.10=h56bac16_0
--  - eclib=20231212=h960c116_1
-+  - eclib=20231212=ha63dd29_2
-   - ecm=7.0.5=h4f6b447_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -71,14 +71,14 @@ dependencies:
-   - fontconfig=2.15.0=h37eeddb_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py311ha3cf9ac_0
--  - fortran-compiler=1.8.0=h33d1f46_1
--  - fplll=5.4.5=hb7981ad_0
--  - fpylll=0.6.1=py311h85fbf69_0
-+  - fonttools=4.55.6=py311ha3cf9ac_0
-+  - fortran-compiler=1.9.0=h02557f8_0
-+  - fplll=5.5.0=h6ede486_0
-+  - fpylll=0.6.2=py311h793c761_0
-   - freetype=2.12.1=h60636b9_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=hb9686a1_1
--  - gap-defaults=4.14.0=h694c41f_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=hb9686a1_2
-+  - gap-defaults=4.14.0=h694c41f_2
-   - gettext=0.22.5=hdfe23c8_3
-   - gettext-tools=0.22.5=hdfe23c8_3
-   - gf2x=1.3.0=h35ac7d9_3
-@@ -86,37 +86,37 @@ dependencies:
-   - gfortran=13.2.0=h2c809b3_1
-   - gfortran_impl_osx-64=13.2.0=h2bc304d_3
-   - gfortran_osx-64=13.2.0=h18f7dce_1
--  - giac=1.9.0.21=h92f3f65_1
-+  - giac=1.9.0.21=h381f543_2
-   - givaro=4.2.0=h1b3d6f7_0
-   - glpk=5.0=h3cb5acd_0
-   - gmp=6.3.0=hf036a51_2
-   - gmpy2=2.1.5=py311h7945f45_3
-   - gsl=2.7=h93259b0_0
-   - h2=4.1.0=pyhd8ed1ab_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=h120a0e1_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h5479cbe_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h61918c1_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh57ce528_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - isl=0.26=imath32_h2e86a7b_101
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-   - kiwisolver=1.4.7=py311hf2f7c97_0
-   - krb5=1.21.3=h37d8d59_0
--  - lcalc=2.0.5=h547a6ed_2
-+  - lcalc=2.0.5=h0f747f7_3
-   - lcms2=2.16=ha2f27b4_0
--  - ld64=951.9=h0a3eb4e_2
--  - ld64_osx-64=951.9=h5ffbe8e_2
-+  - ld64=951.9=h4e51db5_2
-+  - ld64_osx-64=951.9=hc8d1a19_2
-   - lerc=4.0.0=hb486fe8_0
-   - libasprintf=0.22.5=hdfe23c8_3
-   - libasprintf-devel=0.22.5=hdfe23c8_3
-@@ -130,17 +130,17 @@ dependencies:
-   - libbrotlidec=1.1.0=h00291cd_2
-   - libbrotlienc=1.1.0=h00291cd_2
-   - libcblas=3.9.0=26_osx64_openblas
--  - libclang-cpp17=17.0.6=default_hb173f14_7
-+  - libclang-cpp18.1=18.1.8=default_h0c94c6a_5
-   - libcurl=8.11.1=h5dec5d8_0
--  - libcxx=19.1.6=hf95d169_1
--  - libcxx-devel=17.0.6=h8f8a49f_6
-+  - libcxx=19.1.7=hf95d169_0
-+  - libcxx-devel=18.1.8=h7c275be_7
-   - libdeflate=1.23=he65b83e_0
--  - libedit=3.1.20191231=h0678c8f_2
-+  - libedit=3.1.20240808=pl5321ha958ccf_0
-   - libev=4.33=h10d778d_2
-   - libexpat=2.6.4=h240833e_0
-   - libffi=3.4.2=h0d85af4_5
--  - libflint=3.1.2=h1d27844_101
--  - libgd=2.3.3=h2e77e4f_10
-+  - libflint=3.1.3.1=h9ab60bc_101
-+  - libgd=2.3.3=h8555400_11
-   - libgettextpo=0.22.5=hdfe23c8_3
-   - libgettextpo-devel=0.22.5=hdfe23c8_3
-   - libgfortran=5.0.0=13_2_0_h97931a8_3
-@@ -153,23 +153,24 @@ dependencies:
-   - libjpeg-turbo=3.0.0=h0dc2134_1
-   - liblapack=3.9.0=26_osx64_openblas
-   - liblapacke=3.9.0=26_osx64_openblas
--  - libllvm17=17.0.6=hbedff68_1
-+  - libllvm18=18.1.8=h9ce406d_2
-   - liblzma=5.6.3=hd471939_1
-   - liblzma-devel=5.6.3=hd471939_1
-   - libnghttp2=1.64.0=hc7306c3_0
-   - libopenblas=0.3.28=openmp_hbf64a52_1
--  - libpng=1.6.44=h4b8f8c9_0
-+  - libpng=1.6.45=h3c4a55f_0
-   - libsodium=1.0.20=hfdf4475_0
--  - libsqlite=3.47.2=hdb6dae5_0
-+  - libsqlite=3.48.0=hdb6dae5_1
-   - libssh2=1.11.1=h3dc7d44_0
-   - libtiff=4.7.0=hb77a491_3
--  - libwebp-base=1.4.0=h10d778d_0
-+  - libwebp-base=1.5.0=h6cf52b4_0
-   - libxcb=1.17.0=hf1f96e2_0
-   - libxml2=2.13.5=hebb159f_1
-   - libzlib=1.3.1=hd23fc13_2
-   - linbox=1.7.0=h9325161_1
--  - llvm-openmp=19.1.6=ha54dae1_0
--  - llvm-tools=17.0.6=hbedff68_1
-+  - llvm-openmp=19.1.7=ha54dae1_0
-+  - llvm-tools=18.1.8=h9ce406d_2
-+  - llvm-tools-18=18.1.8=h9ce406d_2
-   - lrcalc=2.1=hac325c4_7
-   - m4=1.4.18=haf1e3a3_1001
-   - m4ri=20140914=hd82a5f3_1006
-@@ -188,18 +189,18 @@ dependencies:
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
-   - nauty=2.8.8=h10d778d_1
--  - ncurses=6.5=hf036a51_1
-+  - ncurses=6.5=h0622a9a_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h3c5361c_0
-   - ntl=11.4.3=h0ab3c2f_1
--  - numpy=1.26.4=py311hc43a94b_0
-+  - numpy=2.2.2=py311h27c81cd_0
-   - openblas=0.3.28=openmp_h30af337_1
-   - openjpeg=2.5.3=h7fd6d84_0
--  - openssl=3.4.0=hd471939_0
-+  - openssl=3.4.0=hc426f3f_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=hbcb3906_0
--  - pari=2.15.5=h7ba67ff_2_pthread
-+  - pari=2.17.1=h1ed0f1a_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -208,7 +209,7 @@ dependencies:
-   - perl=5.32.1=7_h10d778d_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py311h1f68098_0
-+  - pillow=11.1.0=py311h25da234_0
-   - pip=24.3.1=pyh8b19718_2
-   - pkg-config=0.29.2=hf7e621a_1009
-   - pkgconfig=1.5.5=pyhd8ed1ab_5
-@@ -216,18 +217,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=ha60d53e_1006
--  - pplpy=0.8.9=py311h922ec50_1
--  - primecount=7.6=ha894c9a_0
--  - primecountpy=0.1.0=py311h5fe6e05_4
--  - primesieve=11.0=hf0c8a7f_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py311h1314207_0
-+  - pplpy=0.8.9=py311h221ab62_2
-+  - primecount=7.14=h28dbb38_0
-+  - primecountpy=0.1.0=py311h4e34fa0_5
-+  - primesieve=12.4=hf036a51_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py311h4d7f069_0
-   - pthread-stubs=0.4=h00291cd_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pysocks=1.7.1=pyha55dd90_7
-   - pytest=8.3.4=pyhd8ed1ab_1
-@@ -246,27 +247,27 @@ dependencies:
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py311h86b91e6_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py311h9d25053_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - sigtool=0.1.3=h88f4db0_0
-   - singular=4.4.0=h604985e_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h2e4c9dc_0
-+  - sqlite=3.48.0=h2e4c9dc_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hf0c8a7f_0
--  - sympow=2.023.6=h115ba6a_3
--  - sympy=1.13.3=pyh2585a3b_104
-+  - sympow=2.023.6=h7305399_4
-+  - sympy=1.13.3=pyh2585a3b_105
-   - tachyon=0.99b6=h3a1d103_1002
-   - tapi=1300.6.5=h390ca13_0
-   - tk=8.6.13=h1abcd95_1
-@@ -274,9 +275,9 @@ dependencies:
-   - tornado=6.4.2=py311h4d7f069_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py311h1314207_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py311h4d7f069_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-   - widgetsnbextension=4.0.13=pyhd8ed1ab_1
-diff --git a/environment-3.11-macos.yml b/environment-3.11-macos.yml
-index ec10b78a4b5..84656e580e0 100644
---- a/environment-3.11-macos.yml
-+++ b/environment-3.11-macos.yml
-@@ -1,19 +1,19 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: osx-arm64
--# input_hash: 4396163dbc4fafd471282f306c16bb7bd73ecc3c006335c8faf512742014e1e4
-+# input_hash: 5e8fbac460b9515b4cab214ac84ab31b22e5e12e86962f7770faaa3a3c662466
- 
- channels:
-   - conda-forge
- dependencies:
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - appnope=0.1.4=pyhd8ed1ab_1
--  - arpack=3.9.1=nompi_h593882a_101
-+  - arpack=3.9.1=nompi_h1f29f7c_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321hcd07c0c_1
-   - automake=1.17=pl5321hce30654_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=hc021e02_0
-+  - bdw-gc=8.2.8=h286801f_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - blas=2.126=openblas
-   - blas-devel=3.9.0=26_osxarm64_openblas
-@@ -24,40 +24,40 @@ dependencies:
-   - brotli-python=1.1.0=py311h3f08180_2
-   - bzip2=1.0.8=h99b78c6_7
-   - c-ares=1.34.4=h5505292_0
--  - c-compiler=1.8.0=hf48404e_1
-+  - c-compiler=1.9.0=hdf49b6b_0
-   - ca-certificates=2024.12.14=hf0a4a13_0
--  - cctools=1010.6=hf67d63f_2
--  - cctools_osx-arm64=1010.6=h623e0ac_2
-+  - cctools=1010.6=h4c9edd9_2
-+  - cctools_osx-arm64=1010.6=h908b477_2
-   - cddlib=1!0.94m=h6d7a090_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py311h3a79f62_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
--  - clang=17.0.6=default_h360f5da_7
--  - clang-17=17.0.6=default_h146c034_7
--  - clang_impl_osx-arm64=17.0.6=he47c785_23
--  - clang_osx-arm64=17.0.6=h07b0088_23
--  - clangxx=17.0.6=default_h360f5da_7
--  - clangxx_impl_osx-arm64=17.0.6=h50f59cd_23
--  - clangxx_osx-arm64=17.0.6=h07b0088_23
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-+  - clang=18.1.8=default_h675cc0c_5
-+  - clang-18=18.1.8=default_h5c12605_5
-+  - clang_impl_osx-arm64=18.1.8=h2ae9ea5_23
-+  - clang_osx-arm64=18.1.8=h07b0088_23
-+  - clangxx=18.1.8=default_h675cc0c_5
-+  - clangxx_impl_osx-arm64=18.1.8=h555f467_23
-+  - clangxx_osx-arm64=18.1.8=h07b0088_23
-   - cliquer=1.22=h93a5062_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
--  - compiler-rt=17.0.6=h856b3c1_2
--  - compiler-rt_osx-arm64=17.0.6=h832e737_2
-+  - compiler-rt=18.1.8=h856b3c1_1
-+  - compiler-rt_osx-arm64=18.1.8=h832e737_1
-   - contourpy=1.3.1=py311h210dab8_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py311h4921393_0
-+  - coverage=7.6.10=py311h4921393_0
-   - cpython=3.11.11=py311hd8ed1ab_1
--  - cxx-compiler=1.8.0=h18dbf2f_1
-+  - cxx-compiler=1.9.0=hba80287_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py311h2c49a9d_0
--  - cysignals=1.11.2=py311he42fc87_3
-+  - cypari2=2.2.1=py311haabaa81_0
-+  - cysignals=1.12.3=py311h155a34a_0
-   - cython=3.0.11=py311hf7f79b8_3
--  - debugpy=1.8.11=py311h155a34a_0
-+  - debugpy=1.8.12=py311h155a34a_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - ecl=23.9.9=h1d9728a_0
--  - eclib=20231212=h3d50bd9_1
-+  - eclib=20231212=hc39b9a7_2
-   - ecm=7.0.5=h41d338b_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -71,14 +71,14 @@ dependencies:
-   - fontconfig=2.15.0=h1383a14_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py311h4921393_0
--  - fortran-compiler=1.8.0=hc3477c4_1
--  - fplll=5.4.5=hb7d509d_0
--  - fpylll=0.6.1=py311h341b96b_0
-+  - fonttools=4.55.6=py311h4921393_0
-+  - fortran-compiler=1.9.0=h5692697_0
-+  - fplll=5.5.0=h2a2278a_0
-+  - fpylll=0.6.2=py311h4044dbd_0
-   - freetype=2.12.1=hadb7bae_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h25f1785_1
--  - gap-defaults=4.14.0=hce30654_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h25f1785_2
-+  - gap-defaults=4.14.0=hce30654_2
-   - gettext=0.22.5=h8414b35_3
-   - gettext-tools=0.22.5=h8414b35_3
-   - gf2x=1.3.0=hf8f8af4_3
-@@ -86,37 +86,37 @@ dependencies:
-   - gfortran=13.2.0=h1ca8e4b_1
-   - gfortran_impl_osx-arm64=13.2.0=h252ada1_3
-   - gfortran_osx-arm64=13.2.0=h57527a5_1
--  - giac=1.9.0.21=h1c96721_1
-+  - giac=1.9.0.21=h573964a_2
-   - givaro=4.2.0=h018886a_0
-   - glpk=5.0=h6d7a090_0
-   - gmp=6.3.0=h7bae524_2
-   - gmpy2=2.1.5=py311hb5d9ff4_3
-   - gsl=2.7=h6e638da_0
-   - h2=4.1.0=pyhd8ed1ab_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=hfee45f7_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h3fe6531_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=hd73f12c_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh57ce528_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - isl=0.26=imath32_h347afa1_101
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-   - kiwisolver=1.4.7=py311h2c37856_0
-   - krb5=1.21.3=h237132a_0
--  - lcalc=2.0.5=h4a402bc_2
-+  - lcalc=2.0.5=hdaf6845_3
-   - lcms2=2.16=ha0e7c42_0
--  - ld64=951.9=h39a299f_2
--  - ld64_osx-arm64=951.9=h3f9b568_2
-+  - ld64=951.9=h4c6efb1_2
-+  - ld64_osx-arm64=951.9=hfc0fa09_2
-   - lerc=4.0.0=h9a09cb3_0
-   - libasprintf=0.22.5=h8414b35_3
-   - libasprintf-devel=0.22.5=h8414b35_3
-@@ -130,23 +130,23 @@ dependencies:
-   - libbrotlidec=1.1.0=hd74edd7_2
-   - libbrotlienc=1.1.0=hd74edd7_2
-   - libcblas=3.9.0=26_osxarm64_openblas
--  - libclang-cpp17=17.0.6=default_h146c034_7
-+  - libclang-cpp18.1=18.1.8=default_h5c12605_5
-   - libcurl=8.11.1=h73640d1_0
--  - libcxx=19.1.6=ha82da77_1
--  - libcxx-devel=17.0.6=h86353a2_6
-+  - libcxx=19.1.7=ha82da77_0
-+  - libcxx-devel=18.1.8=h6dc3340_7
-   - libdeflate=1.23=hec38601_0
--  - libedit=3.1.20191231=hc8eb9b7_2
-+  - libedit=3.1.20240808=pl5321hafb1f1b_0
-   - libev=4.33=h93a5062_2
-   - libexpat=2.6.4=h286801f_0
-   - libffi=3.4.2=h3422bc3_5
--  - libflint=3.1.2=he28cf6d_101
--  - libgd=2.3.3=hac1b3a8_10
-+  - libflint=3.1.3.1=ha3035ea_101
-+  - libgd=2.3.3=hb2c3a21_11
-   - libgettextpo=0.22.5=h8414b35_3
-   - libgettextpo-devel=0.22.5=h8414b35_3
-   - libgfortran=5.0.0=13_2_0_hd922786_3
-   - libgfortran-devel_osx-arm64=13.2.0=h5d7a38c_3
-   - libgfortran5=13.2.0=hf226fd6_3
--  - libglib=2.82.2=h07bd6cf_0
-+  - libglib=2.82.2=hdff4504_1
-   - libhomfly=1.02r6=h93a5062_1
-   - libiconv=1.17=h0d3ecfb_2
-   - libintl=0.22.5=h8414b35_3
-@@ -154,23 +154,24 @@ dependencies:
-   - libjpeg-turbo=3.0.0=hb547adb_1
-   - liblapack=3.9.0=26_osxarm64_openblas
-   - liblapacke=3.9.0=26_osxarm64_openblas
--  - libllvm17=17.0.6=h5090b49_2
-+  - libllvm18=18.1.8=h5090b49_2
-   - liblzma=5.6.3=h39f12f2_1
-   - liblzma-devel=5.6.3=h39f12f2_1
-   - libnghttp2=1.64.0=h6d7220d_0
-   - libopenblas=0.3.28=openmp_hf332438_1
--  - libpng=1.6.44=hc14010f_0
-+  - libpng=1.6.45=h3783ad8_0
-   - libsodium=1.0.20=h99b78c6_0
--  - libsqlite=3.47.2=h3f77e49_0
-+  - libsqlite=3.48.0=h3f77e49_1
-   - libssh2=1.11.1=h9cc3647_0
-   - libtiff=4.7.0=h551f018_3
--  - libwebp-base=1.4.0=h93a5062_0
-+  - libwebp-base=1.5.0=h2471fea_0
-   - libxcb=1.17.0=hdb1d25a_0
-   - libxml2=2.13.5=h178c5d8_1
-   - libzlib=1.3.1=h8359307_2
-   - linbox=1.7.0=h9da6ecd_1
--  - llvm-openmp=19.1.6=hdb05f8b_0
--  - llvm-tools=17.0.6=h5090b49_2
-+  - llvm-openmp=19.1.7=hdb05f8b_0
-+  - llvm-tools=18.1.8=h5090b49_2
-+  - llvm-tools-18=18.1.8=h5090b49_2
-   - lrcalc=2.1=hf9b8971_7
-   - m4=1.4.18=h642e427_1001
-   - m4ri=20140914=hc97c1ff_1006
-@@ -189,18 +190,18 @@ dependencies:
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
-   - nauty=2.8.8=h93a5062_1
--  - ncurses=6.5=h7bae524_1
-+  - ncurses=6.5=h5e97a16_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h420ef59_0
-   - ntl=11.4.3=hbb3f309_1
--  - numpy=1.26.4=py311h7125741_0
-+  - numpy=2.2.2=py311h762c074_0
-   - openblas=0.3.28=openmp_hea878ba_1
-   - openjpeg=2.5.3=h8a3d83b_0
--  - openssl=3.4.0=h39f12f2_0
-+  - openssl=3.4.0=h81ee809_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=h27ca646_0
--  - pari=2.15.5=h4f2304c_2_pthread
-+  - pari=2.17.1=h49d18c7_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -210,7 +211,7 @@ dependencies:
-   - perl=5.32.1=7_h4614cfb_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py311h3894ae9_0
-+  - pillow=11.1.0=py311hb9ba9e9_0
-   - pip=24.3.1=pyh8b19718_2
-   - pkg-config=0.29.2=hde07d2e_1009
-   - pkgconfig=1.5.5=pyhd8ed1ab_5
-@@ -218,18 +219,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h8b147cf_1006
--  - pplpy=0.8.9=py311h3d77d83_1
--  - primecount=7.6=hb6e4faa_0
--  - primecountpy=0.1.0=py311he4fd1f5_4
--  - primesieve=11.0=hb7217d7_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py311hae2e1ce_0
-+  - pplpy=0.8.9=py311h911f23a_2
-+  - primecount=7.14=ha84d530_0
-+  - primecountpy=0.1.0=py311h210dab8_5
-+  - primesieve=12.4=h00cdb27_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py311h917b07b_0
-   - pthread-stubs=0.4=hd74edd7_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pysocks=1.7.1=pyha55dd90_7
-   - pytest=8.3.4=pyhd8ed1ab_1
-@@ -248,27 +249,27 @@ dependencies:
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py311hf056e50_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py311h809cfb5_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - sigtool=0.1.3=h44b9a77_0
-   - singular=4.4.0=h5a8969a_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=hd7222ec_0
-+  - sqlite=3.48.0=hd7222ec_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hb7217d7_0
--  - sympow=2.023.6=hb0babe8_3
--  - sympy=1.13.3=pyh2585a3b_104
-+  - sympow=2.023.6=hc13a52f_4
-+  - sympy=1.13.3=pyh2585a3b_105
-   - tachyon=0.99b6=hb8a568e_1002
-   - tapi=1300.6.5=h03f4b80_0
-   - tk=8.6.13=h5083fa2_1
-@@ -276,9 +277,9 @@ dependencies:
-   - tornado=6.4.2=py311h917b07b_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py311hae2e1ce_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py311h917b07b_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-   - widgetsnbextension=4.0.13=pyhd8ed1ab_1
-diff --git a/environment-3.12-linux-aarch64.yml b/environment-3.12-linux-aarch64.yml
-index b97f90268d1..2446ad05b1c 100644
---- a/environment-3.12-linux-aarch64.yml
-+++ b/environment-3.12-linux-aarch64.yml
-@@ -1,7 +1,7 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: linux-aarch64
--# input_hash: 28dba81f3f7cbaa4e6f35a34c9679049f47c3d73414a0a80eda04a53603e8a12
-+# input_hash: 7a6a0ff484e658c4a62a4eaf83b31a521a92aa6e6681138a6c141b28e7fa0c44
- 
- channels:
-   - conda-forge
-@@ -9,12 +9,12 @@ dependencies:
-   - _openmp_mutex=4.5=2_kmp_llvm
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - alsa-lib=1.2.13=h86ecc28_0
--  - arpack=3.9.1=nompi_hd363cd0_101
-+  - arpack=3.9.1=nompi_h6fc4d3a_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321h2148fe1_1
-   - automake=1.17=pl5321h8af1aa0_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=hd62202e_0
-+  - bdw-gc=8.2.8=h5ad3122_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - binutils=2.43=hf1166c9_2
-   - binutils_impl_linux-aarch64=2.43=h4c662bb_2
-@@ -28,33 +28,33 @@ dependencies:
-   - brotli-python=1.1.0=py312h6f74592_2
-   - bzip2=1.0.8=h68df207_7
-   - c-ares=1.34.4=h86ecc28_0
--  - c-compiler=1.8.0=h6561dab_1
-+  - c-compiler=1.9.0=h6561dab_0
-   - ca-certificates=2024.12.14=hcefe29a_0
-   - cairo=1.18.2=h83712da_1
-   - cddlib=1!0.94m=h719063d_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py312hac81daf_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-   - cliquer=1.22=h31becfc_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
-   - contourpy=1.3.1=py312h451a7dd_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py312h74ce7d3_0
-+  - coverage=7.6.10=py312h74ce7d3_0
-   - cpython=3.12.8=py312hd8ed1ab_1
--  - cxx-compiler=1.8.0=heb6c788_1
-+  - cxx-compiler=1.9.0=heb6c788_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py312h7f7bc3d_0
-+  - cypari2=2.2.1=py312hb80cc37_0
-   - cyrus-sasl=2.1.27=hf6b2984_7
--  - cysignals=1.11.2=py312haf3d6d2_3
-+  - cysignals=1.12.3=py312h6f74592_0
-   - cython=3.0.11=py312hdfe4e29_3
-   - dbus=1.13.6=h12b9eeb_3
--  - debugpy=1.8.11=py312h6f74592_0
-+  - debugpy=1.8.12=py312h6f74592_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - double-conversion=3.3.0=h2f0025b_0
-   - ecl=24.5.10=h5567cc5_0
--  - eclib=20231212=h154513d_1
-+  - eclib=20231212=h4705ef2_2
-   - ecm=7.0.5=ha2d0fc4_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -68,14 +68,14 @@ dependencies:
-   - fontconfig=2.15.0=h8dda3cd_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py312hcc812fe_0
--  - fortran-compiler=1.8.0=h25a59a9_1
--  - fplll=5.4.5=hb3a790e_0
--  - fpylll=0.6.1=py312h8b93be1_0
-+  - fonttools=4.55.6=py312hcc812fe_0
-+  - fortran-compiler=1.9.0=h25a59a9_0
-+  - fplll=5.5.0=h45c7457_0
-+  - fpylll=0.6.2=py312h37c3976_0
-   - freetype=2.12.1=hf0a5ef3_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h1754e88_1
--  - gap-defaults=4.14.0=h8af1aa0_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h1754e88_2
-+  - gap-defaults=4.14.0=h8af1aa0_2
-   - gcc=13.3.0=h8a56e6e_1
-   - gcc_impl_linux-aarch64=13.3.0=hcdea9b6_1
-   - gcc_linux-aarch64=13.3.0=h1cd514b_7
-@@ -84,7 +84,7 @@ dependencies:
-   - gfortran=13.3.0=h8a56e6e_1
-   - gfortran_impl_linux-aarch64=13.3.0=h174a3c4_1
-   - gfortran_linux-aarch64=13.3.0=h2809cf8_7
--  - giac=1.9.0.21=h04922a4_1
-+  - giac=1.9.0.21=h6e4ddb9_2
-   - givaro=4.2.0=h364d21b_0
-   - glpk=5.0=h66325d0_0
-   - gmp=6.3.0=h0a1ffab_2
-@@ -95,29 +95,29 @@ dependencies:
-   - gxx_impl_linux-aarch64=13.3.0=h1211b58_1
-   - gxx_linux-aarch64=13.3.0=h2864abd_7
-   - h2=4.1.0=pyhd8ed1ab_1
--  - harfbuzz=9.0.0=hbf49d6b_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - harfbuzz=10.2.0=h785c1aa_0
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=hf9b3779_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h207f3e5_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h15043fe_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh3099207_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-   - kernel-headers_linux-aarch64=4.18.0=h05a177a_18
-   - keyutils=1.6.1=h4e544f5_0
--  - kiwisolver=1.4.7=py312h88dc405_0
-+  - kiwisolver=1.4.8=py312h17cf362_0
-   - krb5=1.21.3=h50a48e9_0
--  - lcalc=2.0.5=he588f68_2
-+  - lcalc=2.0.5=h30a6b3d_3
-   - lcms2=2.16=h922389a_0
-   - ld_impl_linux-aarch64=2.43=h80caac9_2
-   - lerc=4.0.0=h4de3ea5_0
-@@ -131,27 +131,27 @@ dependencies:
-   - libbrotlidec=1.1.0=h86ecc28_2
-   - libbrotlienc=1.1.0=h86ecc28_2
-   - libcblas=3.9.0=26_linuxaarch64_openblas
--  - libclang-cpp19.1=19.1.6=default_he324ac1_0
--  - libclang13=19.1.6=default_h4390ef5_0
-+  - libclang-cpp19.1=19.1.7=default_he324ac1_0
-+  - libclang13=19.1.7=default_h4390ef5_0
-   - libcups=2.3.3=h405e4a8_4
-   - libcurl=8.11.1=h6702fde_0
-   - libdeflate=1.23=h5e3c512_0
-   - libdrm=2.4.124=h86ecc28_0
--  - libedit=3.1.20191231=he28a2e2_2
-+  - libedit=3.1.20240808=pl5321h976ea20_0
-   - libegl=1.7.0=hd24410f_2
-   - libev=4.33=h31becfc_2
-   - libexpat=2.6.4=h5ad3122_0
-   - libffi=3.4.2=h3557bc0_5
--  - libflint=3.1.2=h0433c20_101
-+  - libflint=3.1.3.1=hf9b8075_101
-   - libgcc=14.2.0=he277a41_1
-   - libgcc-devel_linux-aarch64=13.3.0=h0c07274_101
-   - libgcc-ng=14.2.0=he9431aa_1
--  - libgd=2.3.3=h6818b27_10
-+  - libgd=2.3.3=hc8d7b1d_11
-   - libgfortran=14.2.0=he9431aa_1
-   - libgfortran-ng=14.2.0=he9431aa_1
-   - libgfortran5=14.2.0=hb6113d0_1
-   - libgl=1.7.0=hd24410f_2
--  - libglib=2.82.2=hc486b8e_0
-+  - libglib=2.82.2=hc486b8e_1
-   - libglvnd=1.7.0=hd24410f_2
-   - libglx=1.7.0=hd24410f_2
-   - libgomp=14.2.0=he277a41_1
-@@ -160,7 +160,7 @@ dependencies:
-   - libjpeg-turbo=3.0.0=h31becfc_1
-   - liblapack=3.9.0=26_linuxaarch64_openblas
-   - liblapacke=3.9.0=26_linuxaarch64_openblas
--  - libllvm19=19.1.6=h2edbd07_0
-+  - libllvm19=19.1.7=h2edbd07_0
-   - liblzma=5.6.3=h86ecc28_1
-   - liblzma-devel=5.6.3=h86ecc28_1
-   - libnghttp2=1.64.0=hc8609a4_0
-@@ -169,18 +169,18 @@ dependencies:
-   - libopenblas=0.3.28=pthreads_h9d3fd7e_1
-   - libopengl=1.7.0=hd24410f_2
-   - libpciaccess=0.18=h31becfc_0
--  - libpng=1.6.44=hc4a20ef_0
-+  - libpng=1.6.45=hec79eb8_0
-   - libpq=17.2=hd56632b_1
-   - libsanitizer=13.3.0=ha58e236_1
-   - libsodium=1.0.20=h68df207_0
--  - libsqlite=3.47.2=h5eb1b54_0
-+  - libsqlite=3.48.0=h5eb1b54_1
-   - libssh2=1.11.1=ha41c0db_0
-   - libstdcxx=14.2.0=h3f4de04_1
-   - libstdcxx-devel_linux-aarch64=13.3.0=h0c07274_101
-   - libstdcxx-ng=14.2.0=hf1166c9_1
-   - libtiff=4.7.0=h88f7998_3
-   - libuuid=2.38.1=hb4cce97_0
--  - libwebp-base=1.4.0=h31becfc_0
-+  - libwebp-base=1.5.0=h0886dbf_0
-   - libxcb=1.17.0=h262b8f6_0
-   - libxcrypt=4.4.36=h31becfc_1
-   - libxkbcommon=1.7.0=h46f2afe_1
-@@ -188,7 +188,7 @@ dependencies:
-   - libxslt=1.1.39=h1cc9640_0
-   - libzlib=1.3.1=h86ecc28_2
-   - linbox=1.7.0=hf74d613_1
--  - llvm-openmp=19.1.6=h013ceaa_0
-+  - llvm-openmp=19.1.7=h013ceaa_0
-   - lrcalc=2.1=h5ad3122_7
-   - m4=1.4.18=h516909a_1001
-   - m4ri=20140914=hedfd65a_1006
-@@ -206,22 +206,22 @@ dependencies:
-   - mpfr=4.2.1=h2305555_3
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
--  - mysql-common=9.0.1=h3f5c77f_3
--  - mysql-libs=9.0.1=h11569fd_3
-+  - mysql-common=9.0.1=h3f5c77f_4
-+  - mysql-libs=9.0.1=h11569fd_4
-   - nauty=2.8.8=h31becfc_1
--  - ncurses=6.5=hcccb83c_1
-+  - ncurses=6.5=ha32ae93_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h70be974_0
-   - ntl=11.4.3=h0d7519b_1
--  - numpy=1.26.4=py312h470d778_0
-+  - numpy=2.2.2=py312hce01fe4_0
-   - openblas=0.3.28=pthreads_h3a8cbd8_1
-   - openjpeg=2.5.3=h3f56577_0
-   - openldap=2.6.9=h30c48ee_0
--  - openssl=3.4.0=h86ecc28_0
-+  - openssl=3.4.0=hd08dc88_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=hb9de7d4_0
--  - pari=2.15.5=h169c2a7_2_pthread
-+  - pari=2.17.1=h45cace7_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -231,7 +231,7 @@ dependencies:
-   - perl=5.32.1=7_h31becfc_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py312h5ab5af3_0
-+  - pillow=11.1.0=py312h719f0cf_0
-   - pip=24.3.1=pyh8b19718_2
-   - pixman=0.44.2=h86a87f0_0
-   - pkg-config=0.29.2=hce167ba_1009
-@@ -240,18 +240,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h984aac9_1006
--  - pplpy=0.8.9=py312hbd99ab9_1
--  - primecount=7.9=hd600fc2_0
--  - primecountpy=0.1.0=py312h8f0b210_4
--  - primesieve=11.1=h2f0025b_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py312hb2c0f52_0
-+  - pplpy=0.8.9=py312h372cae2_2
-+  - primecount=7.14=hfe4b40e_0
-+  - primecountpy=0.1.0=py312h451a7dd_5
-+  - primesieve=12.4=h0a1ffab_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py312hb2c0f52_0
-   - pthread-stubs=0.4=h86ecc28_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pyside6=6.8.1=py312hdd999d0_0
-   - pysocks=1.7.1=pyha55dd90_7
-@@ -265,43 +265,43 @@ dependencies:
-   - pyzmq=26.2.0=py312h2427ae1_3
-   - qd=2.3.22=h05efe27_1004
-   - qhull=2020.2=h70be974_5
--  - qt6-main=6.8.1=h0d3cc05_0
-+  - qt6-main=6.8.1=ha0a94ed_2
-   - readline=8.2=h8fc344f_1
-   - requests=2.32.3=pyhd8ed1ab_1
-   - rw=0.9=h31becfc_2
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py312hcbff3fa_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py312h9941453_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - singular=4.4.0=hee12f27_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h578a6b9_0
-+  - sqlite=3.48.0=h578a6b9_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hd600fc2_0
--  - sympow=2.023.6=h157afb5_3
--  - sympy=1.13.3=pyh2585a3b_104
--  - sysroot_linux-aarch64=2.17=h5b4a56d_18
-+  - sympow=2.023.6=h4d450c3_4
-+  - sympy=1.13.3=pyh2585a3b_105
-+  - sysroot_linux-aarch64=2.17=h68829e0_18
-   - tachyon=0.99b6=ha0bfc61_1002
-   - tk=8.6.13=h194ca79_0
-   - tomli=2.2.1=pyhd8ed1ab_1
-   - tornado=6.4.2=py312h52516f5_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py312hb2c0f52_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py312hb2c0f52_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wayland=1.23.1=h698ed42_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-diff --git a/environment-3.12-linux.yml b/environment-3.12-linux.yml
-index 7b2496e151e..f6deedb5a15 100644
---- a/environment-3.12-linux.yml
-+++ b/environment-3.12-linux.yml
-@@ -1,7 +1,7 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: linux-64
--# input_hash: 40be535db1c7eaa6a4654bde814ad7958eb5c8b150e3158a6897927158b3bd6f
-+# input_hash: ab81a8abe5ec503808a2489bef4941922b01008bd685fc411d26594a68155fbd
- 
- channels:
-   - conda-forge
-@@ -10,12 +10,12 @@ dependencies:
-   - _openmp_mutex=4.5=2_kmp_llvm
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - alsa-lib=1.2.13=hb9d3cd8_0
--  - arpack=3.9.1=nompi_h77f6705_101
-+  - arpack=3.9.1=nompi_hf03ea27_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321h2b4cb7a_1
-   - automake=1.17=pl5321ha770c72_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=h4bd325d_0
-+  - bdw-gc=8.2.8=h5888daf_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - binutils=2.43=h4852527_2
-   - binutils_impl_linux-64=2.43=h4bf12b8_2
-@@ -29,33 +29,33 @@ dependencies:
-   - brotli-python=1.1.0=py312h2ec8cdc_2
-   - bzip2=1.0.8=h4bc722e_7
-   - c-ares=1.34.4=hb9d3cd8_0
--  - c-compiler=1.8.0=h2b85faf_1
-+  - c-compiler=1.9.0=h2b85faf_0
-   - ca-certificates=2024.12.14=hbcca054_0
-   - cairo=1.18.2=h3394656_1
-   - cddlib=1!0.94m=h9202a9a_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py312h06ac9bb_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-   - cliquer=1.22=hd590300_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
-   - contourpy=1.3.1=py312h68727a3_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py312h178313f_0
-+  - coverage=7.6.10=py312h178313f_0
-   - cpython=3.12.8=py312hd8ed1ab_1
--  - cxx-compiler=1.8.0=h1a2810e_1
-+  - cxx-compiler=1.9.0=h1a2810e_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py312h597db99_0
-+  - cypari2=2.2.1=py312hb7bab4f_0
-   - cyrus-sasl=2.1.27=h54b06d7_7
--  - cysignals=1.11.2=py312h9d3d55b_3
-+  - cysignals=1.12.3=py312h2ec8cdc_0
-   - cython=3.0.11=py312h8fd2918_3
-   - dbus=1.13.6=h5008d03_3
--  - debugpy=1.8.11=py312h2ec8cdc_0
-+  - debugpy=1.8.12=py312h2ec8cdc_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - double-conversion=3.3.0=h59595ed_0
-   - ecl=24.5.10=h0f3afd4_0
--  - eclib=20231212=h43e5eba_1
-+  - eclib=20231212=h75fb491_2
-   - ecm=7.0.5=h9458935_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -69,14 +69,14 @@ dependencies:
-   - fontconfig=2.15.0=h7e30c49_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py312h178313f_0
--  - fortran-compiler=1.8.0=h36df796_1
--  - fplll=5.4.5=h384768b_0
--  - fpylll=0.6.1=py312h59a3f1e_0
-+  - fonttools=4.55.6=py312h178313f_0
-+  - fortran-compiler=1.9.0=h36df796_0
-+  - fplll=5.5.0=hd20a173_0
-+  - fpylll=0.6.2=py312ha4ee43a_0
-   - freetype=2.12.1=h267a509_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h3b03731_1
--  - gap-defaults=4.14.0=ha770c72_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h3b03731_2
-+  - gap-defaults=4.14.0=ha770c72_2
-   - gcc=13.3.0=h9576a4e_1
-   - gcc_impl_linux-64=13.3.0=hfea6d02_1
-   - gcc_linux-64=13.3.0=hc28eda2_7
-@@ -85,7 +85,7 @@ dependencies:
-   - gfortran=13.3.0=h9576a4e_1
-   - gfortran_impl_linux-64=13.3.0=h10434e7_1
-   - gfortran_linux-64=13.3.0=hb919d3a_7
--  - giac=1.9.0.21=h673759e_1
-+  - giac=1.9.0.21=hca478b9_2
-   - givaro=4.2.0=hb789bce_0
-   - glpk=5.0=h445213a_0
-   - gmp=6.3.0=hac33072_2
-@@ -96,29 +96,29 @@ dependencies:
-   - gxx_impl_linux-64=13.3.0=hdbfa832_1
-   - gxx_linux-64=13.3.0=h6834431_7
-   - h2=4.1.0=pyhd8ed1ab_1
--  - harfbuzz=9.0.0=hda332d3_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - harfbuzz=10.2.0=h4bba637_0
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=he02047a_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=he44f51b_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h623f65a_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh3099207_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
-   - kernel-headers_linux-64=3.10.0=he073ed8_18
-   - keyutils=1.6.1=h166bdaf_0
--  - kiwisolver=1.4.7=py312h68727a3_0
-+  - kiwisolver=1.4.8=py312h84d6215_0
-   - krb5=1.21.3=h659f571_0
--  - lcalc=2.0.5=h5aac1b6_2
-+  - lcalc=2.0.5=h9cf73fc_3
-   - lcms2=2.16=hb7c19ff_0
-   - ld_impl_linux-64=2.43=h712a8e2_2
-   - lerc=4.0.0=h27087fc_0
-@@ -132,27 +132,27 @@ dependencies:
-   - libbrotlidec=1.1.0=hb9d3cd8_2
-   - libbrotlienc=1.1.0=hb9d3cd8_2
-   - libcblas=3.9.0=26_linux64_openblas
--  - libclang-cpp19.1=19.1.6=default_hb5137d0_0
--  - libclang13=19.1.6=default_h9c6a7e4_0
-+  - libclang-cpp19.1=19.1.7=default_hb5137d0_0
-+  - libclang13=19.1.7=default_h9c6a7e4_0
-   - libcups=2.3.3=h4637d8d_4
-   - libcurl=8.11.1=h332b0f4_0
-   - libdeflate=1.23=h4ddbbb0_0
-   - libdrm=2.4.124=hb9d3cd8_0
--  - libedit=3.1.20191231=he28a2e2_2
-+  - libedit=3.1.20240808=pl5321h7949ede_0
-   - libegl=1.7.0=ha4b6fd6_2
-   - libev=4.33=hd590300_2
-   - libexpat=2.6.4=h5888daf_0
-   - libffi=3.4.2=h7f98852_5
--  - libflint=3.1.2=h6fb9888_101
-+  - libflint=3.1.3.1=h0aae882_101
-   - libgcc=14.2.0=h77fa898_1
-   - libgcc-devel_linux-64=13.3.0=h84ea5a7_101
-   - libgcc-ng=14.2.0=h69a702a_1
--  - libgd=2.3.3=hd3e95f3_10
-+  - libgd=2.3.3=h6f5c62b_11
-   - libgfortran=14.2.0=h69a702a_1
-   - libgfortran-ng=14.2.0=h69a702a_1
-   - libgfortran5=14.2.0=hd5240d6_1
-   - libgl=1.7.0=ha4b6fd6_2
--  - libglib=2.82.2=h2ff4ddf_0
-+  - libglib=2.82.2=h2ff4ddf_1
-   - libglvnd=1.7.0=ha4b6fd6_2
-   - libglx=1.7.0=ha4b6fd6_2
-   - libgomp=14.2.0=h77fa898_1
-@@ -161,27 +161,27 @@ dependencies:
-   - libjpeg-turbo=3.0.0=hd590300_1
-   - liblapack=3.9.0=26_linux64_openblas
-   - liblapacke=3.9.0=26_linux64_openblas
--  - libllvm19=19.1.6=ha7bfdaf_0
-+  - libllvm19=19.1.7=ha7bfdaf_0
-   - liblzma=5.6.3=hb9d3cd8_1
-   - liblzma-devel=5.6.3=hb9d3cd8_1
-   - libnghttp2=1.64.0=h161d5f1_0
-   - libnsl=2.0.1=hd590300_0
--  - libntlm=1.4=h7f98852_1002
-+  - libntlm=1.8=hb9d3cd8_0
-   - libopenblas=0.3.28=pthreads_h94d23a6_1
-   - libopengl=1.7.0=ha4b6fd6_2
-   - libpciaccess=0.18=hd590300_0
--  - libpng=1.6.44=hadc24fc_0
-+  - libpng=1.6.45=h943b412_0
-   - libpq=17.2=h3b95a9b_1
-   - libsanitizer=13.3.0=heb74ff8_1
-   - libsodium=1.0.20=h4ab18f5_0
--  - libsqlite=3.47.2=hee588c1_0
-+  - libsqlite=3.48.0=hee588c1_1
-   - libssh2=1.11.1=hf672d98_0
-   - libstdcxx=14.2.0=hc0a3c3a_1
-   - libstdcxx-devel_linux-64=13.3.0=h84ea5a7_101
-   - libstdcxx-ng=14.2.0=h4852527_1
-   - libtiff=4.7.0=hd9ff511_3
-   - libuuid=2.38.1=h0b41bf4_0
--  - libwebp-base=1.4.0=hd590300_0
-+  - libwebp-base=1.5.0=h851e524_0
-   - libxcb=1.17.0=h8a09558_0
-   - libxcrypt=4.4.36=hd590300_1
-   - libxkbcommon=1.7.0=h2c5496b_1
-@@ -189,7 +189,7 @@ dependencies:
-   - libxslt=1.1.39=h76b75d6_0
-   - libzlib=1.3.1=hb9d3cd8_2
-   - linbox=1.7.0=h7298d08_1
--  - llvm-openmp=19.1.6=h024ca30_0
-+  - llvm-openmp=19.1.7=h024ca30_0
-   - lrcalc=2.1=h5888daf_7
-   - m4=1.4.18=h516909a_1001
-   - m4ri=20140914=hae5d5c5_1006
-@@ -207,22 +207,22 @@ dependencies:
-   - mpfr=4.2.1=h90cbb55_3
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
--  - mysql-common=9.0.1=h266115a_3
--  - mysql-libs=9.0.1=he0572af_3
-+  - mysql-common=9.0.1=h266115a_4
-+  - mysql-libs=9.0.1=he0572af_4
-   - nauty=2.8.8=hd590300_1
--  - ncurses=6.5=he02047a_1
-+  - ncurses=6.5=h2d0b736_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h297d8ca_0
-   - ntl=11.4.3=hef3c4d3_1
--  - numpy=1.26.4=py312heda63a1_0
-+  - numpy=2.2.2=py312h72c5963_0
-   - openblas=0.3.28=pthreads_h6ec200e_1
-   - openjpeg=2.5.3=h5fbd93e_0
-   - openldap=2.6.9=he970967_0
--  - openssl=3.4.0=hb9d3cd8_0
-+  - openssl=3.4.0=h7b32b05_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=h36c2ea0_0
--  - pari=2.15.5=h4d4ae9b_2_pthread
-+  - pari=2.17.1=ha40142e_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -232,7 +232,7 @@ dependencies:
-   - perl=5.32.1=7_hd590300_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py312h7b63e92_0
-+  - pillow=11.1.0=py312h80c1187_0
-   - pip=24.3.1=pyh8b19718_2
-   - pixman=0.44.2=h29eaf8c_0
-   - pkg-config=0.29.2=h4bc722e_1009
-@@ -241,18 +241,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h6ec01c2_1006
--  - pplpy=0.8.9=py312h12a6c6f_1
--  - primecount=7.9=hcb278e6_0
--  - primecountpy=0.1.0=py312h8572e83_4
--  - primesieve=11.1=h59595ed_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py312h66e93f0_0
-+  - pplpy=0.8.9=py312h7383a07_2
-+  - primecount=7.14=h530483c_0
-+  - primecountpy=0.1.0=py312h68727a3_5
-+  - primesieve=12.4=he02047a_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py312h66e93f0_0
-   - pthread-stubs=0.4=hb9d3cd8_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pyside6=6.8.1=py312h91f0f75_0
-   - pysocks=1.7.1=pyha55dd90_7
-@@ -266,43 +266,43 @@ dependencies:
-   - pyzmq=26.2.0=py312hbf22597_3
-   - qd=2.3.22=h2cc385e_1004
-   - qhull=2020.2=h434a139_5
--  - qt6-main=6.8.1=h9d28a51_0
-+  - qt6-main=6.8.1=h588cce1_2
-   - readline=8.2=h8228510_1
-   - requests=2.32.3=pyhd8ed1ab_1
-   - rw=0.9=hd590300_2
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py312h62794b6_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py312h180e4f1_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - singular=4.4.0=hc910cb2_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h9eae976_0
-+  - sqlite=3.48.0=h9eae976_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hcb278e6_0
--  - sympow=2.023.6=hc6ab17c_3
--  - sympy=1.13.3=pyh2585a3b_104
--  - sysroot_linux-64=2.17=h4a8ded7_18
-+  - sympow=2.023.6=h3028977_4
-+  - sympy=1.13.3=pyh2585a3b_105
-+  - sysroot_linux-64=2.17=h0157908_18
-   - tachyon=0.99b6=hba7d16a_1002
-   - tk=8.6.13=noxft_h4845f30_101
-   - tomli=2.2.1=pyhd8ed1ab_1
-   - tornado=6.4.2=py312h66e93f0_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py312h66e93f0_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py312h66e93f0_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wayland=1.23.1=h3e06ad9_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-diff --git a/environment-3.12-macos-x86_64.yml b/environment-3.12-macos-x86_64.yml
-index 4fccaefb570..94056fd6c91 100644
---- a/environment-3.12-macos-x86_64.yml
-+++ b/environment-3.12-macos-x86_64.yml
-@@ -1,19 +1,19 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: osx-64
--# input_hash: 5888a68a5088012ad0dffd6db00812a4e3c24a060219dc73fd975f246c404337
-+# input_hash: ce921f8fe037a17f86cebd1f421ba43e586f9986be056154b1d53d3e0381dec4
- 
- channels:
-   - conda-forge
- dependencies:
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - appnope=0.1.4=pyhd8ed1ab_1
--  - arpack=3.9.1=nompi_hf81eadf_101
-+  - arpack=3.9.1=nompi_hdfe9103_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321hed12c24_1
-   - automake=1.17=pl5321h694c41f_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=h940c156_0
-+  - bdw-gc=8.2.8=h240833e_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - blas=2.126=openblas
-   - blas-devel=3.9.0=26_osx64_openblas
-@@ -24,40 +24,40 @@ dependencies:
-   - brotli-python=1.1.0=py312h5861a67_2
-   - bzip2=1.0.8=hfdf4475_7
-   - c-ares=1.34.4=hf13058a_0
--  - c-compiler=1.8.0=hfc4bf79_1
-+  - c-compiler=1.9.0=h09a7c41_0
-   - ca-certificates=2024.12.14=h8857fd0_0
--  - cctools=1010.6=h5b2de21_2
--  - cctools_osx-64=1010.6=hea4301f_2
-+  - cctools=1010.6=hd3558d4_2
-+  - cctools_osx-64=1010.6=h00edd4c_2
-   - cddlib=1!0.94m=h0f52abe_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py312hf857d28_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
--  - clang=17.0.6=default_he371ed4_7
--  - clang-17=17.0.6=default_hb173f14_7
--  - clang_impl_osx-64=17.0.6=h1af8efd_23
--  - clang_osx-64=17.0.6=h7e5c614_23
--  - clangxx=17.0.6=default_he371ed4_7
--  - clangxx_impl_osx-64=17.0.6=hc3430b7_23
--  - clangxx_osx-64=17.0.6=h7e5c614_23
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-+  - clang=18.1.8=default_h179603d_5
-+  - clang-18=18.1.8=default_h0c94c6a_5
-+  - clang_impl_osx-64=18.1.8=h6a44ed1_23
-+  - clang_osx-64=18.1.8=h7e5c614_23
-+  - clangxx=18.1.8=default_h179603d_5
-+  - clangxx_impl_osx-64=18.1.8=h4b7810f_23
-+  - clangxx_osx-64=18.1.8=h7e5c614_23
-   - cliquer=1.22=h10d778d_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
--  - compiler-rt=17.0.6=h1020d70_2
--  - compiler-rt_osx-64=17.0.6=hf2b8a54_2
-+  - compiler-rt=18.1.8=h1020d70_1
-+  - compiler-rt_osx-64=18.1.8=hf2b8a54_1
-   - contourpy=1.3.1=py312hc47a885_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py312h3520af0_0
-+  - coverage=7.6.10=py312h3520af0_0
-   - cpython=3.12.8=py312hd8ed1ab_1
--  - cxx-compiler=1.8.0=h385f146_1
-+  - cxx-compiler=1.9.0=h20888b2_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py312h88009e3_0
--  - cysignals=1.11.2=py312h0c1623b_3
-+  - cypari2=2.2.1=py312hcedb801_0
-+  - cysignals=1.12.3=py312haafddd8_0
-   - cython=3.0.11=py312h6891801_3
--  - debugpy=1.8.11=py312haafddd8_0
-+  - debugpy=1.8.12=py312haafddd8_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - ecl=24.5.10=h56bac16_0
--  - eclib=20231212=h960c116_1
-+  - eclib=20231212=ha63dd29_2
-   - ecm=7.0.5=h4f6b447_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -71,14 +71,14 @@ dependencies:
-   - fontconfig=2.15.0=h37eeddb_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py312h3520af0_0
--  - fortran-compiler=1.8.0=h33d1f46_1
--  - fplll=5.4.5=hb7981ad_0
--  - fpylll=0.6.1=py312ha9f3631_0
-+  - fonttools=4.55.6=py312h3520af0_0
-+  - fortran-compiler=1.9.0=h02557f8_0
-+  - fplll=5.5.0=h6ede486_0
-+  - fpylll=0.6.2=py312hfffdf69_0
-   - freetype=2.12.1=h60636b9_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=hb9686a1_1
--  - gap-defaults=4.14.0=h694c41f_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=hb9686a1_2
-+  - gap-defaults=4.14.0=h694c41f_2
-   - gettext=0.22.5=hdfe23c8_3
-   - gettext-tools=0.22.5=hdfe23c8_3
-   - gf2x=1.3.0=h35ac7d9_3
-@@ -86,37 +86,37 @@ dependencies:
-   - gfortran=13.2.0=h2c809b3_1
-   - gfortran_impl_osx-64=13.2.0=h2bc304d_3
-   - gfortran_osx-64=13.2.0=h18f7dce_1
--  - giac=1.9.0.21=h92f3f65_1
-+  - giac=1.9.0.21=h381f543_2
-   - givaro=4.2.0=h1b3d6f7_0
-   - glpk=5.0=h3cb5acd_0
-   - gmp=6.3.0=hf036a51_2
-   - gmpy2=2.1.5=py312h068713c_3
-   - gsl=2.7=h93259b0_0
-   - h2=4.1.0=pyhd8ed1ab_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=h120a0e1_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h5479cbe_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=h61918c1_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh57ce528_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - isl=0.26=imath32_h2e86a7b_101
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
--  - kiwisolver=1.4.7=py312hc5c4d5f_0
-+  - kiwisolver=1.4.8=py312h9275861_0
-   - krb5=1.21.3=h37d8d59_0
--  - lcalc=2.0.5=h547a6ed_2
-+  - lcalc=2.0.5=h0f747f7_3
-   - lcms2=2.16=ha2f27b4_0
--  - ld64=951.9=h0a3eb4e_2
--  - ld64_osx-64=951.9=h5ffbe8e_2
-+  - ld64=951.9=h4e51db5_2
-+  - ld64_osx-64=951.9=hc8d1a19_2
-   - lerc=4.0.0=hb486fe8_0
-   - libasprintf=0.22.5=hdfe23c8_3
-   - libasprintf-devel=0.22.5=hdfe23c8_3
-@@ -130,17 +130,17 @@ dependencies:
-   - libbrotlidec=1.1.0=h00291cd_2
-   - libbrotlienc=1.1.0=h00291cd_2
-   - libcblas=3.9.0=26_osx64_openblas
--  - libclang-cpp17=17.0.6=default_hb173f14_7
-+  - libclang-cpp18.1=18.1.8=default_h0c94c6a_5
-   - libcurl=8.11.1=h5dec5d8_0
--  - libcxx=19.1.6=hf95d169_1
--  - libcxx-devel=17.0.6=h8f8a49f_6
-+  - libcxx=19.1.7=hf95d169_0
-+  - libcxx-devel=18.1.8=h7c275be_7
-   - libdeflate=1.23=he65b83e_0
--  - libedit=3.1.20191231=h0678c8f_2
-+  - libedit=3.1.20240808=pl5321ha958ccf_0
-   - libev=4.33=h10d778d_2
-   - libexpat=2.6.4=h240833e_0
-   - libffi=3.4.2=h0d85af4_5
--  - libflint=3.1.2=h1d27844_101
--  - libgd=2.3.3=h2e77e4f_10
-+  - libflint=3.1.3.1=h9ab60bc_101
-+  - libgd=2.3.3=h8555400_11
-   - libgettextpo=0.22.5=hdfe23c8_3
-   - libgettextpo-devel=0.22.5=hdfe23c8_3
-   - libgfortran=5.0.0=13_2_0_h97931a8_3
-@@ -153,23 +153,24 @@ dependencies:
-   - libjpeg-turbo=3.0.0=h0dc2134_1
-   - liblapack=3.9.0=26_osx64_openblas
-   - liblapacke=3.9.0=26_osx64_openblas
--  - libllvm17=17.0.6=hbedff68_1
-+  - libllvm18=18.1.8=h9ce406d_2
-   - liblzma=5.6.3=hd471939_1
-   - liblzma-devel=5.6.3=hd471939_1
-   - libnghttp2=1.64.0=hc7306c3_0
-   - libopenblas=0.3.28=openmp_hbf64a52_1
--  - libpng=1.6.44=h4b8f8c9_0
-+  - libpng=1.6.45=h3c4a55f_0
-   - libsodium=1.0.20=hfdf4475_0
--  - libsqlite=3.47.2=hdb6dae5_0
-+  - libsqlite=3.48.0=hdb6dae5_1
-   - libssh2=1.11.1=h3dc7d44_0
-   - libtiff=4.7.0=hb77a491_3
--  - libwebp-base=1.4.0=h10d778d_0
-+  - libwebp-base=1.5.0=h6cf52b4_0
-   - libxcb=1.17.0=hf1f96e2_0
-   - libxml2=2.13.5=hebb159f_1
-   - libzlib=1.3.1=hd23fc13_2
-   - linbox=1.7.0=h9325161_1
--  - llvm-openmp=19.1.6=ha54dae1_0
--  - llvm-tools=17.0.6=hbedff68_1
-+  - llvm-openmp=19.1.7=ha54dae1_0
-+  - llvm-tools=18.1.8=h9ce406d_2
-+  - llvm-tools-18=18.1.8=h9ce406d_2
-   - lrcalc=2.1=hac325c4_7
-   - m4=1.4.18=haf1e3a3_1001
-   - m4ri=20140914=hd82a5f3_1006
-@@ -188,18 +189,18 @@ dependencies:
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
-   - nauty=2.8.8=h10d778d_1
--  - ncurses=6.5=hf036a51_1
-+  - ncurses=6.5=h0622a9a_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h3c5361c_0
-   - ntl=11.4.3=h0ab3c2f_1
--  - numpy=1.26.4=py312he3a82b2_0
-+  - numpy=2.2.2=py312h6693b03_0
-   - openblas=0.3.28=openmp_h30af337_1
-   - openjpeg=2.5.3=h7fd6d84_0
--  - openssl=3.4.0=hd471939_0
-+  - openssl=3.4.0=hc426f3f_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=hbcb3906_0
--  - pari=2.15.5=h7ba67ff_2_pthread
-+  - pari=2.17.1=h1ed0f1a_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -208,7 +209,7 @@ dependencies:
-   - perl=5.32.1=7_h10d778d_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py312h66fe14f_0
-+  - pillow=11.1.0=py312hd9f36e3_0
-   - pip=24.3.1=pyh8b19718_2
-   - pkg-config=0.29.2=hf7e621a_1009
-   - pkgconfig=1.5.5=pyhd8ed1ab_5
-@@ -216,18 +217,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=ha60d53e_1006
--  - pplpy=0.8.9=py312hb4417ad_1
--  - primecount=7.6=ha894c9a_0
--  - primecountpy=0.1.0=py312h49ebfd2_4
--  - primesieve=11.0=hf0c8a7f_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py312h3d0f464_0
-+  - pplpy=0.8.9=py312h045e30c_2
-+  - primecount=7.14=h28dbb38_0
-+  - primecountpy=0.1.0=py312hc47a885_5
-+  - primesieve=12.4=hf036a51_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py312h01d7ebd_0
-   - pthread-stubs=0.4=h00291cd_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pysocks=1.7.1=pyha55dd90_7
-   - pytest=8.3.4=pyhd8ed1ab_1
-@@ -246,27 +247,27 @@ dependencies:
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py312h3b0f538_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py312hb4e66ee_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - sigtool=0.1.3=h88f4db0_0
-   - singular=4.4.0=h604985e_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=h2e4c9dc_0
-+  - sqlite=3.48.0=h2e4c9dc_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hf0c8a7f_0
--  - sympow=2.023.6=h115ba6a_3
--  - sympy=1.13.3=pyh2585a3b_104
-+  - sympow=2.023.6=h7305399_4
-+  - sympy=1.13.3=pyh2585a3b_105
-   - tachyon=0.99b6=h3a1d103_1002
-   - tapi=1300.6.5=h390ca13_0
-   - tk=8.6.13=h1abcd95_1
-@@ -274,9 +275,9 @@ dependencies:
-   - tornado=6.4.2=py312h01d7ebd_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py312h3d0f464_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py312h01d7ebd_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-   - widgetsnbextension=4.0.13=pyhd8ed1ab_1
-diff --git a/environment-3.12-macos.yml b/environment-3.12-macos.yml
-index 957da365df9..ae5920d5424 100644
---- a/environment-3.12-macos.yml
-+++ b/environment-3.12-macos.yml
-@@ -1,19 +1,19 @@
- name: sage-dev
- # Generated by conda-lock.
- # platform: osx-arm64
--# input_hash: 0c152106e1e870088723e57e0bd27be66ce0a8f2488067475849ebf869659bbe
-+# input_hash: 43b6f301d1166823ad72775146167ccf4e01759b32c0d0726035683651623fd9
- 
- channels:
-   - conda-forge
- dependencies:
-   - alabaster=1.0.0=pyhd8ed1ab_1
-   - appnope=0.1.4=pyhd8ed1ab_1
--  - arpack=3.9.1=nompi_h593882a_101
-+  - arpack=3.9.1=nompi_h1f29f7c_102
-   - asttokens=3.0.0=pyhd8ed1ab_1
-   - autoconf=2.71=pl5321hcd07c0c_1
-   - automake=1.17=pl5321hce30654_0
-   - babel=2.16.0=pyhd8ed1ab_1
--  - bdw-gc=8.0.6=hc021e02_0
-+  - bdw-gc=8.2.8=h286801f_1
-   - beautifulsoup4=4.12.3=pyha770c72_1
-   - blas=2.126=openblas
-   - blas-devel=3.9.0=26_osxarm64_openblas
-@@ -24,40 +24,40 @@ dependencies:
-   - brotli-python=1.1.0=py312hde4cb15_2
-   - bzip2=1.0.8=h99b78c6_7
-   - c-ares=1.34.4=h5505292_0
--  - c-compiler=1.8.0=hf48404e_1
-+  - c-compiler=1.9.0=hdf49b6b_0
-   - ca-certificates=2024.12.14=hf0a4a13_0
--  - cctools=1010.6=hf67d63f_2
--  - cctools_osx-arm64=1010.6=h623e0ac_2
-+  - cctools=1010.6=h4c9edd9_2
-+  - cctools_osx-arm64=1010.6=h908b477_2
-   - cddlib=1!0.94m=h6d7a090_0
-   - certifi=2024.12.14=pyhd8ed1ab_0
-   - cffi=1.17.1=py312h0fad829_0
--  - charset-normalizer=3.4.0=pyhd8ed1ab_1
--  - clang=17.0.6=default_h360f5da_7
--  - clang-17=17.0.6=default_h146c034_7
--  - clang_impl_osx-arm64=17.0.6=he47c785_23
--  - clang_osx-arm64=17.0.6=h07b0088_23
--  - clangxx=17.0.6=default_h360f5da_7
--  - clangxx_impl_osx-arm64=17.0.6=h50f59cd_23
--  - clangxx_osx-arm64=17.0.6=h07b0088_23
-+  - charset-normalizer=3.4.1=pyhd8ed1ab_0
-+  - clang=18.1.8=default_h675cc0c_5
-+  - clang-18=18.1.8=default_h5c12605_5
-+  - clang_impl_osx-arm64=18.1.8=h2ae9ea5_23
-+  - clang_osx-arm64=18.1.8=h07b0088_23
-+  - clangxx=18.1.8=default_h675cc0c_5
-+  - clangxx_impl_osx-arm64=18.1.8=h555f467_23
-+  - clangxx_osx-arm64=18.1.8=h07b0088_23
-   - cliquer=1.22=h93a5062_1
-   - colorama=0.4.6=pyhd8ed1ab_1
-   - comm=0.2.2=pyhd8ed1ab_1
--  - compiler-rt=17.0.6=h856b3c1_2
--  - compiler-rt_osx-arm64=17.0.6=h832e737_2
-+  - compiler-rt=18.1.8=h856b3c1_1
-+  - compiler-rt_osx-arm64=18.1.8=h832e737_1
-   - contourpy=1.3.1=py312hb23fbb9_0
-   - conway-polynomials=0.10=pyhd8ed1ab_0
--  - coverage=7.6.9=py312h998013c_0
-+  - coverage=7.6.10=py312h998013c_0
-   - cpython=3.12.8=py312hd8ed1ab_1
--  - cxx-compiler=1.8.0=h18dbf2f_1
-+  - cxx-compiler=1.9.0=hba80287_0
-   - cycler=0.12.1=pyhd8ed1ab_1
--  - cypari2=2.1.5=py312h2da97d0_0
--  - cysignals=1.11.2=py312heab4d4f_3
-+  - cypari2=2.2.1=py312he7c0534_0
-+  - cysignals=1.12.3=py312hd8f9ff3_0
-   - cython=3.0.11=py312hde4cb15_2
--  - debugpy=1.8.11=py312hd8f9ff3_0
-+  - debugpy=1.8.12=py312hd8f9ff3_0
-   - decorator=5.1.1=pyhd8ed1ab_1
-   - docutils=0.21.2=pyhd8ed1ab_1
-   - ecl=23.9.9=h1d9728a_0
--  - eclib=20231212=h3d50bd9_1
-+  - eclib=20231212=hc39b9a7_2
-   - ecm=7.0.5=h41d338b_0
-   - exceptiongroup=1.2.2=pyhd8ed1ab_1
-   - execnet=2.1.1=pyhd8ed1ab_1
-@@ -71,14 +71,14 @@ dependencies:
-   - fontconfig=2.15.0=h1383a14_1
-   - fonts-conda-ecosystem=1=0
-   - fonts-conda-forge=1=0
--  - fonttools=4.55.3=py312h998013c_0
--  - fortran-compiler=1.8.0=hc3477c4_1
--  - fplll=5.4.5=hb7d509d_0
--  - fpylll=0.6.1=py312h381bdd1_0
-+  - fonttools=4.55.6=py312h998013c_0
-+  - fortran-compiler=1.9.0=h5692697_0
-+  - fplll=5.5.0=h2a2278a_0
-+  - fpylll=0.6.2=py312h03fe13c_0
-   - freetype=2.12.1=hadb7bae_2
--  - furo=2024.8.6=pyhd8ed1ab_1
--  - gap-core=4.14.0=h25f1785_1
--  - gap-defaults=4.14.0=hce30654_1
-+  - furo=2024.8.6=pyhd8ed1ab_2
-+  - gap-core=4.14.0=h25f1785_2
-+  - gap-defaults=4.14.0=hce30654_2
-   - gettext=0.22.5=h8414b35_3
-   - gettext-tools=0.22.5=h8414b35_3
-   - gf2x=1.3.0=hf8f8af4_3
-@@ -86,37 +86,37 @@ dependencies:
-   - gfortran=13.2.0=h1ca8e4b_1
-   - gfortran_impl_osx-arm64=13.2.0=h252ada1_3
-   - gfortran_osx-arm64=13.2.0=h57527a5_1
--  - giac=1.9.0.21=h1c96721_1
-+  - giac=1.9.0.21=h573964a_2
-   - givaro=4.2.0=h018886a_0
-   - glpk=5.0=h6d7a090_0
-   - gmp=6.3.0=h7bae524_2
-   - gmpy2=2.1.5=py312h524cf62_3
-   - gsl=2.7=h6e638da_0
-   - h2=4.1.0=pyhd8ed1ab_1
--  - hpack=4.0.0=pyhd8ed1ab_1
--  - hyperframe=6.0.1=pyhd8ed1ab_1
-+  - hpack=4.1.0=pyhd8ed1ab_0
-+  - hyperframe=6.1.0=pyhd8ed1ab_0
-   - icu=75.1=hfee45f7_0
-   - idna=3.10=pyhd8ed1ab_1
-   - igraph=0.10.15=h3fe6531_1
-   - imagesize=1.4.1=pyhd8ed1ab_0
-   - iml=1.0.5=hd73f12c_1004
--  - importlib-metadata=8.5.0=pyha770c72_1
-+  - importlib-metadata=8.6.1=pyha770c72_0
-   - iniconfig=2.0.0=pyhd8ed1ab_1
-   - ipykernel=6.29.5=pyh57ce528_0
--  - ipython=8.30.0=pyh707e725_0
-+  - ipython=8.31.0=pyh707e725_0
-   - ipywidgets=8.1.5=pyhd8ed1ab_1
-   - isl=0.26=imath32_h347afa1_101
-   - jedi=0.19.2=pyhd8ed1ab_1
--  - jinja2=3.1.4=pyhd8ed1ab_1
-+  - jinja2=3.1.5=pyhd8ed1ab_0
-   - jupyter_client=8.6.3=pyhd8ed1ab_1
-   - jupyter_core=5.7.2=pyh31011fe_1
-   - jupyterlab_widgets=3.0.13=pyhd8ed1ab_1
--  - kiwisolver=1.4.7=py312h6142ec9_0
-+  - kiwisolver=1.4.8=py312h2c4a281_0
-   - krb5=1.21.3=h237132a_0
--  - lcalc=2.0.5=h4a402bc_2
-+  - lcalc=2.0.5=hdaf6845_3
-   - lcms2=2.16=ha0e7c42_0
--  - ld64=951.9=h39a299f_2
--  - ld64_osx-arm64=951.9=h3f9b568_2
-+  - ld64=951.9=h4c6efb1_2
-+  - ld64_osx-arm64=951.9=hfc0fa09_2
-   - lerc=4.0.0=h9a09cb3_0
-   - libasprintf=0.22.5=h8414b35_3
-   - libasprintf-devel=0.22.5=h8414b35_3
-@@ -130,23 +130,23 @@ dependencies:
-   - libbrotlidec=1.1.0=hd74edd7_2
-   - libbrotlienc=1.1.0=hd74edd7_2
-   - libcblas=3.9.0=26_osxarm64_openblas
--  - libclang-cpp17=17.0.6=default_h146c034_7
-+  - libclang-cpp18.1=18.1.8=default_h5c12605_5
-   - libcurl=8.11.1=h73640d1_0
--  - libcxx=19.1.6=ha82da77_1
--  - libcxx-devel=17.0.6=h86353a2_6
-+  - libcxx=19.1.7=ha82da77_0
-+  - libcxx-devel=18.1.8=h6dc3340_7
-   - libdeflate=1.23=hec38601_0
--  - libedit=3.1.20191231=hc8eb9b7_2
-+  - libedit=3.1.20240808=pl5321hafb1f1b_0
-   - libev=4.33=h93a5062_2
-   - libexpat=2.6.4=h286801f_0
-   - libffi=3.4.2=h3422bc3_5
--  - libflint=3.1.2=he28cf6d_101
--  - libgd=2.3.3=hac1b3a8_10
-+  - libflint=3.1.3.1=ha3035ea_101
-+  - libgd=2.3.3=hb2c3a21_11
-   - libgettextpo=0.22.5=h8414b35_3
-   - libgettextpo-devel=0.22.5=h8414b35_3
-   - libgfortran=5.0.0=13_2_0_hd922786_3
-   - libgfortran-devel_osx-arm64=13.2.0=h5d7a38c_3
-   - libgfortran5=13.2.0=hf226fd6_3
--  - libglib=2.82.2=h07bd6cf_0
-+  - libglib=2.82.2=hdff4504_1
-   - libhomfly=1.02r6=h93a5062_1
-   - libiconv=1.17=h0d3ecfb_2
-   - libintl=0.22.5=h8414b35_3
-@@ -154,23 +154,24 @@ dependencies:
-   - libjpeg-turbo=3.0.0=hb547adb_1
-   - liblapack=3.9.0=26_osxarm64_openblas
-   - liblapacke=3.9.0=26_osxarm64_openblas
--  - libllvm17=17.0.6=h5090b49_2
-+  - libllvm18=18.1.8=h5090b49_2
-   - liblzma=5.6.3=h39f12f2_1
-   - liblzma-devel=5.6.3=h39f12f2_1
-   - libnghttp2=1.64.0=h6d7220d_0
-   - libopenblas=0.3.28=openmp_hf332438_1
--  - libpng=1.6.44=hc14010f_0
-+  - libpng=1.6.45=h3783ad8_0
-   - libsodium=1.0.20=h99b78c6_0
--  - libsqlite=3.47.2=h3f77e49_0
-+  - libsqlite=3.48.0=h3f77e49_1
-   - libssh2=1.11.1=h9cc3647_0
-   - libtiff=4.7.0=h551f018_3
--  - libwebp-base=1.4.0=h93a5062_0
-+  - libwebp-base=1.5.0=h2471fea_0
-   - libxcb=1.17.0=hdb1d25a_0
-   - libxml2=2.13.5=h178c5d8_1
-   - libzlib=1.3.1=h8359307_2
-   - linbox=1.7.0=h9da6ecd_1
--  - llvm-openmp=19.1.6=hdb05f8b_0
--  - llvm-tools=17.0.6=h5090b49_2
-+  - llvm-openmp=19.1.7=hdb05f8b_0
-+  - llvm-tools=18.1.8=h5090b49_2
-+  - llvm-tools-18=18.1.8=h5090b49_2
-   - lrcalc=2.1=hf9b8971_7
-   - m4=1.4.18=h642e427_1001
-   - m4ri=20140914=hc97c1ff_1006
-@@ -189,18 +190,18 @@ dependencies:
-   - mpmath=1.3.0=pyhd8ed1ab_1
-   - munkres=1.1.4=pyh9f0ad1d_0
-   - nauty=2.8.8=h93a5062_1
--  - ncurses=6.5=h7bae524_1
-+  - ncurses=6.5=h5e97a16_2
-   - nest-asyncio=1.6.0=pyhd8ed1ab_1
-   - networkx=3.4.2=pyh267e887_2
-   - ninja=1.12.1=h420ef59_0
-   - ntl=11.4.3=hbb3f309_1
--  - numpy=1.26.4=py312h8442bc7_0
-+  - numpy=2.2.2=py312h7c1f314_0
-   - openblas=0.3.28=openmp_hea878ba_1
-   - openjpeg=2.5.3=h8a3d83b_0
--  - openssl=3.4.0=h39f12f2_0
-+  - openssl=3.4.0=h81ee809_1
-   - packaging=24.2=pyhd8ed1ab_2
-   - palp=2.20=h27ca646_0
--  - pari=2.15.5=h4f2304c_2_pthread
-+  - pari=2.17.1=h49d18c7_2_pthread
-   - pari-elldata=0.0.20161017=0
-   - pari-galdata=0.0.20180411=0
-   - pari-seadata=0.0.20090618=0
-@@ -210,7 +211,7 @@ dependencies:
-   - perl=5.32.1=7_h4614cfb_perl5
-   - pexpect=4.9.0=pyhd8ed1ab_1
-   - pickleshare=0.7.5=pyhd8ed1ab_1004
--  - pillow=11.0.0=py312haf37ca6_0
-+  - pillow=11.1.0=py312h50aef2c_0
-   - pip=24.3.1=pyh8b19718_2
-   - pkg-config=0.29.2=hde07d2e_1009
-   - pkgconfig=1.5.5=pyhd8ed1ab_5
-@@ -218,18 +219,18 @@ dependencies:
-   - platformdirs=4.3.6=pyhd8ed1ab_1
-   - pluggy=1.5.0=pyhd8ed1ab_1
-   - ppl=1.2=h8b147cf_1006
--  - pplpy=0.8.9=py312h35b16b8_1
--  - primecount=7.6=hb6e4faa_0
--  - primecountpy=0.1.0=py312h389731b_4
--  - primesieve=11.0=hb7217d7_0
--  - prompt-toolkit=3.0.48=pyha770c72_1
--  - psutil=6.1.0=py312h0bf5046_0
-+  - pplpy=0.8.9=py312he1ec6da_2
-+  - primecount=7.14=ha84d530_0
-+  - primecountpy=0.1.0=py312hb23fbb9_5
-+  - primesieve=12.4=h00cdb27_0
-+  - prompt-toolkit=3.0.50=pyha770c72_0
-+  - psutil=6.1.1=py312hea69d52_0
-   - pthread-stubs=0.4=hd74edd7_1002
-   - ptyprocess=0.7.0=pyhd8ed1ab_1
-   - pure_eval=0.2.3=pyhd8ed1ab_1
-   - pycparser=2.22=pyh29332c3_1
--  - pygments=2.18.0=pyhd8ed1ab_1
--  - pyparsing=3.2.0=pyhd8ed1ab_2
-+  - pygments=2.19.1=pyhd8ed1ab_0
-+  - pyparsing=3.2.1=pyhd8ed1ab_0
-   - pyproject-metadata=0.9.0=pyhd8ed1ab_1
-   - pysocks=1.7.1=pyha55dd90_7
-   - pytest=8.3.4=pyhd8ed1ab_1
-@@ -248,27 +249,27 @@ dependencies:
-   - sagemath-db-elliptic-curves=0.8.1=hecc5488_0
-   - sagemath-db-graphs=20210214=hd8ed1ab_0
-   - sagemath-db-polytopes=20170220=1
--  - scipy=1.14.1=py312h6bb24ec_2
--  - setuptools=75.6.0=pyhff2d567_1
-+  - scipy=1.15.1=py312hb7ffdcd_0
-+  - setuptools=75.8.0=pyhff2d567_0
-   - sigtool=0.1.3=h44b9a77_0
-   - singular=4.4.0=h5a8969a_1
-   - six=1.17.0=pyhd8ed1ab_0
-   - snowballstemmer=2.2.0=pyhd8ed1ab_0
-   - soupsieve=2.5=pyhd8ed1ab_1
-   - sphinx=8.1.3=pyhd8ed1ab_1
--  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_2
--  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_0
-+  - sphinx-basic-ng=1.0.0b2=pyhd8ed1ab_3
-+  - sphinx-inline-tabs=2023.4.21=pyhd8ed1ab_1
-   - sphinxcontrib-applehelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-devhelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-htmlhelp=2.1.0=pyhd8ed1ab_1
-   - sphinxcontrib-jsmath=1.0.1=pyhd8ed1ab_1
-   - sphinxcontrib-qthelp=2.0.0=pyhd8ed1ab_1
-   - sphinxcontrib-serializinghtml=1.1.10=pyhd8ed1ab_1
--  - sqlite=3.47.2=hd7222ec_0
-+  - sqlite=3.48.0=hd7222ec_1
-   - stack_data=0.6.3=pyhd8ed1ab_1
-   - symmetrica=3.0.1=hb7217d7_0
--  - sympow=2.023.6=hb0babe8_3
--  - sympy=1.13.3=pyh2585a3b_104
-+  - sympow=2.023.6=hc13a52f_4
-+  - sympy=1.13.3=pyh2585a3b_105
-   - tachyon=0.99b6=hb8a568e_1002
-   - tapi=1300.6.5=h03f4b80_0
-   - tk=8.6.13=h5083fa2_1
-@@ -276,9 +277,9 @@ dependencies:
-   - tornado=6.4.2=py312hea69d52_0
-   - traitlets=5.14.3=pyhd8ed1ab_1
-   - typing_extensions=4.12.2=pyha770c72_1
--  - tzdata=2024b=hc8b5060_0
--  - unicodedata2=15.1.0=py312h0bf5046_1
--  - urllib3=2.2.3=pyhd8ed1ab_1
-+  - tzdata=2025a=h78e105d_0
-+  - unicodedata2=16.0.0=py312hea69d52_0
-+  - urllib3=2.3.0=pyhd8ed1ab_0
-   - wcwidth=0.2.13=pyhd8ed1ab_1
-   - wheel=0.45.1=pyhd8ed1ab_1
-   - widgetsnbextension=4.0.13=pyhd8ed1ab_1
-diff --git a/pyproject.toml b/pyproject.toml
-index a1febc07917..d2b3374575e 100644
---- a/pyproject.toml
-+++ b/pyproject.toml
-@@ -3,7 +3,7 @@ build-backend = 'mesonpy'
- # Minimum requirements for the build system to execute.
- requires = [
-     'meson-python',
--    'cypari2 >=2.1.1',
-+    'cypari2 >=2.2.1',
-     # Exclude 1.12.0 because of https://github.com/sagemath/cysignals/issues/212
-     'cysignals >=1.11.2, != 1.12.0',
-     # Exclude 3.0.3 because of https://github.com/cython/cython/issues/5748
-@@ -19,7 +19,7 @@ description = "Sage: Open Source Mathematics Software: Standard Python Library"
- dependencies = [
-     'six >=1.15.0',
-     'conway-polynomials >=0.8',
--    'cypari2 >=2.1.1',
-+    'cypari2 >=2.2.1',
-     # Exclude 1.12.0 because of https://github.com/sagemath/cysignals/issues/212
-     'cysignals >=1.11.2, != 1.12.0',
-     'cython >=3.0, != 3.0.3',
-diff --git a/src/pyproject.toml b/src/pyproject.toml
-index 4b70dc133d1..625b08afd7a 100644
---- a/src/pyproject.toml
-+++ b/src/pyproject.toml
-@@ -6,7 +6,7 @@ requires = [
-     'setuptools >= 68.1.1',
-     # version constraint for macOS Big Sur support (see https://github.com/sagemath/sage/issues/31050)
-     'wheel >=0.36.2',
--    'cypari2 >=2.1.1',
-+    'cypari2 >=2.2.1',
-     'cysignals >=1.10.2',
-     # Exclude 3.0.3 because of https://github.com/cython/cython/issues/5748
-     'cython >=3.0, != 3.0.3, <4.0',
-diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py
-index 5525fae666c..822701d6810 100644
---- a/src/sage/arith/misc.py
-+++ b/src/sage/arith/misc.py
-@@ -2691,9 +2691,10 @@ def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
- 
-     Any object which has a factor method can be factored like this::
- 
--        sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
--        sage: factor(122 - 454*i)                                                       # needs sage.rings.number_field
--        (-i) * (-i - 2)^3 * (i + 1)^3 * (-2*i + 3) * (i + 4)
-+        sage: # needs sage.rings.number_field
-+        sage: K.<i> = QuadraticField(-1)
-+        sage: f = factor(122 - 454*i); f
-+        (-1) * (i - 1)^3 * (2*i - 1)^3 * (3*i + 2) * (i + 4)
- 
-     To access the data in a factorization::
- 
-@@ -2776,7 +2777,7 @@ def radical(n, *args, **kwds):
-         ArithmeticError: radical of 0 is not defined
-         sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
-         sage: radical(K(2))                                                             # needs sage.rings.number_field
--        i + 1
-+        i - 1
- 
-     Tests with numpy and gmpy2 numbers::
- 
-@@ -3031,7 +3032,7 @@ def is_squarefree(n):
-         sage: is_squarefree(O(2))
-         False
-         sage: O(2).factor()
--        (-I) * (I + 1)^2
-+        (I) * (I - 1)^2
- 
-     This method fails on domains which are not Unique Factorization Domains::
- 
-diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py
-index 64881aba812..cae93ef8bcd 100644
---- a/src/sage/calculus/calculus.py
-+++ b/src/sage/calculus/calculus.py
-@@ -794,8 +794,7 @@ def nintegral(ex, x, a, b,
-     to high precision::
- 
-         sage: gp.eval('intnum(x=17,42,exp(-x^2)*log(x))')
--        '2.565728500561051474934096410 E-127'            # 32-bit
--        '2.5657285005610514829176211363206621657 E-127'  # 64-bit
-+        '2.5657285005610514829176211363206621657 E-127'
-         sage: old_prec = gp.set_real_precision(50)
-         sage: gp.eval('intnum(x=17,42,exp(-x^2)*log(x))')
-         '2.5657285005610514829173563961304957417746108003917 E-127'
-diff --git a/src/sage/categories/quotient_fields.py b/src/sage/categories/quotient_fields.py
-index 76f0570a819..0e4d13ef889 100644
---- a/src/sage/categories/quotient_fields.py
-+++ b/src/sage/categories/quotient_fields.py
-@@ -100,7 +100,7 @@ def gcd(self, other):
-                 sage: R = ZZ.extension(x^2 + 1, names='i')
-                 sage: i = R.1
-                 sage: gcd(5, 3 + 4*i)
--                -i - 2
-+                2*i - 1
-                 sage: P.<t> = R[]
-                 sage: gcd(t, i)
-                 Traceback (most recent call last):
-diff --git a/src/sage/doctest/sources.py b/src/sage/doctest/sources.py
-index 7589f62922b..9807c1d5e12 100644
---- a/src/sage/doctest/sources.py
-+++ b/src/sage/doctest/sources.py
-@@ -766,11 +766,11 @@ def create_doctests(self, namespace):
- 
-             sage: import sys
-             sage: bitness = '64' if sys.maxsize > (1 << 32) else '32'
--            sage: gp.get_precision() == 38                                              # needs sage.libs.pari
-+            sage: sys.maxsize == 2^63 - 1
-             False # 32-bit
-             True  # 64-bit
-             sage: ex = doctests[20].examples[11]
--            sage: ((bitness == '64' and ex.want == 'True  \n')                          # needs sage.libs.pari
-+            sage: ((bitness == '64' and ex.want == 'True  \n')
-             ....:  or (bitness == '32' and ex.want == 'False \n'))
-             True
- 
-diff --git a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
-index d32ce5c9435..2f7b4a6f04c 100644
---- a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
-+++ b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
-@@ -691,10 +691,10 @@ def conjugate(self, M, adjugate=False, new_ideal=None):
- 
-             sage: # needs sage.rings.number_field
-             sage: ideal = A.ideal(5).factor()[1][0]; ideal
--            Fractional ideal (2*a + 1)
-+            Fractional ideal (-2*a - 1)
-             sage: g = f.conjugate(conj, new_ideal=ideal)
-             sage: g.domain().ideal()
--            Fractional ideal (2*a + 1)
-+            Fractional ideal (-2*a - 1)
-         """
-         if self.domain().is_padic_base():
-             return DynamicalSystem_Berkovich(self._system.conjugate(M, adjugate=adjugate))
-diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
-index 591693e5af8..fa9d808fd33 100644
---- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
-+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
-@@ -1791,7 +1791,7 @@ def primes_of_bad_reduction(self, check=True):
-             sage: P.<x,y> = ProjectiveSpace(K,1)
-             sage: f = DynamicalSystem_projective([1/3*x^2+1/a*y^2, y^2])
-             sage: f.primes_of_bad_reduction()                                           # needs sage.rings.function_field
--            [Fractional ideal (a), Fractional ideal (3)]
-+            [Fractional ideal (-a), Fractional ideal (3)]
- 
-         This is an example where ``check=False`` returns extra primes::
- 
-diff --git a/src/sage/interfaces/gp.py b/src/sage/interfaces/gp.py
-index b98c050d889..712a37a6dc6 100644
---- a/src/sage/interfaces/gp.py
-+++ b/src/sage/interfaces/gp.py
-@@ -48,11 +48,9 @@
- ::
- 
-     sage: gp("a = intnum(x=0,6,sin(x))")
--    0.03982971334963397945434770208               # 32-bit
--    0.039829713349633979454347702077075594548     # 64-bit
-+    0.039829713349633979454347702077075594548
-     sage: gp("a")
--    0.03982971334963397945434770208               # 32-bit
--    0.039829713349633979454347702077075594548     # 64-bit
-+    0.039829713349633979454347702077075594548
-     sage: gp.kill("a")
-     sage: gp("a")
-     a
-@@ -375,8 +373,7 @@ def get_precision(self):
-         EXAMPLES::
- 
-             sage: gp.get_precision()
--            28              # 32-bit
--            38              # 64-bit
-+            38
-         """
-         return self.get_default('realprecision')
- 
-@@ -396,15 +393,13 @@ def set_precision(self, prec):
-         EXAMPLES::
- 
-             sage: old_prec = gp.set_precision(53); old_prec
--            28              # 32-bit
--            38              # 64-bit
-+            38
-             sage: gp.get_precision()
-             57
-             sage: gp.set_precision(old_prec)
-             57
-             sage: gp.get_precision()
--            28              # 32-bit
--            38              # 64-bit
-+            38
-         """
-         return self.set_default('realprecision', prec)
- 
-@@ -520,8 +515,7 @@ def set_default(self, var, value):
-             sage: gp.set_default('realprecision', old_prec)
-             115
-             sage: gp.get_default('realprecision')
--            28              # 32-bit
--            38              # 64-bit
-+            38
-         """
-         old = self.get_default(var)
-         self._eval_line('default(%s,%s)' % (var, value))
-@@ -547,8 +541,7 @@ def get_default(self, var):
-             sage: gp.get_default('seriesprecision')
-             16
-             sage: gp.get_default('realprecision')
--            28              # 32-bit
--            38              # 64-bit
-+            38
-         """
-         return eval(self._eval_line('default(%s)' % var))
- 
-@@ -773,8 +766,7 @@ def _exponent_symbol(self):
-         ::
- 
-             sage: repr(gp(10.^80)).replace(gp._exponent_symbol(), 'e')
--            '1.0000000000000000000000000000000000000e80'    # 64-bit
--            '1.000000000000000000000000000e80'              # 32-bit
-+            '1.0000000000000000000000000000000000000e80'
-         """
-         return ' E'
- 
-@@ -800,18 +792,15 @@ def new_with_bits_prec(self, s, precision=0):
- 
-             sage: # needs sage.symbolic
-             sage: pi_def = gp(pi); pi_def
--            3.141592653589793238462643383                  # 32-bit
--            3.1415926535897932384626433832795028842        # 64-bit
-+            3.1415926535897932384626433832795028842
-             sage: pi_def.precision()
--            28                                             # 32-bit
--            38                                             # 64-bit
-+            38
-             sage: pi_150 = gp.new_with_bits_prec(pi, 150)
-             sage: new_prec = pi_150.precision(); new_prec
-             48                                             # 32-bit
-             57                                             # 64-bit
-             sage: old_prec = gp.set_precision(new_prec); old_prec
--            28                                             # 32-bit
--            38                                             # 64-bit
-+            38
-             sage: pi_150
-             3.14159265358979323846264338327950288419716939938  # 32-bit
-             3.14159265358979323846264338327950288419716939937510582098  # 64-bit
-@@ -819,8 +808,7 @@ def new_with_bits_prec(self, s, precision=0):
-             48                                             # 32-bit
-             57                                             # 64-bit
-             sage: gp.get_precision()
--            28                                             # 32-bit
--            38                                             # 64-bit
-+            38
-         """
-         if precision:
-             old_prec = self.get_real_precision()
-@@ -856,11 +844,9 @@ class GpElement(ExpectElement, sage.interfaces.abc.GpElement):
-         sage: loads(dumps(x)) == x
-         False
-         sage: x
--        1.047197551196597746154214461            # 32-bit
--        1.0471975511965977461542144610931676281  # 64-bit
-+        1.0471975511965977461542144610931676281
-         sage: loads(dumps(x))
--        1.047197551196597746154214461            # 32-bit
--        1.0471975511965977461542144610931676281  # 64-bit
-+        1.0471975511965977461542144610931676281
- 
-     The two elliptic curves look the same, but internally the floating
-     point numbers are slightly different.
-diff --git a/src/sage/interfaces/interface.py b/src/sage/interfaces/interface.py
-index 22fb4b8487c..49a41772aac 100644
---- a/src/sage/interfaces/interface.py
-+++ b/src/sage/interfaces/interface.py
-@@ -1045,8 +1045,7 @@ def _sage_repr(self):
-         ::
- 
-             sage: gp(10.^80)._sage_repr()
--            '1.0000000000000000000000000000000000000e80'    # 64-bit
--            '1.000000000000000000000000000e80'              # 32-bit
-+            '1.0000000000000000000000000000000000000e80'
-             sage: mathematica('10.^80')._sage_repr()  # optional - mathematica
-             '1.e80'
- 
-diff --git a/src/sage/interfaces/mathematica.py b/src/sage/interfaces/mathematica.py
-index 488a1fb1af5..fb8eebd8118 100644
---- a/src/sage/interfaces/mathematica.py
-+++ b/src/sage/interfaces/mathematica.py
-@@ -187,8 +187,7 @@
- Note that this agrees with what the PARI interpreter gp produces::
- 
-     sage: gp('solve(x=1,2,exp(x)-3*x)')
--    1.512134551657842473896739678              # 32-bit
--    1.5121345516578424738967396780720387046    # 64-bit
-+    1.5121345516578424738967396780720387046
- 
- Next we find the minimum of a polynomial using the two different
- ways of accessing Mathematica::
-diff --git a/src/sage/interfaces/mathics.py b/src/sage/interfaces/mathics.py
-index 3ca4bee83ef..6bed0895729 100644
---- a/src/sage/interfaces/mathics.py
-+++ b/src/sage/interfaces/mathics.py
-@@ -196,8 +196,7 @@
- Note that this agrees with what the PARI interpreter gp produces::
- 
-     sage: gp('solve(x=1,2,exp(x)-3*x)')
--    1.512134551657842473896739678              # 32-bit
--    1.5121345516578424738967396780720387046    # 64-bit
-+    1.5121345516578424738967396780720387046
- 
- Next we find the minimum of a polynomial using the two different
- ways of accessing Mathics::
-diff --git a/src/sage/interfaces/maxima_abstract.py b/src/sage/interfaces/maxima_abstract.py
-index b8df280857c..234e9373fca 100644
---- a/src/sage/interfaces/maxima_abstract.py
-+++ b/src/sage/interfaces/maxima_abstract.py
-@@ -1489,8 +1489,7 @@ def nintegral(self, var='x', a=0, b=1,
-         high precision very quickly::
- 
-             sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
--            0.5284822353142307136179049194             # 32-bit
--            0.52848223531423071361790491935415653022   # 64-bit
-+            0.52848223531423071361790491935415653022
-             sage: _ = gp.set_precision(80)
-             sage: gp('intnum(x=0,1,exp(-sqrt(x)))')
-             0.52848223531423071361790491935415653021675547587292866196865279321015401702040079
-diff --git a/src/sage/libs/pari/__init__.py b/src/sage/libs/pari/__init__.py
-index b5bc281db4d..2c4f8fa4b24 100644
---- a/src/sage/libs/pari/__init__.py
-+++ b/src/sage/libs/pari/__init__.py
-@@ -165,12 +165,11 @@
-     sage: e = pari([0,0,0,-82,0]).ellinit()
-     sage: eta1 = e.elleta(precision=50)[0]
-     sage: eta1.sage()
--    3.6054636014326520859158205642077267748 # 64-bit
--    3.605463601432652085915820564           # 32-bit
-+    3.6054636014326520859158205642077267748
-     sage: eta1 = e.elleta(precision=150)[0]
-     sage: eta1.sage()
-     3.605463601432652085915820564207726774810268996598024745444380641429820491740 # 64-bit
--    3.60546360143265208591582056420772677481026899659802474544                    # 32-bit
-+    3.605463601432652085915820564207726774810268996598024745444380641430          # 32-bit
- """
- 
- 
-diff --git a/src/sage/libs/pari/convert_sage.pyx b/src/sage/libs/pari/convert_sage.pyx
-index e26238d7c38..48338e0279c 100644
---- a/src/sage/libs/pari/convert_sage.pyx
-+++ b/src/sage/libs/pari/convert_sage.pyx
-@@ -573,17 +573,16 @@ cpdef list pari_prime_range(long c_start, long c_stop, bint py_ints=False):
-         sage: pari_prime_range(2, 19)
-         [2, 3, 5, 7, 11, 13, 17]
-     """
--    cdef long p = 0
--    cdef byteptr pari_prime_ptr = diffptr
-+    cdef ulong i = 1
-     res = []
--    while p < c_start:
--        NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
--    while p < c_stop:
-+    while pari_PRIMES[i] < c_start:
-+        i+=1
-+    while pari_PRIMES[i] < c_stop:
-         if py_ints:
--            res.append(p)
-+            res.append(pari_PRIMES[i])
-         else:
-             z = <Integer>PY_NEW(Integer)
--            mpz_set_ui(z.value, p)
-+            mpz_set_ui(z.value, pari_PRIMES[i])
-             res.append(z)
--        NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
-+        i+=1
-     return res
-diff --git a/src/sage/libs/pari/convert_sage_real_mpfr.pyx b/src/sage/libs/pari/convert_sage_real_mpfr.pyx
-index 98db6023dc9..5fd7fba1c47 100644
---- a/src/sage/libs/pari/convert_sage_real_mpfr.pyx
-+++ b/src/sage/libs/pari/convert_sage_real_mpfr.pyx
-@@ -28,7 +28,7 @@ cpdef Gen new_gen_from_real_mpfr_element(RealNumber self):
- 
-     # We round up the precision to the nearest multiple of wordsize.
-     cdef int rounded_prec
--    rounded_prec = (self.prec() + wordsize - 1) & ~(wordsize - 1)
-+    rounded_prec = nbits2prec(self.prec())
- 
-     # Yes, assigning to self works fine, even in Cython.
-     if rounded_prec > prec:
-@@ -48,7 +48,7 @@ cpdef Gen new_gen_from_real_mpfr_element(RealNumber self):
-         exponent = mpfr_get_z_exp(mantissa, self.value)
- 
-         # Create a PARI REAL
--        pari_float = cgetr(2 + rounded_prec / wordsize)
-+        pari_float = cgetr(rounded_prec)
-         pari_float[1] = evalexpo(exponent + rounded_prec - 1) + evalsigne(mpfr_sgn(self.value))
-         mpz_export(&pari_float[2], NULL, 1, wordsize // 8, 0, 0, mantissa)
-         mpz_clear(mantissa)
-diff --git a/src/sage/libs/pari/tests.py b/src/sage/libs/pari/tests.py
-index 1ed571cd4b9..38fee89202b 100644
---- a/src/sage/libs/pari/tests.py
-+++ b/src/sage/libs/pari/tests.py
-@@ -94,8 +94,7 @@
-     [4, 2]
- 
-     sage: int(pari(RealField(63)(2^63 - 1)))                                            # needs sage.rings.real_mpfr
--    9223372036854775807   # 32-bit
--    9223372036854775807   # 64-bit
-+    9223372036854775807
-     sage: int(pari(RealField(63)(2^63 + 2)))                                            # needs sage.rings.real_mpfr
-     9223372036854775810
- 
-@@ -1231,8 +1230,7 @@
-     sage: e.ellheight([1,0])
-     0.476711659343740
-     sage: e.ellheight([1,0], precision=128).sage()
--    0.47671165934373953737948605888465305945902294218            # 32-bit
--    0.476711659343739537379486058884653059459022942211150879336  # 64-bit
-+    0.476711659343739537379486058884653059459022942211150879336
-     sage: e.ellheight([1, 0], [-1, 1])
-     0.418188984498861
- 
-@@ -1502,7 +1500,7 @@
-     sage: pari(-104).quadclassunit()
-     [6, [6], [Qfb(5, -4, 6)], 1]
-     sage: pari(109).quadclassunit()
--    [1, [], [], 5.56453508676047]
-+    [1, [], [], 5.56453508676047, -1]
-     sage: pari(10001).quadclassunit() # random generators
-     [16, [16], [Qfb(10, 99, -5, 0.E-38)], 5.29834236561059]
-     sage: pari(10001).quadclassunit()[0]
-@@ -1749,13 +1747,13 @@
-     sage: y = QQ['yy'].0; _ = pari(y) # pari has variable ordering rules
-     sage: x = QQ['zz'].0; nf = pari(x^2 + 2).nfinit()
-     sage: nf.nfroots(y^2 + 2)
--    [Mod(-zz, zz^2 + 2), Mod(zz, zz^2 + 2)]
-+    [Mod(-zz, zz^2 + 2), Mod(zz, zz^2 + 2)]~
-     sage: nf = pari(x^3 + 2).nfinit()
-     sage: nf.nfroots(y^3 + 2)
--    [Mod(zz, zz^3 + 2)]
-+    [Mod(zz, zz^3 + 2)]~
-     sage: nf = pari(x^4 + 2).nfinit()
-     sage: nf.nfroots(y^4 + 2)
--    [Mod(-zz, zz^4 + 2), Mod(zz, zz^4 + 2)]
-+    [Mod(-zz, zz^4 + 2), Mod(zz, zz^4 + 2)]~
- 
-     sage: nf = pari('x^2 + 1').nfinit()
-     sage: nf.nfrootsof1()
-@@ -1806,12 +1804,11 @@
-     sage: e = pari([0,0,0,-82,0]).ellinit()
-     sage: eta1 = e.elleta(precision=50)[0]
-     sage: eta1.sage()
--    3.6054636014326520859158205642077267748 # 64-bit
--    3.605463601432652085915820564           # 32-bit
-+    3.6054636014326520859158205642077267748
-     sage: eta1 = e.elleta(precision=150)[0]
-     sage: eta1.sage()
-     3.605463601432652085915820564207726774810268996598024745444380641429820491740 # 64-bit
--    3.60546360143265208591582056420772677481026899659802474544                    # 32-bit
-+    3.605463601432652085915820564207726774810268996598024745444380641430          # 32-bit
-     sage: from cypari2 import Pari
-     sage: pari = Pari()
- 
-diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
-index 852d749e1e6..9f8a33adeb6 100644
---- a/src/sage/matrix/matrix2.pyx
-+++ b/src/sage/matrix/matrix2.pyx
-@@ -16575,7 +16575,7 @@ cdef class Matrix(Matrix1):
-             ....:   -2*a^2 + 4*a - 2, -2*a^2 + 1, 2*a, a^2 - 6, 3*a^2 - a ])
-             sage: r,s,p = m._echelon_form_PID()
-             sage: s[2]
--            (0, 0, -3*a^2 - 18*a + 34, -68*a^2 + 134*a - 53, -111*a^2 + 275*a - 90)
-+            (0, 0, 3*a^2 + 18*a - 34, 68*a^2 - 134*a + 53, 111*a^2 - 275*a + 90)
-             sage: r * m == s and r.det() == 1
-             True
- 
-diff --git a/src/sage/modular/cusps_nf.py b/src/sage/modular/cusps_nf.py
-index 2fdfc7cdc02..ef86da65c12 100644
---- a/src/sage/modular/cusps_nf.py
-+++ b/src/sage/modular/cusps_nf.py
-@@ -1184,9 +1184,9 @@ def NFCusps_ideal_reps_for_levelN(N, nlists=1):
-         sage: from sage.modular.cusps_nf import NFCusps_ideal_reps_for_levelN
-         sage: NFCusps_ideal_reps_for_levelN(N)
-         [(Fractional ideal (1),
--          Fractional ideal (67, a + 17),
--          Fractional ideal (127, a + 48),
--          Fractional ideal (157, a - 19))]
-+          Fractional ideal (67, -4/7*a^3 + 13/7*a^2 + 39/7*a - 43),
-+          Fractional ideal (127, -4/7*a^3 + 13/7*a^2 + 39/7*a - 42),
-+          Fractional ideal (157, -4/7*a^3 + 13/7*a^2 + 39/7*a + 48))]
-         sage: L = NFCusps_ideal_reps_for_levelN(N, 5)
-         sage: all(len(L[i]) == k.class_number() for i in range(len(L)))
-         True
-@@ -1244,7 +1244,7 @@ def units_mod_ideal(I):
-         sage: I = k.ideal(5, a + 1)
-         sage: units_mod_ideal(I)
-         [1,
--        -2*a^2 - 4*a + 1,
-+        2*a^2 + 4*a - 1,
-         ...]
- 
-     ::
-diff --git a/src/sage/modular/dirichlet.py b/src/sage/modular/dirichlet.py
-index f93984335bd..ddbfa6371ba 100644
---- a/src/sage/modular/dirichlet.py
-+++ b/src/sage/modular/dirichlet.py
-@@ -2394,13 +2394,13 @@ class DirichletGroupFactory(UniqueFactory):
-         sage: parent(val)
-         Gaussian Integers generated by zeta4 in Cyclotomic Field of order 4 and degree 2
-         sage: r4_29_0 = r4.residue_field(K(29).factor()[0][0]); r4_29_0(val)
--        17
-+        12
-         sage: r4_29_0(val) * GF(29)(3)
--        22
-+        7
-         sage: r4_29_0(G.gens()[2].values_on_gens()[2]) * 3
--        22
-+        7
-         sage: parent(r4_29_0(G.gens()[2].values_on_gens()[2]) * 3)
--        Residue field of Fractional ideal (-2*zeta4 + 5)
-+        Residue field of Fractional ideal (-2*zeta4 - 5)
- 
-     ::
- 
-diff --git a/src/sage/modular/modsym/p1list_nf.py b/src/sage/modular/modsym/p1list_nf.py
-index 86d33071974..00bb0979ea4 100644
---- a/src/sage/modular/modsym/p1list_nf.py
-+++ b/src/sage/modular/modsym/p1list_nf.py
-@@ -61,7 +61,7 @@
- 
-     sage: alpha = MSymbol(N, a + 2, 3*a^2)
-     sage: alpha.lift_to_sl2_Ok()
--    [-1, 4*a^2 - 13*a + 23, a + 2, 5*a^2 + 3*a - 3]
-+    [-a - 1, 15*a^2 - 38*a + 86, a + 2, -a^2 + 9*a - 19]
-     sage: Ok = k.ring_of_integers()
-     sage: M = Matrix(Ok, 2, alpha.lift_to_sl2_Ok())
-     sage: det(M)
-@@ -977,11 +977,11 @@ def apply_J_epsilon(self, i, e1, e2=1):
-             sage: N = k.ideal(5, a + 1)
-             sage: P = P1NFList(N)
-             sage: u = k.unit_group().gens_values(); u
--            [-1, -2*a^2 - 4*a + 1]
-+            [-1, 2*a^2 + 4*a - 1]
-             sage: P.apply_J_epsilon(4, -1)
-             2
-             sage: P.apply_J_epsilon(4, u[0], u[1])
--            5
-+            1
- 
-         ::
- 
-@@ -1122,7 +1122,7 @@ def lift_to_sl2_Ok(N, c, d):
-         sage: M = Matrix(Ok, 2, lift_to_sl2_Ok(N, 0, 7))
-         Traceback (most recent call last):
-         ...
--        ValueError: <0> + <7> and the Fractional ideal (7, a) are not coprime.
-+        ValueError: <0> + <7> and the Fractional ideal (7, -4/7*a^3 + 13/7*a^2 + 39/7*a - 19) are not coprime.
-     """
-     k = N.number_field()
-     # check the input
-diff --git a/src/sage/quadratic_forms/binary_qf.py b/src/sage/quadratic_forms/binary_qf.py
-index 202da0652ff..083bdee237d 100644
---- a/src/sage/quadratic_forms/binary_qf.py
-+++ b/src/sage/quadratic_forms/binary_qf.py
-@@ -1646,7 +1646,7 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
-             sage: Q = BinaryQF([1, 0, 12345])
-             sage: n = 2^99 + 5273
-             sage: Q.solve_integer(n)                                                    # needs sage.libs.pari
--            (-67446480057659, 7139620553488)
-+            (67446480057659, 7139620553488)
-             sage: Q.solve_integer(n, algorithm='cornacchia')                            # needs sage.libs.pari
-             (67446480057659, 7139620553488)
-             sage: timeit('Q.solve_integer(n)')                          # not tested
-@@ -1661,7 +1661,7 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
-             sage: Qs
-             [x^2 + x*y + 6*y^2, 2*x^2 - x*y + 3*y^2, 2*x^2 + x*y + 3*y^2]
-             sage: [Q.solve_integer(3) for Q in Qs]
--            [None, (0, -1), (0, -1)]
-+            [None, (0, 1), (0, 1)]
-             sage: [Q.solve_integer(5) for Q in Qs]
-             [None, None, None]
-             sage: [Q.solve_integer(6) for Q in Qs]
-@@ -1741,11 +1741,11 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
-             sage: # needs sage.libs.pari
-             sage: Q = BinaryQF([1, 0, 5])
-             sage: Q.solve_integer(126, _flag=1)
--            [(11, -1), (-1, -5), (-1, 5), (-11, -1)]
-+            [(-11, -1), (-1, -5), (-1, 5), (11, -1)]
-             sage: Q.solve_integer(126, _flag=2)
-             (11, -1)
-             sage: Q.solve_integer(126, _flag=3)
--            [(11, -1), (-1, -5), (-1, 5), (-11, -1), (-9, -3), (9, -3)]
-+            [(-11, -1), (-9, -3), (-1, -5), (-1, 5), (9, -3), (11, -1)]
-         """
-         if self.is_negative_definite():  # not supported by PARI
-             return (-self).solve_integer(-n)
-diff --git a/src/sage/rings/finite_rings/finite_field_prime_modn.py b/src/sage/rings/finite_rings/finite_field_prime_modn.py
-index d94b0a4335a..0978c7328fe 100644
---- a/src/sage/rings/finite_rings/finite_field_prime_modn.py
-+++ b/src/sage/rings/finite_rings/finite_field_prime_modn.py
-@@ -114,9 +114,9 @@ def _coerce_map_from_(self, S):
-             sage: RF13 = K.residue_field(pp)
-             sage: RF13.hom([GF(13)(1)])
-             Ring morphism:
--             From: Residue field of Fractional ideal (-w - 18)
--             To:   Finite Field of size 13
--             Defn: 1 |--> 1
-+              From: Residue field of Fractional ideal (w + 18)
-+              To:   Finite Field of size 13
-+              Defn: 1 |--> 1
- 
-         Check that :issue:`19573` is resolved::
- 
-diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx
-index f6f8c08666f..5c6f41b63c5 100644
---- a/src/sage/rings/finite_rings/residue_field.pyx
-+++ b/src/sage/rings/finite_rings/residue_field.pyx
-@@ -22,14 +22,13 @@ monogenic (i.e., 2 is an essential discriminant divisor)::
-     sage: # needs sage.rings.number_field
-     sage: K.<a> = NumberField(x^3 + x^2 - 2*x + 8)
-     sage: F = K.factor(2); F
--    (Fractional ideal (-1/2*a^2 + 1/2*a - 1)) * (Fractional ideal (-a^2 + 2*a - 3))
--    * (Fractional ideal (3/2*a^2 - 5/2*a + 4))
-+    (Fractional ideal (-1/2*a^2 + 1/2*a - 1)) * (Fractional ideal (a^2 - 2*a + 3)) * (Fractional ideal (-3/2*a^2 + 5/2*a - 4))
-     sage: F[0][0].residue_field()
-     Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
-     sage: F[1][0].residue_field()
--    Residue field of Fractional ideal (-a^2 + 2*a - 3)
-+    Residue field of Fractional ideal (a^2 - 2*a + 3)
-     sage: F[2][0].residue_field()
--    Residue field of Fractional ideal (3/2*a^2 - 5/2*a + 4)
-+    Residue field of Fractional ideal (-3/2*a^2 + 5/2*a - 4)
- 
- We can also form residue fields from `\ZZ`::
- 
-@@ -126,10 +125,10 @@ First over a small non-prime field::
-     sage: I = ideal([ubar*X + Y]); I
-     Ideal (ubar*X + Y) of Multivariate Polynomial Ring in X, Y over
-      Residue field in ubar of Fractional ideal
--      (47, 517/55860*u^5 + 235/3724*u^4 + 9829/13965*u^3
--            + 54106/13965*u^2 + 64517/27930*u + 755696/13965)
-+      (47, 4841/93100*u^5 + 34451/139650*u^4 + 303697/69825*u^3
-+            + 297893/27930*u^2 + 1649764/23275*u + 2633506/69825)
-     sage: I.groebner_basis()                                                            # needs sage.libs.singular
--    [X + (-19*ubar^2 - 5*ubar - 17)*Y]
-+    [X + (-15*ubar^2 + 3*ubar - 2)*Y]
- 
- And now over a large prime field::
- 
-@@ -496,9 +495,9 @@ class ResidueField_generic(Field):
- 
-         sage: # needs sage.rings.number_field
-         sage: I = QQ[i].factor(2)[0][0]; I
--        Fractional ideal (I + 1)
-+        Fractional ideal (I - 1)
-         sage: k = I.residue_field(); k
--        Residue field of Fractional ideal (I + 1)
-+        Residue field of Fractional ideal (I - 1)
-         sage: type(k)
-         <class 'sage.rings.finite_rings.residue_field.ResidueFiniteField_prime_modn_with_category'>
- 
-@@ -1008,7 +1007,7 @@ cdef class ReductionMap(Map):
-             sage: cr
-             Partially defined reduction map:
-               From: Number Field in a with defining polynomial x^2 + 1
--              To:   Residue field of Fractional ideal (a + 1)
-+              To:   Residue field of Fractional ideal (a - 1)
-             sage: cr == r                       # not implemented
-             True
-             sage: r(2 + a) == cr(2 + a)
-@@ -1039,7 +1038,7 @@ cdef class ReductionMap(Map):
-             sage: cr
-             Partially defined reduction map:
-               From: Number Field in a with defining polynomial x^2 + 1
--              To:   Residue field of Fractional ideal (a + 1)
-+              To:   Residue field of Fractional ideal (a - 1)
-             sage: cr == r                       # not implemented
-             True
-             sage: r(2 + a) == cr(2 + a)
-@@ -1071,7 +1070,7 @@ cdef class ReductionMap(Map):
-             sage: r = F.reduction_map(); r
-             Partially defined reduction map:
-               From: Number Field in a with defining polynomial x^2 + 1
--              To:   Residue field of Fractional ideal (a + 1)
-+              To:   Residue field of Fractional ideal (a - 1)
- 
-         We test that calling the function also works after copying::
- 
-@@ -1083,7 +1082,7 @@ cdef class ReductionMap(Map):
-             Traceback (most recent call last):
-             ...
-             ZeroDivisionError: Cannot reduce field element 1/2*a
--            modulo Fractional ideal (a + 1): it has negative valuation
-+            modulo Fractional ideal (a - 1): it has negative valuation
- 
-             sage: # needs sage.rings.finite_rings
-             sage: R.<t> = GF(2)[]; h = t^5 + t^2 + 1
-@@ -1105,11 +1104,11 @@ cdef class ReductionMap(Map):
-             sage: # needs sage.rings.number_field
-             sage: K.<i> = NumberField(x^2 + 1)
-             sage: P1, P2 = [g[0] for g in K.factor(5)]; P1, P2
--            (Fractional ideal (-i - 2), Fractional ideal (2*i + 1))
-+            (Fractional ideal (2*i - 1), Fractional ideal (-2*i - 1))
-             sage: a = 1/(1+2*i)
-             sage: F1, F2 = [g.residue_field() for g in [P1,P2]]; F1, F2
--            (Residue field of Fractional ideal (-i - 2),
--             Residue field of Fractional ideal (2*i + 1))
-+            (Residue field of Fractional ideal (2*i - 1),
-+             Residue field of Fractional ideal (-2*i - 1))
-             sage: a.valuation(P1)
-             0
-             sage: F1(i/7)
-@@ -1122,7 +1121,7 @@ cdef class ReductionMap(Map):
-             Traceback (most recent call last):
-             ...
-             ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5
--            modulo Fractional ideal (2*i + 1): it has negative valuation
-+            modulo Fractional ideal (-2*i - 1): it has negative valuation
-         """
-         # The reduction map is just x |--> F(to_vs(x) * (PB**(-1))) if
-         # either x is integral or the denominator of x is coprime to
-@@ -1188,8 +1187,7 @@ cdef class ReductionMap(Map):
-             sage: f = k.convert_map_from(K)
-             sage: s = f.section(); s
-             Lifting map:
--              From: Residue field in abar of
--                    Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
-+              From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
-               To:   Number Field in a with defining polynomial x^5 - 5*x + 2
-             sage: s(k.gen())
-             a
-@@ -1424,8 +1422,7 @@ cdef class ResidueFieldHomomorphism_global(RingHomomorphism):
-             sage: f = k.coerce_map_from(K.ring_of_integers())
-             sage: s = f.section(); s
-             Lifting map:
--              From: Residue field in abar of
--                    Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
-+              From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
-               To:   Maximal Order generated by a in Number Field in a with defining polynomial x^5 - 5*x + 2
-             sage: s(k.gen())
-             a
-@@ -1678,7 +1675,7 @@ cdef class LiftingMap(Section):
-             sage: F.<tmod> = K.factor(7)[0][0].residue_field()
-             sage: F.lift_map() #indirect doctest
-             Lifting map:
--              From: Residue field in tmod of Fractional ideal (theta_12^2 + 2)
-+              From: Residue field in tmod of Fractional ideal (2*theta_12^3 + theta_12)
-               To:   Maximal Order generated by theta_12 in Cyclotomic Field of order 12 and degree 4
-         """
-         return "Lifting"
-diff --git a/src/sage/rings/finite_rings/residue_field_pari_ffelt.pyx b/src/sage/rings/finite_rings/residue_field_pari_ffelt.pyx
-index e9962c3ccde..90a68c619f6 100644
---- a/src/sage/rings/finite_rings/residue_field_pari_ffelt.pyx
-+++ b/src/sage/rings/finite_rings/residue_field_pari_ffelt.pyx
-@@ -103,7 +103,7 @@ class ResidueFiniteField_pari_ffelt(ResidueField_generic, FiniteField_pari_ffelt
-             sage: P.residue_class_degree()
-             2
-             sage: ff.<alpha> = P.residue_field(); ff
--            Residue field in alpha of Fractional ideal (-12*aa^2 + 189*aa - 475)
-+            Residue field in alpha of Fractional ideal (12*aa^2 - 189*aa + 475)
-             sage: type(ff)
-             <class 'sage.rings.finite_rings.residue_field_pari_ffelt.ResidueFiniteField_pari_ffelt_with_category'>
-             sage: ff(alpha^2 + 1)
-diff --git a/src/sage/rings/number_field/S_unit_solver.py b/src/sage/rings/number_field/S_unit_solver.py
-index 0ffac369720..836edae5464 100644
---- a/src/sage/rings/number_field/S_unit_solver.py
-+++ b/src/sage/rings/number_field/S_unit_solver.py
-@@ -12,10 +12,10 @@
-     sage: x = polygen(ZZ, 'x')
-     sage: K.<xi> = NumberField(x^2 + x + 1)
-     sage: S = K.primes_above(3)
--    sage: expected = [((0, 1), (4, 0), xi + 2, -xi - 1),
--    ....:             ((1, -1), (0, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
-+    sage: expected = [((4, 1), (4, 0), xi + 2, -xi - 1),
-+    ....:             ((3, -1), (2, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
-     ....:             ((1, 0), (5, 0), xi + 1, -xi),
--    ....:             ((2, 0), (5, 1), xi, -xi + 1)]
-+    ....:             ((2, 0), (3, 1), xi, -xi + 1)]
-     sage: sols = solve_S_unit_equation(K, S, 200)
-     sage: eq_up_to_order(sols, expected)
-     True
-@@ -1381,7 +1381,7 @@ def defining_polynomial_for_Kp(prime, prec=106):
-         sage: from sage.rings.number_field.S_unit_solver import defining_polynomial_for_Kp
-         sage: K.<a> = QuadraticField(2)
-         sage: p2 = K.prime_above(7); p2
--        Fractional ideal (-2*a + 1)
-+        Fractional ideal (2*a - 1)
-         sage: defining_polynomial_for_Kp(p2, 10)
-         x + 266983762
- 
-@@ -1448,7 +1448,7 @@ def embedding_to_Kp(a, prime, prec):
-         sage: from sage.rings.number_field.S_unit_solver import embedding_to_Kp
-         sage: K.<a> = QuadraticField(17)
-         sage: p = K.prime_above(13); p
--        Fractional ideal (-a + 2)
-+        Fractional ideal (a - 2)
-         sage: embedding_to_Kp(a-3, p, 15)
-         -20542890112375827
- 
-@@ -1791,10 +1791,10 @@ def sieve_ordering(SUK, q):
-          Residue field of Fractional ideal (2*xi + 1))
- 
-         sage: sieve_data[2]
--        ([18, 12, 16, 8], [18, 16, 10, 4], [18, 10, 12, 10])
-+        ([18, 9, 16, 8], [18, 7, 10, 4], [18, 3, 12, 10])
- 
-         sage: sieve_data[3]
--        (648, 2916, 3888)
-+        (972, 972, 3888)
-     """
- 
-     K = SUK.number_field()
-@@ -2170,23 +2170,23 @@ def construct_complement_dictionaries(split_primes_list, SUK, verbose=False):
-         sage: SUK = K.S_unit_group(S=K.primes_above(H))
-         sage: split_primes_list = [3, 7]
-         sage: actual = construct_complement_dictionaries(split_primes_list, SUK)
--        sage: expected = {3: {(0, 1, 0): [(1, 0, 0), (0, 1, 0)],
--        ....:                 (1, 0, 0): [(1, 0, 0), (0, 1, 0)]},
--        ....:             7: {(0, 1, 0): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
-+        sage: expected = {3: {(0, 1, 0): [(0, 1, 0), (1, 0, 0)],
-+        ....:                 (1, 0, 0): [(0, 1, 0), (1, 0, 0)]},
-+        ....:             7: {(0, 1, 0): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
-         ....:                 (0, 1, 2): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
--        ....:                 (0, 3, 2): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
-+        ....:                 (0, 3, 2): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
-         ....:                 (0, 3, 4): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
-         ....:                 (0, 5, 0): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
--        ....:                 (0, 5, 4): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
--        ....:                 (1, 0, 0): [(0, 5, 4), (0, 3, 2), (0, 1, 0)],
--        ....:                 (1, 0, 2): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
--        ....:                 (1, 0, 4): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
--        ....:                 (1, 2, 0): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
--        ....:                 (1, 2, 2): [(0, 5, 4), (0, 3, 2), (0, 1, 0)],
--        ....:                 (1, 2, 4): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
--        ....:                 (1, 4, 0): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
--        ....:                 (1, 4, 2): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
--        ....:                 (1, 4, 4): [(0, 5, 4), (0, 3, 2), (0, 1, 0)]}}
-+        ....:                 (0, 5, 4): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
-+        ....:                 (1, 0, 0): [(0, 1, 0), (0, 3, 2), (0, 5, 4)],
-+        ....:                 (1, 0, 2): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
-+        ....:                 (1, 0, 4): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
-+        ....:                 (1, 2, 0): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
-+        ....:                 (1, 2, 2): [(0, 1, 0), (0, 3, 2), (0, 5, 4)],
-+        ....:                 (1, 2, 4): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
-+        ....:                 (1, 4, 0): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
-+        ....:                 (1, 4, 2): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
-+        ....:                 (1, 4, 4): [(0, 1, 0), (0, 3, 2), (0, 5, 4)]}}
-         sage: all(set(actual[p][vec]) == set(expected[p][vec])
-         ....:     for p in [3, 7] for vec in expected[p])
-         True
-@@ -2693,9 +2693,9 @@ def sieve_below_bound(K, S, bound=10, bump=10, split_primes_list=[], verbose=Fal
-         sage: SUK = UnitGroup(K, S=tuple(K.primes_above(3)))
-         sage: S = SUK.primes()
-         sage: sols = sieve_below_bound(K, S, 10)
--        sage: expected = [((1, -1), (0, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
--        ....:             ((0, 1), (4, 0), xi + 2, -xi - 1),
--        ....:             ((2, 0), (5, 1), xi, -xi + 1),
-+        sage: expected = [((3, -1), (2, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
-+        ....:             ((4, 1), (4, 0), xi + 2, -xi - 1),
-+        ....:             ((2, 0), (3, 1), xi, -xi + 1),
-         ....:             ((1, 0), (5, 0), xi + 1, -xi)]
-         sage: eq_up_to_order(sols, expected)
-         True
-@@ -2758,10 +2758,10 @@ def solve_S_unit_equation(K, S, prec=106, include_exponents=True, include_bound=
-         sage: K.<xi> = NumberField(x^2 + x + 1)
-         sage: S = K.primes_above(3)
-         sage: sols = solve_S_unit_equation(K, S, 200)
--        sage: expected = [((0, 1), (4, 0), xi + 2, -xi - 1),
--        ....:             ((1, -1), (0, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
-+        sage: expected = [((4, 1), (4, 0), xi + 2, -xi - 1),
-+        ....:             ((3, -1), (2, -1), 1/3*xi + 2/3, -1/3*xi + 1/3),
-         ....:             ((1, 0), (5, 0), xi + 1, -xi),
--        ....:             ((2, 0), (5, 1), xi, -xi + 1)]
-+        ....:             ((2, 0), (3, 1), xi, -xi + 1)]
-         sage: eq_up_to_order(sols, expected)
-         True
- 
-@@ -2769,7 +2769,7 @@ def solve_S_unit_equation(K, S, prec=106, include_exponents=True, include_bound=
- 
-         sage: solutions, bound = solve_S_unit_equation(K, S, 100, include_bound=True)
-         sage: bound
--        7
-+        6
- 
-     You can omit the exponent vectors::
- 
-diff --git a/src/sage/rings/number_field/bdd_height.py b/src/sage/rings/number_field/bdd_height.py
-index 9635afa3613..8ac8904662c 100644
---- a/src/sage/rings/number_field/bdd_height.py
-+++ b/src/sage/rings/number_field/bdd_height.py
-@@ -236,7 +236,8 @@ def bdd_norm_pr_ideal_gens(K, norm_list):
-         sage: from sage.rings.number_field.bdd_height import bdd_norm_pr_ideal_gens
-         sage: K.<g> = QuadraticField(123)
-         sage: bdd_norm_pr_ideal_gens(K, range(5))
--        {0: [0], 1: [1], 2: [g + 11], 3: [], 4: [2]}
-+        {0: [0], 1: [1], 2: [g + 11], 3: [], 4: [2]}  # 64-bit
-+        {0: [0], 1: [1], 2: [g - 11], 3: [], 4: [2]}  # 32-bit
- 
-     ::
- 
-diff --git a/src/sage/rings/number_field/class_group.py b/src/sage/rings/number_field/class_group.py
-index e1185a499bb..a9832527ce2 100644
---- a/src/sage/rings/number_field/class_group.py
-+++ b/src/sage/rings/number_field/class_group.py
-@@ -524,9 +524,9 @@ def gens_ideals(self):
-             Class group of order 68 with structure C34 x C2 of Number Field
-             in a with defining polynomial x^2 + x + 23899
-             sage: C.gens()
--            (Fractional ideal class (7, a + 5), Fractional ideal class (5, a + 3))
-+            (Fractional ideal class (83, a + 21), Fractional ideal class (15, a + 8))
-             sage: C.gens_ideals()
--            (Fractional ideal (7, a + 5), Fractional ideal (5, a + 3))
-+            (Fractional ideal (83, a + 21), Fractional ideal (15, a + 8))
-         """
-         return self.gens_values()
- 
-diff --git a/src/sage/rings/number_field/galois_group.py b/src/sage/rings/number_field/galois_group.py
-index bb4e453c650..ac7f14da21d 100644
---- a/src/sage/rings/number_field/galois_group.py
-+++ b/src/sage/rings/number_field/galois_group.py
-@@ -994,9 +994,11 @@ def artin_symbol(self, P):
-             sage: x = polygen(ZZ, 'x')
-             sage: K.<b> = NumberField(x^4 - 2*x^2 + 2, 'a').galois_closure()
-             sage: G = K.galois_group()
--            sage: [G.artin_symbol(P) for P in K.primes_above(7)]  # random (see remark in primes_above)
--            [(1,4)(2,3)(5,8)(6,7), (1,4)(2,3)(5,8)(6,7),
--             (1,5)(2,6)(3,7)(4,8), (1,5)(2,6)(3,7)(4,8)]
-+            sage: sorted([G.artin_symbol(P) for P in K.primes_above(7)])  # random (see remark in primes_above)
-+            [(1,4)(2,3)(5,8)(6,7),
-+             (1,4)(2,3)(5,8)(6,7),
-+             (1,5)(2,6)(3,7)(4,8),
-+             (1,5)(2,6)(3,7)(4,8)]
-             sage: G.artin_symbol(17)
-             Traceback (most recent call last):
-             ...
-diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
-index 05371850c83..324db212f61 100644
---- a/src/sage/rings/number_field/number_field.py
-+++ b/src/sage/rings/number_field/number_field.py
-@@ -3621,7 +3621,7 @@ def fractional_ideal(self, *gens, **kwds):
-             sage: L.<b> = K.extension(x^2 - 3, x^2 + 1)
-             sage: M.<c> = L.extension(x^2 + 1)
-             sage: L.ideal(K.ideal(2, a))
--            Fractional ideal (a)
-+            Fractional ideal (-a)
-             sage: M.ideal(K.ideal(2, a)) == M.ideal(a*(b - c)/2)
-             True
- 
-@@ -3664,35 +3664,37 @@ def ideals_of_bdd_norm(self, bound):
-             ....:     print(n)
-             ....:     for I in sorted(d[n]):
-             ....:         print(I)
--            1
--            Fractional ideal (1)
--            2
--            Fractional ideal (2, 1/2*a - 1/2)
--            Fractional ideal (2, 1/2*a + 1/2)
--            3
--            Fractional ideal (3, 1/2*a - 1/2)
--            Fractional ideal (3, 1/2*a + 1/2)
--            4
--            Fractional ideal (2)
--            Fractional ideal (4, 1/2*a + 3/2)
--            Fractional ideal (4, 1/2*a + 5/2)
--            5
--            6
--            Fractional ideal (1/2*a - 1/2)
--            Fractional ideal (1/2*a + 1/2)
--            Fractional ideal (6, 1/2*a + 5/2)
--            Fractional ideal (6, 1/2*a + 7/2)
--            7
--            8
--            Fractional ideal (4, a - 1)
--            Fractional ideal (4, a + 1)
--            Fractional ideal (1/2*a + 3/2)
--            Fractional ideal (1/2*a - 3/2)
--            9
--            Fractional ideal (3)
--            Fractional ideal (9, 1/2*a + 7/2)
--            Fractional ideal (9, 1/2*a + 11/2)
--            10
-+                1
-+                Fractional ideal (1)
-+                2
-+                Fractional ideal (2, 1/2*a - 1/2)
-+                Fractional ideal (2, 1/2*a + 1/2)
-+                3
-+                Fractional ideal (3, 1/2*a - 1/2)
-+                Fractional ideal (3, 1/2*a + 1/2)
-+                4
-+                Fractional ideal (2)
-+                Fractional ideal (4, 1/2*a + 3/2)
-+                Fractional ideal (4, 1/2*a + 5/2)
-+                5
-+                6
-+                Fractional ideal (-1/2*a + 1/2)
-+                Fractional ideal (1/2*a + 1/2)
-+                Fractional ideal (6, 1/2*a + 5/2)
-+                Fractional ideal (6, 1/2*a + 7/2)
-+                7
-+                8
-+                Fractional ideal (4, a - 1)
-+                Fractional ideal (4, a + 1)
-+                Fractional ideal (-1/2*a - 3/2)
-+                Fractional ideal (1/2*a - 3/2)
-+                9
-+                Fractional ideal (3)
-+                Fractional ideal (9, 1/2*a + 7/2)
-+                Fractional ideal (9, 1/2*a + 11/2)
-+                10
-+            sage: [[I.norm() for I in sorted(d[n])] for n in d]
-+                [[1], [2, 2], [3, 3], [4, 4, 4], [], [6, 6, 6, 6], [], [8, 8, 8, 8], [9, 9, 9], []]
-         """
-         hnf_ideals = self.pari_nf().ideallist(bound)
-         d = {}
-@@ -3923,8 +3925,10 @@ def primes_of_bounded_norm(self, B):
- 
-             sage: K.<i> = QuadraticField(-1)
-             sage: K.primes_of_bounded_norm(10)
--            [Fractional ideal (i + 1), Fractional ideal (-i - 2),
--             Fractional ideal (2*i + 1), Fractional ideal (3)]
-+            [Fractional ideal (i - 1),
-+             Fractional ideal (2*i - 1),
-+             Fractional ideal (-2*i - 1),
-+             Fractional ideal (3)]
-             sage: K.primes_of_bounded_norm(1)
-             []
-             sage: x = polygen(QQ, 'x')
-@@ -3933,10 +3937,10 @@ def primes_of_bounded_norm(self, B):
-             sage: P
-             [Fractional ideal (a),
-              Fractional ideal (a + 1),
--             Fractional ideal (-a^2 - 1),
-+             Fractional ideal (a^2 + 1),
-              Fractional ideal (a^2 + a - 1),
-              Fractional ideal (2*a + 1),
--             Fractional ideal (-2*a^2 - a - 1),
-+             Fractional ideal (2*a^2 + a + 1),
-              Fractional ideal (a^2 - 2*a - 1),
-              Fractional ideal (a + 3)]
-             sage: [p.norm() for p in P]
-@@ -3986,10 +3990,10 @@ def primes_of_bounded_norm_iter(self, B):
-             sage: K.<i> = QuadraticField(-1)
-             sage: it = K.primes_of_bounded_norm_iter(10)
-             sage: list(it)
--            [Fractional ideal (i + 1),
-+            [Fractional ideal (i - 1),
-              Fractional ideal (3),
--             Fractional ideal (-i - 2),
--             Fractional ideal (2*i + 1)]
-+             Fractional ideal (2*i - 1),
-+             Fractional ideal (-2*i - 1)]
-             sage: list(K.primes_of_bounded_norm_iter(1))
-             []
-         """
-@@ -4314,7 +4318,7 @@ def pari_nf(self, important=True):
-             sage: k.<a> = NumberField(x^4 - 3/2*x + 5/3); k
-             Number Field in a with defining polynomial x^4 - 3/2*x + 5/3
-             sage: k.pari_nf()
--            [y^4 - 324*y + 2160, [0, 2], 48918708, 216, ..., [36, 36*y, y^3 + 6*y^2 - 252, 6*y^2], [1, 0, 0, 252; 0, 1, 0, 0; 0, 0, 0, 36; 0, 0, 6, -36], [1, 0, 0, 0, 0, 0, -18, 42, 0, -18, -46, -60, 0, 42, -60, -60; 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, -11, -1, 0, 0, -1, 9; 0, 0, 1, 0, 0, 0, 6, 6, 1, 6, -5, 0, 0, 6, 0, 0; 0, 0, 0, 1, 0, 6, -6, -6, 0, -6, -1, 2, 1, -6, 2, 0]]
-+            [y^4 - 324*y + 2160, [0, 2], 48918708, 216, ..., [36, 36*y, y^3 + 6*y^2 - 252, -6*y^2], [1, 0, 0, 252; 0, 1, 0, 0; 0, 0, 0, 36; 0, 0, -6, 36], [1, 0, 0, 0, 0, 0, -18, -42, 0, -18, -46, 60, 0, -42, 60, -60; 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, -11, 1, 0, 0, 1, 9; 0, 0, 1, 0, 0, 0, 6, -6, 1, 6, -5, 0, 0, -6, 0, 0; 0, 0, 0, 1, 0, -6, 6, -6, 0, 6, 1, 2, 1, -6, 2, 0]]
-             sage: pari(k)
-             [y^4 - 324*y + 2160, [0, 2], 48918708, 216, ...]
-             sage: gp(k)
-@@ -4441,10 +4445,14 @@ def pari_bnf(self, proof=None, units=True):
-             bnf = self._pari_bnf
-         except AttributeError:
-             f = self.pari_polynomial("y")
-+            _saved_rand = pari.getrand()
-+            # make this deterministic, it affects printing of ideals
-+            pari.setrand(1)
-             if units:
-                 self._pari_bnf = f.bnfinit(1)
-             else:
-                 self._pari_bnf = f.bnfinit()
-+            pari.setrand(_saved_rand)
-             bnf = self._pari_bnf
-         # Certify if needed
-         if proof and not getattr(self, "_pari_bnf_certified", False):
-@@ -4804,7 +4812,7 @@ def _S_class_group_and_units(self, S, proof=True):
-              1/13*a^2 + 7/13*a - 332/13,
-              -1/13*a^2 + 6/13*a + 345/13,
-              -1,
--             -2/13*a^2 - 1/13*a + 755/13]
-+             1/13*a^2 - 19/13*a - 7/13]
-             sage: units[5] in (1/13*a^2 - 19/13*a - 7/13, 1/13*a^2 + 20/13*a - 7/13)
-             True
-             sage: len(units) == 6
-@@ -4815,7 +4823,8 @@ def _S_class_group_and_units(self, S, proof=True):
- 
-             sage: K.<a> = NumberField(2*x^2 - 1/3)
-             sage: K._S_class_group_and_units(tuple(K.primes_above(2) + K.primes_above(3)))
--            ([6*a + 2, 6*a + 3, -1, -12*a + 5], [])
-+            ([6*a + 2, -6*a + 3, -1, -12*a - 5], [])  # 64-bit
-+            ([6*a + 2, -6*a - 3, -1, -12*a - 5], [])  # 32-bit
-         """
-         K_pari = self.pari_bnf(proof=proof)
-         S_pari = [p.pari_prime() for p in sorted(set(S))]
-@@ -4993,7 +5002,7 @@ def selmer_generators(self, S, m, proof=True, orders=False):
-              1/13*a^2 + 7/13*a - 332/13,
-              -1/13*a^2 + 6/13*a + 345/13,
-              -1,
--             -2/13*a^2 - 1/13*a + 755/13]
-+             1/13*a^2 - 19/13*a - 7/13]
-             sage: gens[5] in (1/13*a^2 - 19/13*a - 7/13, 1/13*a^2 + 20/13*a - 7/13)
-             True
-             sage: gens[6] in (-1/13*a^2 + 45/13*a - 97/13, 1/13*a^2 - 45/13*a + 97/13)
-@@ -5157,9 +5166,7 @@ def selmer_space(self, S, p, proof=None):
- 
-             sage: [K.ideal(g).factor() for g in gens]
-             [(Fractional ideal (2, a + 1)) * (Fractional ideal (3, a + 1)),
--             Fractional ideal (a),
--             (Fractional ideal (2, a + 1))^2,
--             1]
-+             Fractional ideal (-a), (Fractional ideal (2, a + 1))^2, 1]
- 
-             sage: toKS2(10)
-             (0, 0, 1, 1)
-@@ -5637,7 +5644,7 @@ def different(self):
-             sage: k.<a> = NumberField(x^2 + 23)
-             sage: d = k.different()
-             sage: d
--            Fractional ideal (-a)
-+            Fractional ideal (a)
-             sage: d.norm()
-             23
-             sage: k.disc()
-@@ -5757,7 +5764,7 @@ def elements_of_norm(self, n, proof=None) -> list:
-             sage: K.elements_of_norm(3)
-             []
-             sage: K.elements_of_norm(50)
--            [-a - 7, 5*a - 5, 7*a + 1]
-+            [7*a - 1, 5*a - 5, -7*a - 1]
- 
-         TESTS:
- 
-@@ -5869,10 +5876,9 @@ def factor(self, n):
-             sage: K.factor(1/3)
-             (Fractional ideal (3))^-1
-             sage: K.factor(1+a)
--            Fractional ideal (a + 1)
-+            Fractional ideal (a - 1)
-             sage: K.factor(1+a/5)
--            (Fractional ideal (a + 1)) * (Fractional ideal (-a - 2))^-1
--              * (Fractional ideal (2*a + 1))^-1 * (Fractional ideal (-2*a + 3))
-+            (Fractional ideal (a - 1)) * (Fractional ideal (2*a - 1))^-1 * (Fractional ideal (-2*a - 1))^-1 * (Fractional ideal (3*a + 2))
- 
-         An example over a relative number field::
- 
-@@ -5905,9 +5911,9 @@ def factor(self, n):
-             sage: (fi, fj) = f[::]
-             sage: (fi[1], fj[1])
-             (1, 1)
--            sage: fi[0] == L.fractional_ideal(1/2*a*b - a + 1/2)
-+            sage: fi[0] == L.fractional_ideal(-1/2*a*b - a + 1/2)
-             True
--            sage: fj[0] == L.fractional_ideal(-1/2*a*b - a + 1/2)
-+            sage: fj[0] == L.fractional_ideal(1/2*a*b - a + 1/2)
-             True
-         """
-         return self.ideal(n).factor()
-@@ -6519,13 +6525,15 @@ def reduced_basis(self, prec=None):
-         # the inner product on the Minkowski embedding, which is
-         # faster than computing all the conjugates, etc ...
- 
-+        # flag to disable FLATTER, which is much more unstable than fplll
-+        flag = 1 if pari.version() >= (2,17) else 0
-         if self.is_totally_real():
-             from sage.matrix.constructor import matrix
-             M = matrix(ZZ, d, d, [[(x*y).trace() for x in ZK] for y in ZK])
--            T = pari(M).qflllgram()
-+            T = pari(M).qflllgram(flag=flag)
-         else:
-             M = self.minkowski_embedding(ZK, prec=prec)
--            T = pari(M).qflll()
-+            T = pari(M).qflll(flag=flag)
- 
-         return [sum([ZZ(T[i][j]) * ZK[j] for j in range(d)]) for i in range(d)]
- 
-@@ -7102,14 +7110,14 @@ def units(self, proof=None):
-             sage: K.units(proof=True)  # takes forever, not tested
-             ...
-             sage: K.units(proof=False)  # result not independently verified
--            (-a^9 - a + 1,
-+            (a^9 + a - 1,
-+             -a^15 + a^12 - a^10 + a^9 + 2*a^8 - 3*a^7 - a^6 + 3*a^5 - a^4 - 4*a^3 + 3*a^2 + 2*a - 2,
-+             a^15 + a^14 + a^13 + a^12 + a^10 - a^7 - a^6 - a^2 - 1,
-+             2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4,
-              -a^16 + a^15 - a^14 + a^12 - a^11 + a^10 + a^8 - a^7 + 2*a^6 - a^4 + 3*a^3 - 2*a^2 + 2*a - 1,
--             2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4,
--             a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1,
--             -a^16 - a^15 - a^14 - a^13 - a^12 - a^11 - a^10 - a^9 - a^8 - a^7 - a^6 - a^5 - a^4 - a^3 - a^2 + 2,
--             -2*a^16 + 3*a^15 - 3*a^14 + 3*a^13 - 3*a^12 + a^11 - a^9 + 3*a^8 - 4*a^7 + 5*a^6 - 6*a^5 + 4*a^4 - 3*a^3 + 2*a^2 + 2*a - 4,
--             a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2,
--             2*a^16 + a^15 - a^11 - 3*a^10 - 4*a^9 - 4*a^8 - 4*a^7 - 5*a^6 - 7*a^5 - 8*a^4 - 6*a^3 - 5*a^2 - 6*a - 7)
-+             a^16 - 2*a^15 - 2*a^13 - a^12 - a^11 - 2*a^10 + a^9 - 2*a^8 + 2*a^7 - 3*a^6 - 3*a^4 - 2*a^3 - a^2 - 4*a + 2,
-+             -a^15 - a^14 - 2*a^11 - a^10 + a^9 - a^8 - 2*a^7 + a^5 - 2*a^3 + a^2 + 3*a - 1,
-+             -3*a^16 - 3*a^15 - 3*a^14 - 3*a^13 - 3*a^12 - 2*a^11 - 2*a^10 - 2*a^9 - a^8 + a^7 + 2*a^6 + 3*a^5 + 3*a^4 + 4*a^3 + 6*a^2 + 8*a + 8)
- 
-         TESTS:
- 
-@@ -7118,7 +7126,7 @@ def units(self, proof=None):
- 
-             sage: K.<a> = NumberField(1/2*x^2 - 1/6)
-             sage: K.units()
--            (3*a - 2,)
-+            (3*a + 2,)
-         """
-         proof = proof_flag(proof)
- 
-@@ -7200,14 +7208,14 @@ def unit_group(self, proof=None):
-             (u0, u1, u2, u3, u4, u5, u6, u7, u8)
-             sage: U.gens_values()  # result not independently verified
-             [-1,
--             -a^9 - a + 1,
-+             a^9 + a - 1,
-+             -a^15 + a^12 - a^10 + a^9 + 2*a^8 - 3*a^7 - a^6 + 3*a^5 - a^4 - 4*a^3 + 3*a^2 + 2*a - 2,
-+             a^15 + a^14 + a^13 + a^12 + a^10 - a^7 - a^6 - a^2 - 1,
-+             2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4,
-              -a^16 + a^15 - a^14 + a^12 - a^11 + a^10 + a^8 - a^7 + 2*a^6 - a^4 + 3*a^3 - 2*a^2 + 2*a - 1,
--             2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4,
--             a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1,
--             -a^16 - a^15 - a^14 - a^13 - a^12 - a^11 - a^10 - a^9 - a^8 - a^7 - a^6 - a^5 - a^4 - a^3 - a^2 + 2,
--             -2*a^16 + 3*a^15 - 3*a^14 + 3*a^13 - 3*a^12 + a^11 - a^9 + 3*a^8 - 4*a^7 + 5*a^6 - 6*a^5 + 4*a^4 - 3*a^3 + 2*a^2 + 2*a - 4,
--             a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2,
--             2*a^16 + a^15 - a^11 - 3*a^10 - 4*a^9 - 4*a^8 - 4*a^7 - 5*a^6 - 7*a^5 - 8*a^4 - 6*a^3 - 5*a^2 - 6*a - 7]
-+             a^16 - 2*a^15 - 2*a^13 - a^12 - a^11 - 2*a^10 + a^9 - 2*a^8 + 2*a^7 - 3*a^6 - 3*a^4 - 2*a^3 - a^2 - 4*a + 2,
-+             -a^15 - a^14 - 2*a^11 - a^10 + a^9 - a^8 - 2*a^7 + a^5 - 2*a^3 + a^2 + 3*a - 1,
-+             -3*a^16 - 3*a^15 - 3*a^14 - 3*a^13 - 3*a^12 - 2*a^11 - 2*a^10 - 2*a^9 - a^8 + a^7 + 2*a^6 + 3*a^5 + 3*a^4 + 4*a^3 + 6*a^2 + 8*a + 8]
-         """
-         proof = proof_flag(proof)
- 
-@@ -7256,8 +7264,8 @@ def S_unit_group(self, proof=None, S=None):
-             sage: U = K.S_unit_group(S=a); U
-             S-unit group with structure C10 x Z x Z x Z of
-              Number Field in a with defining polynomial x^4 - 10*x^3 + 100*x^2 - 375*x + 1375
--             with S = (Fractional ideal (5, 1/275*a^3 + 4/55*a^2 - 5/11*a + 5),
--                       Fractional ideal (11, 1/275*a^3 + 4/55*a^2 - 5/11*a + 9))
-+             with S = (Fractional ideal (5, -7/275*a^3 + 1/11*a^2 - 9/11*a),
-+                       Fractional ideal (11, -7/275*a^3 + 1/11*a^2 - 9/11*a + 3))
-             sage: U.gens()
-             (u0, u1, u2, u3)
-             sage: U.gens_values()  # random
-@@ -7268,8 +7276,8 @@ def S_unit_group(self, proof=None, S=None):
-             sage: [u.multiplicative_order() for u in U.gens()]
-             [10, +Infinity, +Infinity, +Infinity]
-             sage: U.primes()
--            (Fractional ideal (5, 1/275*a^3 + 4/55*a^2 - 5/11*a + 5),
--             Fractional ideal (11, 1/275*a^3 + 4/55*a^2 - 5/11*a + 9))
-+            (Fractional ideal (5, -7/275*a^3 + 1/11*a^2 - 9/11*a),
-+             Fractional ideal (11, -7/275*a^3 + 1/11*a^2 - 9/11*a + 3))
- 
-         With the default value of `S`, the S-unit group is the same as
-         the global unit group::
-@@ -7422,7 +7430,7 @@ def S_unit_solutions(self, S=[], prec=106, include_exponents=False, include_boun
-             sage: # needs sage.rings.padics
-             sage: solutions, bound = K.S_unit_solutions(S, prec=100, include_bound=True)
-             sage: bound
--            7
-+            6
-         """
-         from .S_unit_solver import solve_S_unit_equation
-         return solve_S_unit_equation(self, S, prec, include_exponents, include_bound, proof)
-diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
-index 27432813b2b..a22b68e6093 100644
---- a/src/sage/rings/number_field/number_field_element.pyx
-+++ b/src/sage/rings/number_field/number_field_element.pyx
-@@ -1954,14 +1954,14 @@ cdef class NumberFieldElement(NumberFieldElement_base):
-             sage: x = polygen(ZZ, 'x')
-             sage: K.<i> = NumberField(x^2 + 1)
-             sage: (6*i + 6).factor()
--            (-i) * (i + 1)^3 * 3
-+            (i - 1)^3 * 3
- 
-         In the following example, the class number is 2.  If a factorization
-         in prime elements exists, we will find it::
- 
-             sage: K.<a> = NumberField(x^2 - 10)
-             sage: factor(169*a + 531)
--            (-6*a - 19) * (-3*a - 1) * (-2*a + 9)
-+            (-6*a - 19) * (2*a - 9) * (3*a + 1)
-             sage: factor(K(3))
-             Traceback (most recent call last):
-             ...
-@@ -2043,7 +2043,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
-             0
-             sage: R = K.maximal_order()
-             sage: R(i+1).gcd(2)
--            i + 1
-+            i - 1
-             sage: R = K.order(2*i)
-             sage: R(1).gcd(R(4*i))
-             1
-@@ -4238,7 +4238,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
- 
-             sage: P5s = F(5).support()
-             sage: P5s
--            [Fractional ideal (-t^2 - 1), Fractional ideal (t^2 - 2*t - 1)]
-+            [Fractional ideal (t^2 + 1), Fractional ideal (t^2 - 2*t - 1)]
-             sage: all(5 in P5 for P5 in P5s)
-             True
-             sage: all(P5.is_prime() for P5 in P5s)
-@@ -4487,7 +4487,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
-             sage: f = Qi.embeddings(K)[0]
-             sage: a = f(2+3*i) * (2-zeta)^2
-             sage: a.descend_mod_power(Qi,2)
--            [-2*i + 3, 3*i + 2]
-+            [3*i + 2, 2*i - 3]
- 
-         An absolute example::
- 
-diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py
-index 30fc8326917..60ac76e1ddc 100644
---- a/src/sage/rings/number_field/number_field_ideal.py
-+++ b/src/sage/rings/number_field/number_field_ideal.py
-@@ -75,7 +75,7 @@ class NumberFieldIdeal(Ideal_generic):
-         Fractional ideal (3)
-         sage: F = pari(K).idealprimedec(5)
-         sage: K.ideal(F[0])
--        Fractional ideal (2*i + 1)
-+        Fractional ideal (-2*i - 1)
- 
-     TESTS:
- 
-@@ -241,7 +241,7 @@ def _richcmp_(self, other, op):
-             sage: K.<a> = NumberField(x^2 + 3); K
-             Number Field in a with defining polynomial x^2 + 3
-             sage: f = K.factor(15); f
--            (Fractional ideal (1/2*a + 3/2))^2 * (Fractional ideal (5))
-+            (Fractional ideal (-a))^2 * (Fractional ideal (5))
-             sage: (f[0][0] < f[1][0])  # potentially random
-             True
-             sage: (f[0][0] == f[0][0])
-@@ -278,7 +278,7 @@ def _mul_(self, other):
-             sage: A = K.ideal([5, 2 + I])
-             sage: B = K.ideal([13, 5 + 12*I])
-             sage: A*B
--            Fractional ideal (4*I - 7)
-+            Fractional ideal (-4*I + 7)
-             sage: (K.ideal(3 + I) * K.ideal(7 + I)).gens()
-             (10*I + 20,)
- 
-@@ -688,17 +688,17 @@ def free_module(self):
-             sage: I.free_module()
-             Free module of degree 4 and rank 4 over Integer Ring
-             User basis matrix:
--            [  4   0   0   0]
--            [ -3   7  -1   1]
--            [  3   7   1   1]
--            [  0 -10   0  -2]
-+            [ 4  0  0  0]
-+            [ 3  7  1  1]
-+            [ 0 10  0  2]
-+            [ 3 -7  1 -1]
-             sage: J = I^(-1); J.free_module()
-             Free module of degree 4 and rank 4 over Integer Ring
-             User basis matrix:
-             [  1/4     0     0     0]
--            [-3/16  7/16 -1/16  1/16]
-             [ 3/16  7/16  1/16  1/16]
--            [    0  -5/8     0  -1/8]
-+            [    0   5/8     0   1/8]
-+            [ 3/16 -7/16  1/16 -1/16]
- 
-         An example of intersecting ideals by intersecting free modules.::
- 
-@@ -795,7 +795,7 @@ def gens_reduced(self, proof=None):
-             sage: J.is_principal()
-             False
-             sage: J.gens_reduced()
--            (5, a)
-+            (5, -a)
-             sage: all(j.parent() is K for j in J.gens())
-             True
-             sage: all(j.parent() is K for j in J.gens_reduced())
-@@ -2422,9 +2422,9 @@ def denominator(self):
-             sage: I = K.ideal((3+4*i)/5); I
-             Fractional ideal (4/5*i + 3/5)
-             sage: I.denominator()
--            Fractional ideal (2*i + 1)
-+            Fractional ideal (-2*i - 1)
-             sage: I.numerator()
--            Fractional ideal (-i - 2)
-+            Fractional ideal (2*i - 1)
-             sage: I.numerator().is_integral() and I.denominator().is_integral()
-             True
-             sage: I.numerator() + I.denominator() == K.unit_ideal()
-@@ -2453,9 +2453,9 @@ def numerator(self):
-             sage: I = K.ideal((3+4*i)/5); I
-             Fractional ideal (4/5*i + 3/5)
-             sage: I.denominator()
--            Fractional ideal (2*i + 1)
-+            Fractional ideal (-2*i - 1)
-             sage: I.numerator()
--            Fractional ideal (-i - 2)
-+            Fractional ideal (2*i - 1)
-             sage: I.numerator().is_integral() and I.denominator().is_integral()
-             True
-             sage: I.numerator() + I.denominator() == K.unit_ideal()
-@@ -3170,11 +3170,11 @@ def _p_quotient(self, p):
-             Partially defined quotient map
-              from Number Field in i with defining polynomial x^2 + 1
-                to an explicit vector space representation for the quotient of
--                  the ring of integers by (p,I) for the ideal I=Fractional ideal (-i - 2).
-+                  the ring of integers by (p,I) for the ideal I=Fractional ideal (2*i - 1).
-             sage: lift
-             Lifting map
-                to Gaussian Integers generated by i in Number Field in i with defining polynomial x^2 + 1
--               from quotient of integers by Fractional ideal (-i - 2)
-+               from quotient of integers by Fractional ideal (2*i - 1)
-         """
-         return quotient_char_p(self, p)
- 
-@@ -3219,11 +3219,11 @@ def residue_field(self, names=None):
- 
-             sage: K.<i> = NumberField(x^2 + 1)
-             sage: P1, P2 = [g[0] for g in K.factor(5)]; P1, P2
--            (Fractional ideal (-i - 2), Fractional ideal (2*i + 1))
-+            (Fractional ideal (2*i - 1), Fractional ideal (-2*i - 1))
-             sage: a = 1/(1+2*i)
-             sage: F1, F2 = [g.residue_field() for g in [P1, P2]]; F1, F2
--            (Residue field of Fractional ideal (-i - 2),
--             Residue field of Fractional ideal (2*i + 1))
-+            (Residue field of Fractional ideal (2*i - 1),
-+             Residue field of Fractional ideal (-2*i - 1))
-             sage: a.valuation(P1)
-             0
-             sage: F1(i/7)
-@@ -3236,7 +3236,7 @@ def residue_field(self, names=None):
-             Traceback (most recent call last):
-             ...
-             ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5
--            modulo Fractional ideal (2*i + 1): it has negative valuation
-+            modulo Fractional ideal (-2*i - 1): it has negative valuation
- 
-         An example with a relative number field::
- 
-@@ -3497,7 +3497,7 @@ def quotient_char_p(I, p):
-         []
- 
-         sage: I = K.factor(13)[0][0]; I
--        Fractional ideal (-2*i + 3)
-+        Fractional ideal (3*i + 2)
-         sage: I.residue_class_degree()
-         1
-         sage: quotient_char_p(I, 13)[0]
-diff --git a/src/sage/rings/number_field/number_field_ideal_rel.py b/src/sage/rings/number_field/number_field_ideal_rel.py
-index 7f6cfd9b1b7..129d0288024 100644
---- a/src/sage/rings/number_field/number_field_ideal_rel.py
-+++ b/src/sage/rings/number_field/number_field_ideal_rel.py
-@@ -11,7 +11,7 @@
-     sage: G = [from_A(z) for z in I.gens()]; G
-     [7, -2*b*a - 1]
-     sage: K.fractional_ideal(G)
--    Fractional ideal ((1/2*b + 2)*a - 1/2*b + 2)
-+    Fractional ideal ((-1/2*b + 2)*a - 1/2*b - 2)
-     sage: K.fractional_ideal(G).absolute_norm().factor()
-     7^2
- 
-@@ -189,7 +189,7 @@ def absolute_ideal(self, names='a'):
-             sage: J.absolute_norm()
-             2
-             sage: J.ideal_below()
--            Fractional ideal (b)
-+            Fractional ideal (-b)
-             sage: J.ideal_below().norm()
-             2
-         """
-@@ -277,7 +277,7 @@ def gens_reduced(self):
-             sage: L.<b> = K.extension(5*x^2 + 1)
-             sage: P = L.primes_above(2)[0]
-             sage: P.gens_reduced()
--            (2, -15*a*b + 3*a + 1)
-+            (2, -15*a*b - 3*a + 1)
-         """
-         try:
-             # Compute the single generator, if it exists
-@@ -548,14 +548,12 @@ def factor(self):
-             sage: x = polygen(ZZ, 'x')
-             sage: K.<a, b> = QQ.extension([x^2 + 11, x^2 - 5])
-             sage: K.factor(5)
--            (Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 3/4))^2
--             * (Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 7/4))^2
-+            (Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 3/4))^2 * (Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 7/4))^2
-             sage: K.ideal(5).factor()
--            (Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 3/4))^2
--             * (Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 7/4))^2
-+            (Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 3/4))^2 * (Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 7/4))^2
-             sage: K.ideal(5).prime_factors()
--            [Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 3/4),
--             Fractional ideal (5, (-1/4*b - 1/4)*a + 1/4*b - 7/4)]
-+            [Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 3/4),
-+             Fractional ideal (5, (1/4*b - 1/4)*a + 1/4*b + 7/4)]
- 
-             sage: PQ.<X> = QQ[]
-             sage: F.<a, b> = NumberFieldTower([X^2 - 2, X^2 - 3])
-diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
-index 970707f2457..07b075060c6 100644
---- a/src/sage/rings/number_field/number_field_rel.py
-+++ b/src/sage/rings/number_field/number_field_rel.py
-@@ -233,21 +233,21 @@ def __init__(self, base, polynomial, name,
-             sage: l.<b> = k.extension(5*x^2 + 3); l
-             Number Field in b with defining polynomial 5*x^2 + 3 over its base field
-             sage: l.pari_rnf()
--            [x^2 + (-y^3 + 1/2*y^2 - 6*y + 3/2)*x + (-3/4*y^3 - 1/4*y^2 - 17/4*y - 19/4), ..., y^4 + 6*y^2 + 1, x^2 + (-y^3 + 1/2*y^2 - 6*y + 3/2)*x + (-3/4*y^3 - 1/4*y^2 - 17/4*y - 19/4)], [0, 0]]
-+            [x^2 + (5/4*y^3 - 1/4*y^2 + 27/4*y - 3/4)*x + (-9/4*y^3 - 1/4*y^2 - 47/4*y - 7/4), ..., y^4 + 6*y^2 + 1, x^2 + (5/4*y^3 - 1/4*y^2 + 27/4*y - 3/4)*x + (-9/4*y^3 - 1/4*y^2 - 47/4*y - 7/4)], [0, 0]]
-             sage: b
-             b
- 
-             sage: l.<b> = k.extension(x^2 + 3/5); l
-             Number Field in b with defining polynomial x^2 + 3/5 over its base field
-             sage: l.pari_rnf()
--            [x^2 + (-y^3 + 1/2*y^2 - 6*y + 3/2)*x + (-3/4*y^3 - 1/4*y^2 - 17/4*y - 19/4), ..., y^4 + 6*y^2 + 1, x^2 + (-y^3 + 1/2*y^2 - 6*y + 3/2)*x + (-3/4*y^3 - 1/4*y^2 - 17/4*y - 19/4)], [0, 0]]
-+            [x^2 + (5/4*y^3 - 1/4*y^2 + 27/4*y - 3/4)*x + (-9/4*y^3 - 1/4*y^2 - 47/4*y - 7/4), ..., y^4 + 6*y^2 + 1, x^2 + (5/4*y^3 - 1/4*y^2 + 27/4*y - 3/4)*x + (-9/4*y^3 - 1/4*y^2 - 47/4*y - 7/4)], [0, 0]]
-             sage: b
-             b
- 
-             sage: l.<b> = k.extension(x - 1/a0); l
-             Number Field in b with defining polynomial x + 1/2*a0 over its base field
-             sage: l.pari_rnf()
--            [x, [4, -x^3 - x^2 - 7*x - 3, -x^3 + x^2 - 7*x + 3, 2*x^3 + 10*x], ..., [x^4 + 6*x^2 + 1, -x, -1, y^4 + 6*y^2 + 1, x], [0, 0]]
-+            [x, [4, -x^3 + x^2 - 7*x + 3, -2*x^3 - 10*x, x^3 + x^2 + 7*x + 3], ..., [x^4 + 6*x^2 + 1, -x, -1, y^4 + 6*y^2 + 1, x], [0, 0]]
-             sage: b
-             -1/2*a0
- 
-@@ -1624,9 +1624,9 @@ def _pari_relative_structure(self):
-             sage: K.<a> = NumberField(x^2 + 1)
-             sage: L.<b> = K.extension(x^2 - 1/2)
-             sage: L._pari_relative_structure()
--            (x^2 + Mod(-y, y^2 + 1),
--             Mod(Mod(1/2*y - 1/2, y^2 + 1)*x, x^2 + Mod(-y, y^2 + 1)),
--             Mod(Mod(-y - 1, y^2 + 1)*x, Mod(1, y^2 + 1)*x^2 + Mod(-1/2, y^2 + 1)))
-+            (x^2 + Mod(y, y^2 + 1),
-+             Mod(Mod(-1/2*y - 1/2, y^2 + 1)*x, x^2 + Mod(y, y^2 + 1)),
-+             Mod(Mod(y - 1, y^2 + 1)*x, x^2 + Mod(-1/2, y^2 + 1)))
- 
-         An example where both fields are defined by non-integral or
-         non-monic polynomials::
-@@ -1926,7 +1926,7 @@ def absolute_polynomial(self):
-             sage: k.relative_polynomial()
-             x^2 + 1/3
-             sage: k.pari_relative_polynomial()
--            x^2 + Mod(y, y^2 + 1)*x - 1
-+            x^2 + Mod(-y, y^2 + 1)*x - 1
-         """
-         return QQ['x'](self._pari_rnfeq()[0])
- 
-@@ -2699,7 +2699,7 @@ def uniformizer(self, P, others='positive'):
-             sage: x = polygen(ZZ, 'x')
-             sage: K.<a, b> = NumberField([x^2 + 23, x^2 - 3])
-             sage: P = K.prime_factors(5)[0]; P
--            Fractional ideal (5, 1/2*a + b - 5/2)
-+            Fractional ideal (5, -1/2*a + b + 5/2)
-             sage: u = K.uniformizer(P)
-             sage: u.valuation(P)
-             1
-diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
-index fd5662048df..d1c055bf549 100644
---- a/src/sage/rings/number_field/order.py
-+++ b/src/sage/rings/number_field/order.py
-@@ -2935,7 +2935,7 @@ def GaussianIntegers(names='I', latex_name='i'):
-         sage: ZZI
-         Gaussian Integers generated by I in Number Field in I with defining polynomial x^2 + 1 with I = 1*I
-         sage: factor(3 + I)
--        (-I) * (I + 1) * (2*I + 1)
-+        (-2*I - 1) * (I - 1)
-         sage: CC(I)
-         1.00000000000000*I
-         sage: I.minpoly()
-@@ -2966,7 +2966,7 @@ def EisensteinIntegers(names='omega'):
-          with defining polynomial x^2 + x + 1
-          with omega = -0.50000000000000000? + 0.866025403784439?*I
-         sage: factor(3 + omega)
--        (-1) * (-omega - 3)
-+        (omega) * (-3*omega - 2)
-         sage: CC(omega)
-         -0.500000000000000 + 0.866025403784439*I
-         sage: omega.minpoly()
-diff --git a/src/sage/rings/number_field/selmer_group.py b/src/sage/rings/number_field/selmer_group.py
-index 283db17c84e..a940c95731d 100644
---- a/src/sage/rings/number_field/selmer_group.py
-+++ b/src/sage/rings/number_field/selmer_group.py
-@@ -71,7 +71,7 @@ def _ideal_generator(I):
- 
-         sage: K.<a> = QuadraticField(-11)
-         sage: [_ideal_generator(K.prime_above(p)) for p in primes(25)]
--        [2, 1/2*a - 1/2, -1/2*a - 3/2, 7, -a, 13, 17, 19, 1/2*a + 9/2]
-+        [2, 1/2*a - 1/2, -1/2*a - 3/2, 7, a, 13, 17, 19, 1/2*a + 9/2]
-     """
-     try:
-         return I.gens_reduced()[0]
-@@ -489,9 +489,9 @@ def pSelmerGroup(K, S, p, proof=None, debug=False):
- 
-         sage: [K.ideal(g).factor() for g in gens]
-         [(Fractional ideal (2, a + 1)) * (Fractional ideal (3, a + 1)),
--        Fractional ideal (a),
--        (Fractional ideal (2, a + 1))^2,
--        1]
-+         Fractional ideal (-a),
-+         (Fractional ideal (2, a + 1))^2,
-+         1]
- 
-         sage: toKS2(10)
-         (0, 0, 1, 1)
-diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
-index 627765cf8f0..627034877f3 100644
---- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
-+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
-@@ -1430,13 +1430,13 @@ def S_class_group(self, S, proof=True):
-             sage: R.<x> = K[]
-             sage: S.<xbar> = R.quotient(x^2 + 23)
-             sage: S.S_class_group([])
--            [((2, -a + 1, 1/2*xbar + 1/2, -1/2*a*xbar + 1/2*a + 1), 6)]
-+            [((2, a + 1, -1/2*xbar + 3/2, 1/2*a*xbar - 1/2*a + 1), 6)]
-             sage: S.S_class_group([K.ideal(3, a-1)])
-             []
-             sage: S.S_class_group([K.ideal(2, a+1)])
-             []
-             sage: S.S_class_group([K.ideal(a)])
--            [((2, -a + 1, 1/2*xbar + 1/2, -1/2*a*xbar + 1/2*a + 1), 6)]
-+            [((2, a + 1, -1/2*xbar + 3/2, 1/2*a*xbar - 1/2*a + 1), 6)]
- 
-         Now we take an example over a nontrivial base with two factors, each
-         contributing to the class group::
-@@ -1496,14 +1496,14 @@ def S_class_group(self, S, proof=True):
-             sage: C = S.S_class_group([])
-             sage: C[:2]
-             [((1/4*xbar^2 + 31/4,
--               (-1/8*a + 1/8)*xbar^2 - 31/8*a + 31/8,
--               1/16*xbar^3 + 1/16*xbar^2 + 31/16*xbar + 31/16,
--               -1/16*a*xbar^3 + (1/16*a + 1/8)*xbar^2 - 31/16*a*xbar + 31/16*a + 31/8),
-+               (1/8*a + 1/8)*xbar^2 + 31/8*a + 31/8,
-+               -1/16*xbar^3 + 3/16*xbar^2 - 31/16*xbar + 93/16,
-+               1/16*a*xbar^3 + (-1/16*a + 1/8)*xbar^2 + 31/16*a*xbar - 31/16*a + 31/8),
-               6),
-              ((-1/4*xbar^2 - 23/4,
--               (1/8*a - 1/8)*xbar^2 + 23/8*a - 23/8,
--               -1/16*xbar^3 - 1/16*xbar^2 - 23/16*xbar - 23/16,
--               1/16*a*xbar^3 + (-1/16*a - 1/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 23/8),
-+               (-1/8*a - 1/8)*xbar^2 - 23/8*a - 23/8,
-+               1/16*xbar^3 + 1/16*xbar^2 + 23/16*xbar + 23/16,
-+               -1/16*a*xbar^3 + (1/16*a - 1/8)*xbar^2 - 23/16*a*xbar + 23/16*a - 23/8),
-               6)]
-             sage: C[2][1]
-             2
-@@ -1515,11 +1515,11 @@ def S_class_group(self, S, proof=True):
-             ....:     1/16*a*xbar^3 - 1/16*a*xbar^2 + 23/16*a*xbar - 23/16*a)
-             sage: gens[0] == expected_gens[0]
-             True
--            sage: gens[1] in (expected_gens[1], expected_gens[1]/2 + expected_gens[0]/2)
-+            sage: gens[1] in (expected_gens[1], expected_gens[1]/2 + expected_gens[0]/2, -expected_gens[1]/2 + expected_gens[0]/2)
-             True
--            sage: gens[2] in (expected_gens[2], expected_gens[2] + expected_gens[0]/2)
-+            sage: gens[2] in (expected_gens[2], expected_gens[2] + expected_gens[0]/2, -expected_gens[2] + expected_gens[0]/2)
-             True
--            sage: gens[3] in (expected_gens[3], expected_gens[3] + expected_gens[0]/2)
-+            sage: gens[3] in (expected_gens[3], expected_gens[3] + expected_gens[0]/2, -expected_gens[3] + expected_gens[0]/2)
-             True
-         """
-         fields, isos, iso_classes = self._S_decomposition(tuple(S))
-@@ -1612,7 +1612,7 @@ def class_group(self, proof=True):
-             sage: R.<x> = K[]
-             sage: S.<xbar> = R.quotient(x^2 + 23)
-             sage: S.class_group()
--            [((2, -a + 1, 1/2*xbar + 1/2, -1/2*a*xbar + 1/2*a + 1), 6)]
-+            [((2, a + 1, -1/2*xbar + 3/2, 1/2*a*xbar - 1/2*a + 1), 6)]
- 
-         Here is an example of a product of number fields, both of which
-         contribute to the class group::
-@@ -1712,19 +1712,19 @@ def S_units(self, S, proof=True):
-              with defining polynomial x^2 + 3 with a = 1.732050807568878?*I
-              with modulus y^3 + 5
-             sage: [u for u, o in L.S_units([]) if o is Infinity]
--            [(-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2,
--             2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
-+            [(-1/3*a - 1)*b^2 - 4/3*a*b - 4/3*a + 3,
-+             (-1/3*a - 1)*b^2 + (2/3*a - 2)*b + 13/6*a - 1/2]
-             sage: [u for u, o in L.S_units([K.ideal(1/2*a - 3/2)])
-             ....:  if o is Infinity]
-             [(-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a,
--             (-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2,
--             2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
-+             (-1/3*a - 1)*b^2 - 4/3*a*b - 4/3*a + 3,
-+             (-1/3*a - 1)*b^2 + (2/3*a - 2)*b + 13/6*a - 1/2]
-             sage: [u for u, o in L.S_units([K.ideal(2)]) if o is Infinity]
-             [(1/2*a - 1/2)*b^2 + (a + 1)*b + 3,
--             (1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a + 1/2,
-              (1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2,
--             (-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2,
--             2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
-+             1/3*a*b^2 + (1/3*a + 1)*b - 1/6*a + 3/2,
-+             (-1/3*a - 1)*b^2 - 4/3*a*b - 4/3*a + 3,
-+             (-1/3*a - 1)*b^2 + (2/3*a - 2)*b + 13/6*a - 1/2]
- 
-         Note that all the returned values live where we expect them to::
- 
-@@ -1809,8 +1809,8 @@ def units(self, proof=True):
-              with defining polynomial x^2 + 3 with a = 1.732050807568878?*I
-              with modulus y^3 + 5
-             sage: [u for u, o in L.units() if o is Infinity]
--            [(-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2,
--             2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
-+            [(-1/3*a - 1)*b^2 - 4/3*a*b - 4/3*a + 3,
-+             (-1/3*a - 1)*b^2 + (2/3*a - 2)*b + 13/6*a - 1/2]
-             sage: L.<b> = K.extension(y^3 + 5)
-             sage: L.unit_group()
-             Unit group with structure C6 x Z x Z of
-@@ -1818,8 +1818,8 @@ def units(self, proof=True):
-             sage: L.unit_group().gens()    # abstract generators
-             (u0, u1, u2)
-             sage: L.unit_group().gens_values()[1:]
--            [(-1/3*a - 1)*b^2 - 4/3*a*b - 5/6*a + 7/2,
--             2/3*a*b^2 + (2/3*a - 2)*b - 5/6*a - 7/2]
-+            [(-1/3*a - 1)*b^2 - 4/3*a*b - 4/3*a + 3,
-+             (-1/3*a - 1)*b^2 + (2/3*a - 2)*b + 13/6*a - 1/2]
- 
-         Note that all the returned values live where we expect them to::
- 
-@@ -1877,7 +1877,7 @@ def selmer_generators(self, S, m, proof=True):
-             sage: D.selmer_generators([K.ideal(2, -a + 1),
-             ....:                      K.ideal(3, a + 1),
-             ....:                      K.ideal(a)], 3)
--            [2, a + 1, -a]
-+            [2, a + 1, a]
-         """
-         fields, isos, iso_classes = self._S_decomposition(tuple(S))
-         n = len(fields)
-diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
-index 050ab750117..4b6980c9143 100644
---- a/src/sage/rings/qqbar.py
-+++ b/src/sage/rings/qqbar.py
-@@ -2777,11 +2777,12 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
-             To:   Algebraic Real Field
-             Defn: a |--> 1.732050807568878?)
-         sage: number_field_elements_from_algebraics((rt2,qqI))                          # needs sage.symbolic
--        (Number Field in a with defining polynomial y^4 + 1, [-a^3 + a, a^2],
-+        (Number Field in a with defining polynomial y^4 + 1,
-+         [a^3 - a, a^2],
-          Ring morphism:
--            From: Number Field in a with defining polynomial y^4 + 1
--            To:   Algebraic Field
--            Defn: a |--> 0.7071067811865475? + 0.7071067811865475?*I)
-+           From: Number Field in a with defining polynomial y^4 + 1
-+           To:   Algebraic Field
-+           Defn: a |--> -0.7071067811865475? - 0.7071067811865475?*I)
- 
-     Note that for the first example, where \sage does not realize that
-     the number is real, we get a homomorphism to ``QQbar``::
-@@ -4660,8 +4661,7 @@ def _exact_field(self):
-             Number Field in a with defining polynomial y^4 - 20*y^2 + 81
-              with a in -3.789313782671036?
-             sage: (QQbar(7)^(3/5))._exact_field()
--            Number Field in a with defining polynomial
--             y^5 - 2*y^4 - 18*y^3 + 38*y^2 + 82*y - 181 with a in 2.554256611698490?
-+            Number Field in a with defining polynomial y^5 - 7 with a in 1.475773161594552?
-         """
-         sd = self._descr
-         if isinstance(sd, (ANRational, ANExtensionElement)):
-@@ -4681,7 +4681,7 @@ def _exact_value(self):
-             sage: (sqrt(QQbar(2)) + sqrt(QQbar(19)))._exact_value()
-             -1/9*a^3 + a^2 + 11/9*a - 10 where a^4 - 20*a^2 + 81 = 0 and a in -3.789313782671036?
-             sage: (QQbar(7)^(3/5))._exact_value()
--            2*a^4 + 2*a^3 - 34*a^2 - 17*a + 150 where a^5 - 2*a^4 - 18*a^3 + 38*a^2 + 82*a - 181 = 0 and a in 2.554256611698490?
-+            a^3 where a^5 - 7 = 0 and a in 1.475773161594552?
-         """
-         sd = self._descr
-         if isinstance(sd, (ANRational, ANExtensionElement)):
-@@ -7925,8 +7925,8 @@ def handle_sage_input(self, sib, coerce, is_qqbar):
-             sage: sage_input(v, verify=True)
-             # Verified
-             R.<y> = QQ[]
--            v = QQbar.polynomial_root(AA.common_polynomial(y^8 - y^7 + y^5 - y^4 + y^3 - y + 1), CIF(RIF(RR(0.91354545764260087), RR(0.91354545764260098)), RIF(RR(0.40673664307580015), RR(0.40673664307580021))))
--            v^5 + v^3
-+            v = QQbar.polynomial_root(AA.common_polynomial(y^8 - y^7 + y^5 - y^4 + y^3 - y + 1), CIF(RIF(RR(0.66913060635885813), RR(0.66913060635885824)), RIF(-RR(0.74314482547739424), -RR(0.74314482547739413))))
-+            v^6 + v^5
-             sage: v = QQbar(sqrt(AA(2)))
-             sage: v.exactify()
-             sage: sage_input(v, verify=True)
-diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
-index 68ee004a251..d1def05ac18 100644
---- a/src/sage/rings/rational.pyx
-+++ b/src/sage/rings/rational.pyx
-@@ -1558,7 +1558,7 @@ cdef class Rational(sage.structure.element.FieldElement):
-         EXAMPLES::
- 
-             sage: QQ(2)._bnfisnorm(QuadraticField(-1, 'i'))                             # needs sage.rings.number_field
--            (i + 1, 1)
-+            (i - 1, 1)
-             sage: x = polygen(QQ, 'x')
-             sage: 7._bnfisnorm(NumberField(x^3 - 2, 'b'))                               # needs sage.rings.number_field
-             (1, 7)
-diff --git a/src/sage/schemes/affine/affine_morphism.py b/src/sage/schemes/affine/affine_morphism.py
-index baa58aeb639..ca414d6d60c 100644
---- a/src/sage/schemes/affine/affine_morphism.py
-+++ b/src/sage/schemes/affine/affine_morphism.py
-@@ -1158,13 +1158,11 @@ def reduce_base_field(self):
-             sage: H = End(A)
-             sage: f = H([QQbar(3^(1/3))*x^2 + QQbar(sqrt(-2))])                         # needs sage.symbolic
-             sage: f.reduce_base_field()                                                 # needs sage.symbolic
--            Scheme endomorphism of Affine Space of dimension 1 over Number
--            Field in a with defining polynomial y^6 + 6*y^4 - 6*y^3 + 12*y^2 + 36*y + 17
--             with a = 1.442249570307409? + 1.414213562373095?*I
-+            Scheme endomorphism of Affine Space of dimension 1 over Number Field in a with defining polynomial y^6 + 6*y^4 - 6*y^3 + 12*y^2 + 36*y + 17 with a = 1.442249570307409? - 1.414213562373095?*I
-               Defn: Defined on coordinates by sending (x) to
-                     ((-48/269*a^5 + 27/269*a^4 - 320/269*a^3 + 468/269*a^2 - 772/269*a
--                    - 1092/269)*x^2 + (48/269*a^5 - 27/269*a^4 + 320/269*a^3 - 468/269*a^2
--                    + 1041/269*a + 1092/269))
-+                    - 1092/269)*x^2 + (-48/269*a^5 + 27/269*a^4 - 320/269*a^3 + 468/269*a^2
-+                    - 1041/269*a - 1092/269))
- 
-         ::
- 
-diff --git a/src/sage/schemes/berkovich/berkovich_space.py b/src/sage/schemes/berkovich/berkovich_space.py
-index f5455937b43..1330c408f4a 100644
---- a/src/sage/schemes/berkovich/berkovich_space.py
-+++ b/src/sage/schemes/berkovich/berkovich_space.py
-@@ -201,7 +201,7 @@ def ideal(self):
-             sage: ideal = A.prime_above(5)
-             sage: B = Berkovich_Cp_Projective(A, ideal)
-             sage: B.ideal()
--            Fractional ideal (-a - 2)
-+            Fractional ideal (2*a - 1)
- 
-         ::
- 
-diff --git a/src/sage/schemes/elliptic_curves/ell_field.py b/src/sage/schemes/elliptic_curves/ell_field.py
-index 376568cc90b..63ef460af6c 100644
---- a/src/sage/schemes/elliptic_curves/ell_field.py
-+++ b/src/sage/schemes/elliptic_curves/ell_field.py
-@@ -902,7 +902,7 @@ def division_field(self, n, names='t', map=False, **kwds):
-              by y^2 = x^3 + 5*a0*x^2 + (-200*a0^2)*x + (-42000*a0^2+42000*a0+126000)
-              over Number Field in a0 with defining polynomial x^3 - 3*x^2 + 3*x + 9
-             sage: K.<b> = E.division_field(3, simplify_all=True); K
--            Number Field in b with defining polynomial x^12 - 25*x^10 + 130*x^8 + 645*x^6 + 1050*x^4 + 675*x^2 + 225
-+            Number Field in b with defining polynomial x^12 + 5*x^10 + 40*x^8 + 315*x^6 + 750*x^4 + 675*x^2 + 2025
- 
-         Some higher-degree examples::
- 
-diff --git a/src/sage/schemes/elliptic_curves/ell_local_data.py b/src/sage/schemes/elliptic_curves/ell_local_data.py
-index 7434659b5a2..df076ed62b6 100644
---- a/src/sage/schemes/elliptic_curves/ell_local_data.py
-+++ b/src/sage/schemes/elliptic_curves/ell_local_data.py
-@@ -1161,7 +1161,7 @@ def check_prime(K, P):
-         sage: check_prime(K, a + 1)
-         Fractional ideal (a + 1)
-         sage: [check_prime(K, P) for P in K.primes_above(31)]
--        [Fractional ideal (5/2*a + 1/2), Fractional ideal (5/2*a - 1/2)]
-+        [Fractional ideal (-5/2*a - 1/2), Fractional ideal (-5/2*a + 1/2)]
-         sage: L.<b> = NumberField(x^2 + 3)
-         sage: check_prime(K, L.ideal(5))
-         Traceback (most recent call last):
-diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
-index 518fda03481..e36bf28499f 100644
---- a/src/sage/schemes/elliptic_curves/ell_number_field.py
-+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
-@@ -229,9 +229,9 @@ def simon_two_descent(self, verbose=0, lim1=2, lim3=4, limtriv=2,
-             sage: E == loads(dumps(E))
-             True
-             sage: E.simon_two_descent()
--            (2, 2, [(0 : 0 : 1), (1/18*a + 7/18 : -5/54*a - 17/54 : 1)])
-+            (2, 2, [(0 : 0 : 1), (1/8*a + 5/8 : -3/16*a - 7/16 : 1)])
-             sage: E.simon_two_descent(lim1=5, lim3=5, limtriv=10, maxprob=7, limbigprime=10)
--            (2, 2, [(-1 : 0 : 1), (-2 : -1/2*a - 1/2 : 1)])
-+            (2, 2, [(-1 : 0 : 1), (1/2*a - 5/2 : -1/2*a - 13/2 : 1)])
- 
-         ::
- 
-@@ -277,7 +277,7 @@ def simon_two_descent(self, verbose=0, lim1=2, lim3=4, limtriv=2,
-             sage: E.simon_two_descent()  # long time (4s on sage.math, 2013)
-             (3,
-              3,
--             [(1/8*zeta43_0^2 - 3/8*zeta43_0 - 1/4 : -5/16*zeta43_0^2 + 7/16*zeta43_0 + 1/8 : 1),
-+             [(-1/2*zeta43_0^2 - 1/2*zeta43_0 + 7 : -3/2*zeta43_0^2 - 5/2*zeta43_0 + 18 : 1),
-               (0 : 0 : 1)])
-         """
-         verbose = int(verbose)
-@@ -873,7 +873,7 @@ def local_data(self, P=None, proof=None, algorithm='pari', globally=False):
-             sage: K.<i> = NumberField(x^2 + 1)
-             sage: E = EllipticCurve([1 + i, 0, 1, 0, 0])
-             sage: E.local_data()
--            [Local data at Fractional ideal (2*i + 1):
-+            [Local data at Fractional ideal (-2*i - 1):
-                Reduction type: bad non-split multiplicative
-                Local minimal model: Elliptic Curve defined by y^2 + (i+1)*x*y + y = x^3
-                                     over Number Field in i with defining polynomial x^2 + 1
-@@ -881,7 +881,7 @@ def local_data(self, P=None, proof=None, algorithm='pari', globally=False):
-                Conductor exponent: 1
-                Kodaira Symbol: I1
-                Tamagawa Number: 1,
--             Local data at Fractional ideal (-2*i + 3):
-+             Local data at Fractional ideal (3*i + 2):
-                Reduction type: bad split multiplicative
-                Local minimal model: Elliptic Curve defined by y^2 + (i+1)*x*y + y = x^3
-                                     over Number Field in i with defining polynomial x^2 + 1
-@@ -899,7 +899,7 @@ def local_data(self, P=None, proof=None, algorithm='pari', globally=False):
-               Kodaira Symbol: I0
-               Tamagawa Number: 1
-             sage: E.local_data(2*i + 1)
--            Local data at Fractional ideal (2*i + 1):
-+            Local data at Fractional ideal (-2*i - 1):
-               Reduction type: bad non-split multiplicative
-               Local minimal model: Elliptic Curve defined by y^2 + (i+1)*x*y + y = x^3
-                                    over Number Field in i with defining polynomial x^2 + 1
-@@ -1457,8 +1457,10 @@ def kodaira_symbol(self, P, proof=None):
-             sage: K.<a> = NumberField(x^2 - 5)
-             sage: E = EllipticCurve([20, 225, 750, 625*a + 6875, 31250*a + 46875])
-             sage: bad_primes = E.discriminant().support(); bad_primes
--            [Fractional ideal (-a), Fractional ideal (7/2*a - 81/2),
--             Fractional ideal (-a - 52), Fractional ideal (2)]
-+            [Fractional ideal (-a),
-+             Fractional ideal (-7/2*a + 81/2),
-+             Fractional ideal (-a - 52),
-+             Fractional ideal (2)]
-             sage: [E.kodaira_symbol(P) for P in bad_primes]
-             [I0, I1, I1, II]
-             sage: K.<a> = QuadraticField(-11)
-@@ -1484,10 +1486,10 @@ def conductor(self):
- 
-             sage: K.<i> = NumberField(x^2 + 1)
-             sage: EllipticCurve([i, i - 1, i + 1, 24*i + 15, 14*i + 35]).conductor()
--            Fractional ideal (21*i - 3)
-+            Fractional ideal (3*i + 21)
-             sage: K.<a> = NumberField(x^2 - x + 3)
-             sage: EllipticCurve([1 + a, -1 + a, 1 + a, -11 + a, 5 - 9*a]).conductor()
--            Fractional ideal (-6*a)
-+            Fractional ideal (6*a)
- 
-         A not so well known curve with everywhere good reduction::
- 
-@@ -2585,8 +2587,8 @@ def isogeny_class(self, reducible_primes=None, algorithm='Billerey', minimal_mod
-             sage: [E1.ainvs() for E1 in C]
-             [(0, 0, 0, 0, -27),
-             (0, 0, 0, 0, 1),
--            (i + 1, i, i + 1, -i + 3, 4*i),
--            (i + 1, i, i + 1, -i + 33, -58*i)]
-+            (i + 1, i, 0, 3, -i),
-+            (i + 1, i, 0, 33, 91*i)]
- 
-         The matrix of degrees of cyclic isogenies between curves::
- 
-@@ -2617,13 +2619,13 @@ class :class:`EllipticCurveIsogeny` allowed composition.  In
-             sage: [((i,j), isogs[i][j].x_rational_map())
-             ....:  for i in range(4) for j in range(4) if isogs[i][j] != 0]
-             [((0, 1), (1/9*x^3 - 12)/x^2),
--             ((0, 3), (-1/2*i*x^2 + i*x - 12*i)/(x - 3)),
-+             ((0, 3), (1/2*i*x^2 - 2*i*x + 15*i)/(x - 3)),
-              ((1, 0), (x^3 + 4)/x^2),
--             ((1, 2), (-1/2*i*x^2 - i*x - 2*i)/(x + 1)),
--             ((2, 1), (1/2*i*x^2 - x)/(x + 3/2*i)),
--             ((2, 3), (x^3 + 4*i*x^2 - 10*x - 10*i)/(x^2 + 4*i*x - 4)),
--             ((3, 0), (1/2*i*x^2 + x + 4*i)/(x - 5/2*i)),
--             ((3, 2), (1/9*x^3 - 4/3*i*x^2 - 34/3*x + 226/9*i)/(x^2 - 8*i*x - 16))]
-+             ((1, 2), (1/2*i*x^2 + i)/(x + 1)),
-+             ((2, 1), (-1/2*i*x^2 - 1/2*i)/(x - 1/2*i)),
-+             ((2, 3), (x^3 - 2*i*x^2 - 7*x + 4*i)/(x^2 - 2*i*x - 1)),
-+             ((3, 0), (-1/2*i*x^2 + 2*x - 5/2*i)/(x + 7/2*i)),
-+             ((3, 2), (1/9*x^3 + 2/3*i*x^2 - 13/3*x - 116/9*i)/(x^2 + 10*i*x - 25))]
- 
-         The isogeny class may be visualized by obtaining its graph and
-         plotting it::
-@@ -3104,10 +3106,10 @@ def is_isogenous(self, other, proof=True, maxnorm=100):
-             sage: K.<i> = QuadraticField(-1)
-             sage: E1 = EllipticCurve([i + 1, 0, 1, -240*i - 400, -2869*i - 2627])
-             sage: E1.conductor()
--            Fractional ideal (-4*i - 7)
-+            Fractional ideal (4*i + 7)
-             sage: E2 = EllipticCurve([1+i,0,1,0,0])
-             sage: E2.conductor()
--            Fractional ideal (-4*i - 7)
-+            Fractional ideal (4*i + 7)
-             sage: E1.is_isogenous(E2) # long time
-             True
-             sage: E1.is_isogenous(E2, proof=False) # faster  (~170ms)
-@@ -3434,8 +3436,8 @@ def lll_reduce(self, points, height_matrix=None, precision=None):
-             sage: Q = E(0,-1)
-             sage: E.lll_reduce([P,Q])
-             (
--                                                     [0 1]
--            [(0 : -1 : 1), (-2 : -1/2*a - 1/2 : 1)], [1 0]
-+                                                    [ 0 -1]
-+            [(0 : -1 : 1), (-2 : 1/2*a - 1/2 : 1)], [ 1  0]
-             )
- 
-         ::
-@@ -3446,9 +3448,10 @@ def lll_reduce(self, points, height_matrix=None, precision=None):
-             ....:           E.point([-17/18*a - 1/9, -109/108*a - 277/108])]
-             sage: E.lll_reduce(points)
-             (
--            [(-a + 4 : -3*a + 7 : 1), (-17/18*a - 1/9 : 109/108*a + 277/108 : 1)],
--            [ 1  0]
--            [ 1 -1]
-+            [(-a + 4 : -3*a + 7 : 1), (-17/18*a - 1/9 : -109/108*a - 277/108 : 1)],
-+            <BLANKLINE>
-+            [1 0]
-+            [1 1]
-             )
-         """
-         r = len(points)
-diff --git a/src/sage/schemes/elliptic_curves/ell_point.py b/src/sage/schemes/elliptic_curves/ell_point.py
-index 1d980d60666..7c18a464559 100644
---- a/src/sage/schemes/elliptic_curves/ell_point.py
-+++ b/src/sage/schemes/elliptic_curves/ell_point.py
-@@ -3052,9 +3052,9 @@ def has_good_reduction(self, P=None):
-             sage: E = EllipticCurve(K, [0,1,0,-160,308])
-             sage: P = E(26, -120)
-             sage: E.discriminant().support()
--            [Fractional ideal (i + 1),
--             Fractional ideal (-i - 2),
--             Fractional ideal (2*i + 1),
-+            [Fractional ideal (i - 1),
-+             Fractional ideal (2*i - 1),
-+             Fractional ideal (-2*i - 1),
-              Fractional ideal (3)]
-             sage: [E.tamagawa_exponent(p) for p in E.discriminant().support()]
-             [1, 4, 4, 4]
-diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py
-index 134531ad1a5..27b33b46e67 100644
---- a/src/sage/schemes/elliptic_curves/ell_rational_field.py
-+++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py
-@@ -1863,7 +1863,7 @@ def simon_two_descent(self, verbose=0, lim1=5, lim3=50, limtriv=3,
-             sage: E = EllipticCurve('389a1')
-             sage: E._known_points = []  # clear cached points
-             sage: E.simon_two_descent()
--            (2, 2, [(5/4 : 5/8 : 1), (-3/4 : 7/8 : 1)])
-+            (2, 2, [(-3/4 : 7/8 : 1), (5/4 : 5/8 : 1)])
-             sage: E = EllipticCurve('5077a1')
-             sage: E.simon_two_descent()
-             (3, 3, [(1 : 0 : 1), (2 : 0 : 1), (0 : 2 : 1)])
-diff --git a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
-index 7824893b05f..609aab5f4bf 100644
---- a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
-+++ b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
-@@ -800,17 +800,17 @@ def deg_one_primes_iter(K, principal_only=False):
-         [Fractional ideal (2, a + 1),
-          Fractional ideal (3, a + 1),
-          Fractional ideal (3, a + 2),
--         Fractional ideal (a),
-+         Fractional ideal (-a),
-          Fractional ideal (7, a + 3),
-          Fractional ideal (7, a + 4)]
-         sage: it = deg_one_primes_iter(K, True)
-         sage: [next(it) for _ in range(6)]
--        [Fractional ideal (a),
--         Fractional ideal (-2*a + 3),
--         Fractional ideal (2*a + 3),
-+        [Fractional ideal (-a),
-+         Fractional ideal (2*a - 3),
-+         Fractional ideal (-2*a - 3),
-          Fractional ideal (a + 6),
-          Fractional ideal (a - 6),
--         Fractional ideal (-3*a + 4)]
-+         Fractional ideal (3*a - 4)]
-     """
-     # imaginary quadratic fields have no principal primes of norm < disc / 4
-     start = K.discriminant().abs() // 4 if principal_only and K.signature() == (0,1) else 2
-diff --git a/src/sage/schemes/elliptic_curves/gp_simon.py b/src/sage/schemes/elliptic_curves/gp_simon.py
-index 6be377e2f74..4134ae1b7a6 100644
---- a/src/sage/schemes/elliptic_curves/gp_simon.py
-+++ b/src/sage/schemes/elliptic_curves/gp_simon.py
-@@ -49,7 +49,7 @@ def simon_two_descent(E, verbose=0, lim1=None, lim3=None, limtriv=None,
-         doctest:warning...:
-         DeprecationWarning: please use the 2-descent algorithm over QQ inside pari
-         See https://github.com/sagemath/sage/issues/38461 for details.
--        (2, 2, [(5/4 : 5/8 : 1), (-3/4 : 7/8 : 1)])
-+        (2, 2, [(-3/4 : 7/8 : 1), (5/4 : 5/8 : 1)])
- 
-     TESTS::
- 
-diff --git a/src/sage/schemes/elliptic_curves/isogeny_class.py b/src/sage/schemes/elliptic_curves/isogeny_class.py
-index 13edc68a022..a83fd8705ac 100644
---- a/src/sage/schemes/elliptic_curves/isogeny_class.py
-+++ b/src/sage/schemes/elliptic_curves/isogeny_class.py
-@@ -223,8 +223,8 @@ def _repr_(self):
-             sage: C.curves
-             [Elliptic Curve defined by y^2 = x^3 + (-27) over Number Field in i with defining polynomial x^2 + 1 with i = 1*I,
-              Elliptic Curve defined by y^2 = x^3 + 1 over Number Field in i with defining polynomial x^2 + 1 with i = 1*I,
--             Elliptic Curve defined by y^2 + (i+1)*x*y + (i+1)*y = x^3 + i*x^2 + (-i+3)*x + 4*i over Number Field in i with defining polynomial x^2 + 1 with i = 1*I,
--             Elliptic Curve defined by y^2 + (i+1)*x*y + (i+1)*y = x^3 + i*x^2 + (-i+33)*x + (-58*i) over Number Field in i with defining polynomial x^2 + 1 with i = 1*I]
-+             Elliptic Curve defined by y^2 + (i+1)*x*y = x^3 + i*x^2 + 3*x + (-i) over Number Field in i with defining polynomial x^2 + 1 with i = 1*I,
-+             Elliptic Curve defined by y^2 + (i+1)*x*y = x^3 + i*x^2 + 33*x + 91*i over Number Field in i with defining polynomial x^2 + 1 with i = 1*I]
-         """
-         if self._label:
-             return "Elliptic curve isogeny class %s" % (self._label)
-@@ -615,8 +615,8 @@ def __init__(self, E, reducible_primes=None, algorithm='Billerey', minimal_model
-             sage: [E1.ainvs() for E1 in C]
-             [(0, 0, 0, 0, -27),
-              (0, 0, 0, 0, 1),
--             (i + 1, i, i + 1, -i + 3, 4*i),
--             (i + 1, i, i + 1, -i + 33, -58*i)]
-+             (i + 1, i, 0, 3, -i),
-+             (i + 1, i, 0, 33, 91*i)]
- 
-         The matrix of degrees of cyclic isogenies between curves::
- 
-@@ -647,13 +647,13 @@ class :class:`EllipticCurveIsogeny` allowed composition.  In
-             sage: [((i,j), isogs[i][j].x_rational_map())
-             ....:  for i in range(4) for j in range(4) if isogs[i][j] != 0]
-             [((0, 1), (1/9*x^3 - 12)/x^2),
--             ((0, 3), (-1/2*i*x^2 + i*x - 12*i)/(x - 3)),
-+             ((0, 3), (1/2*i*x^2 - 2*i*x + 15*i)/(x - 3)),
-              ((1, 0), (x^3 + 4)/x^2),
--             ((1, 2), (-1/2*i*x^2 - i*x - 2*i)/(x + 1)),
--             ((2, 1), (1/2*i*x^2 - x)/(x + 3/2*i)),
--             ((2, 3), (x^3 + 4*i*x^2 - 10*x - 10*i)/(x^2 + 4*i*x - 4)),
--             ((3, 0), (1/2*i*x^2 + x + 4*i)/(x - 5/2*i)),
--             ((3, 2), (1/9*x^3 - 4/3*i*x^2 - 34/3*x + 226/9*i)/(x^2 - 8*i*x - 16))]
-+             ((1, 2), (1/2*i*x^2 + i)/(x + 1)),
-+             ((2, 1), (-1/2*i*x^2 - 1/2*i)/(x - 1/2*i)),
-+             ((2, 3), (x^3 - 2*i*x^2 - 7*x + 4*i)/(x^2 - 2*i*x - 1)),
-+             ((3, 0), (-1/2*i*x^2 + 2*x - 5/2*i)/(x + 7/2*i)),
-+             ((3, 2), (1/9*x^3 + 2/3*i*x^2 - 13/3*x - 116/9*i)/(x^2 + 10*i*x - 25))]
- 
-             sage: K.<i> = QuadraticField(-1)
-             sage: E = EllipticCurve([1+i, -i, i, 1, 0])
-diff --git a/src/sage/schemes/elliptic_curves/isogeny_small_degree.py b/src/sage/schemes/elliptic_curves/isogeny_small_degree.py
-index 6a0194fb0f9..90f7382a94e 100644
---- a/src/sage/schemes/elliptic_curves/isogeny_small_degree.py
-+++ b/src/sage/schemes/elliptic_curves/isogeny_small_degree.py
-@@ -886,15 +886,15 @@ def isogenies_5_0(E, minimal_models=True):
-           from Elliptic Curve defined by y^2 + y = x^3
-                over Number Field in a with defining polynomial x^6 - 320*x^3 - 320
-             to Elliptic Curve defined by
--               y^2 + y = x^3 + (241565/32*a^5-362149/48*a^4+180281/24*a^3-9693307/4*a^2+14524871/6*a-7254985/3)*x
--                          + (1660391123/192*a^5-829315373/96*a^4+77680504/9*a^3-66622345345/24*a^2+33276655441/12*a-24931615912/9)
-+               y^2 + y = x^3 + (643/8*a^5-15779/48*a^4-32939/24*a^3-71989/2*a^2+214321/6*a-112115/3)*x
-+                          + (2901961/96*a^5+4045805/48*a^4+12594215/18*a^3-30029635/6*a^2+15341626/3*a-38944312/9)
-                over Number Field in a with defining polynomial x^6 - 320*x^3 - 320,
-          Isogeny of degree 5
-           from Elliptic Curve defined by y^2 + y = x^3
-                over Number Field in a with defining polynomial x^6 - 320*x^3 - 320
-             to Elliptic Curve defined by
--               y^2 + y = x^3 + (47519/32*a^5-72103/48*a^4+32939/24*a^3-1909753/4*a^2+2861549/6*a-1429675/3)*x
--                          + (-131678717/192*a^5+65520419/96*a^4-12594215/18*a^3+5280985135/24*a^2-2637787519/12*a+1976130088/9)
-+               y^2 + y = x^3 + (-1109/8*a^5-53873/48*a^4-180281/24*a^3-14491/2*a^2+35899/6*a-43745/3)*x
-+                          + (-17790679/96*a^5-60439571/48*a^4-77680504/9*a^3+1286245/6*a^2-4961854/3*a-73854632/9)
-                over Number Field in a with defining polynomial x^6 - 320*x^3 - 320]
-     """
-     F = E.base_field()
-diff --git a/src/sage/schemes/plane_conics/con_number_field.py b/src/sage/schemes/plane_conics/con_number_field.py
-index e09a1f60262..2b084b57dc6 100644
---- a/src/sage/schemes/plane_conics/con_number_field.py
-+++ b/src/sage/schemes/plane_conics/con_number_field.py
-@@ -121,7 +121,7 @@ def has_rational_point(self, point=False, obstruction=False,
-             sage: K.<i> = QuadraticField(-1)
-             sage: C = Conic(K, [1, 3, -5])
-             sage: C.has_rational_point(point=True, obstruction=True)
--            (False, Fractional ideal (-i - 2))
-+            (False, Fractional ideal (2*i - 1))
-             sage: C.has_rational_point(algorithm='rnfisnorm')
-             False
-             sage: C.has_rational_point(algorithm='rnfisnorm', obstruction=True,
-@@ -135,7 +135,7 @@ def has_rational_point(self, point=False, obstruction=False,
-             sage: L.<b> = NumberField(x^3 - 5)
-             sage: C = Conic(L, [1, 2, -3])
-             sage: C.has_rational_point(point=True, algorithm='rnfisnorm')
--            (True, (5/3 : -1/3 : 1))
-+            (True, (-5/3 : 1/3 : 1))
- 
-             sage: K.<a> = NumberField(x^4+2)
-             sage: Conic(QQ, [4,5,6]).has_rational_point()
-diff --git a/src/sage/schemes/projective/projective_morphism.py b/src/sage/schemes/projective/projective_morphism.py
-index 20031e81a41..fcbb0c01e82 100644
---- a/src/sage/schemes/projective/projective_morphism.py
-+++ b/src/sage/schemes/projective/projective_morphism.py
-@@ -928,7 +928,7 @@ def normalize_coordinates(self, **kwds):
-             Dynamical System of Projective Space of dimension 1 over
-             Number Field in a with defining polynomial 3*x^2 + 1
-             Defn: Defined on coordinates by sending (z : w) to
--                ((-3/2*a + 1/2)*z^2 + (-3/2*a + 1/2)*w^2 : (-3/2*a - 3/2)*z*w)
-+                ((3/2*a + 1/2)*z^2 + (3/2*a + 1/2)*w^2 : (-3/2*a + 3/2)*z*w)
- 
-         ::
- 
-@@ -1728,11 +1728,11 @@ def _number_field_from_algebraics(self):
-             sage: f._number_field_from_algebraics()                                     # needs sage.symbolic
-             Scheme endomorphism of Projective Space of dimension 1 over Number
-              Field in a with defining polynomial y^6 + 6*y^4 - 6*y^3 + 12*y^2 + 36*y + 17
--             with a = 1.442249570307409? + 1.414213562373095?*I
-+             with a = 1.442249570307409? - 1.414213562373095?*I
-               Defn: Defined on coordinates by sending (x : y) to
-                     ((-48/269*a^5 + 27/269*a^4 - 320/269*a^3 + 468/269*a^2 - 772/269*a
--                    - 1092/269)*x^2 + (48/269*a^5 - 27/269*a^4 + 320/269*a^3 - 468/269*a^2
--                    + 1041/269*a + 1092/269)*y^2 : y^2)
-+                    - 1092/269)*x^2 + (-48/269*a^5 + 27/269*a^4 - 320/269*a^3 + 468/269*a^2
-+                    - 1041/269*a - 1092/269)*y^2 : y^2)
- 
-         ::
- 
-@@ -1745,12 +1745,12 @@ def _number_field_from_algebraics(self):
-             Scheme morphism:
-               From: Projective Space of dimension 1 over Number Field in a
-                     with defining polynomial y^4 + 3*y^2 + 1
--                    with a = 0.?e-113 + 0.618033988749895?*I
-+                    with a = 0.?e-166 + 1.618033988749895?*I
-               To:   Projective Space of dimension 2 over Number Field in a
-                     with defining polynomial y^4 + 3*y^2 + 1
--                    with a = 0.?e-113 + 0.618033988749895?*I
-+                    with a = 0.?e-166 + 1.618033988749895?*I
-               Defn: Defined on coordinates by sending (x : y) to
--                    (x^2 + (a^3 + 2*a)*x*y + 3*y^2 : y^2 : (2*a^2 + 3)*x*y)
-+                    (x^2 + (-a^3 - 2*a)*x*y + 3*y^2 : y^2 : (-2*a^2 - 3)*x*y)
- 
-         The following was fixed in :issue:`23808`::
- 
-diff --git a/src/sage/schemes/projective/projective_point.py b/src/sage/schemes/projective/projective_point.py
-index 88ab4eadcfc..95ee97a7d19 100644
---- a/src/sage/schemes/projective/projective_point.py
-+++ b/src/sage/schemes/projective/projective_point.py
-@@ -1246,10 +1246,10 @@ def _number_field_from_algebraics(self):
-             sage: P.<x,y> = ProjectiveSpace(QQbar, 1)
-             sage: Q = P([-1/2*QQbar(sqrt(2)) + QQbar(I), 1])
-             sage: S = Q._number_field_from_algebraics(); S
--            (1/2*a^3 + a^2 - 1/2*a : 1)
-+            (-1/2*a^3 + a^2 + 1/2*a : 1)
-             sage: S.codomain()
-             Projective Space of dimension 1 over Number Field in a with defining
--             polynomial y^4 + 1 with a = 0.7071067811865475? + 0.7071067811865475?*I
-+             polynomial y^4 + 1 with a = -0.7071067811865475? - 0.7071067811865475?*I
- 
-         The following was fixed in :issue:`23808`::
- 
-@@ -1259,7 +1259,7 @@ def _number_field_from_algebraics(self):
-             sage: Q = P([-1/2*QQbar(sqrt(2)) + QQbar(I), 1]);Q
-             (-0.7071067811865475? + 1*I : 1)
-             sage: S = Q._number_field_from_algebraics(); S
--            (1/2*a^3 + a^2 - 1/2*a : 1)
-+            (-1/2*a^3 + a^2 + 1/2*a : 1)
-             sage: T = S.change_ring(QQbar)  # Used to fail
-             sage: T
-             (-0.7071067811865475? + 1.000000000000000?*I : 1)
-diff --git a/src/sage/structure/factorization.py b/src/sage/structure/factorization.py
-index ab3fa717031..b16822791dc 100644
---- a/src/sage/structure/factorization.py
-+++ b/src/sage/structure/factorization.py
-@@ -143,17 +143,17 @@
-     sage: K.<a> = NumberField(x^2 + 3); K
-     Number Field in a with defining polynomial x^2 + 3
-     sage: f = K.factor(15); f
--    (Fractional ideal (1/2*a + 3/2))^2 * (Fractional ideal (5))
-+    (Fractional ideal (-a))^2 * (Fractional ideal (5))
-     sage: f.universe()
-     Monoid of ideals of Number Field in a with defining polynomial x^2 + 3
-     sage: f.unit()
-     Fractional ideal (1)
-     sage: g = K.factor(9); g
--    (Fractional ideal (1/2*a + 3/2))^4
-+    (Fractional ideal (-a))^4
-     sage: f.lcm(g)
--    (Fractional ideal (1/2*a + 3/2))^4 * (Fractional ideal (5))
-+    (Fractional ideal (-a))^4 * (Fractional ideal (5))
-     sage: f.gcd(g)
--    (Fractional ideal (1/2*a + 3/2))^2
-+    (Fractional ideal (-a))^2
-     sage: f.is_integral()
-     True
- 
-diff --git a/src/sage/symbolic/constants.py b/src/sage/symbolic/constants.py
-index 20a293fbb7b..dac8c4bc833 100644
---- a/src/sage/symbolic/constants.py
-+++ b/src/sage/symbolic/constants.py
-@@ -38,8 +38,7 @@
-     sage: gap(pi)
-     pi
-     sage: gp(pi)
--    3.141592653589793238462643383     # 32-bit
--    3.1415926535897932384626433832795028842   # 64-bit
-+    3.1415926535897932384626433832795028842
-     sage: pari(pi)
-     3.14159265358979
-     sage: kash(pi)                    # optional - kash
-@@ -63,8 +62,7 @@
-     sage: RealField(15)(a)           # 15 *bits* of precision
-     5.316
-     sage: gp(a)
--    5.316218116357029426750873360              # 32-bit
--    5.3162181163570294267508733603616328824    # 64-bit
-+    5.3162181163570294267508733603616328824
-     sage: print(mathematica(a))                  # optional - mathematica
-      4 E
-      --- + Pi
-@@ -882,8 +880,7 @@ class Log2(Constant):
-         sage: maxima(log2).float()
-         0.6931471805599453
-         sage: gp(log2)
--        0.6931471805599453094172321215             # 32-bit
--        0.69314718055994530941723212145817656807   # 64-bit
-+        0.69314718055994530941723212145817656807
-         sage: RealField(150)(2).log()
-         0.69314718055994530941723212145817656807550013
-     """
-diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
-index da4d5db908f..3c2f93e3355 100644
---- a/src/sage/symbolic/expression.pyx
-+++ b/src/sage/symbolic/expression.pyx
-@@ -9799,8 +9799,7 @@ cdef class Expression(Expression_abc):
-         ::
- 
-             sage: gp('gamma(1+I)')
--            0.4980156681183560427136911175 - 0.1549498283018106851249551305*I # 32-bit
--            0.49801566811835604271369111746219809195 - 0.15494982830181068512495513048388660520*I # 64-bit
-+            0.49801566811835604271369111746219809195 - 0.15494982830181068512495513048388660520*I
- 
-         We plot the familiar plot of this log-convex function::
- 
diff --git a/gnu/packages/sagemath.scm b/gnu/packages/sagemath.scm
index b543d4aa534..4f67ef92929 100644
--- a/gnu/packages/sagemath.scm
+++ b/gnu/packages/sagemath.scm
@@ -360,7 +360,7 @@ database.")
 (define-public sage
   (package
     (name "sage")
-    (version "10.6.beta7")
+    (version "10.6.beta9")
     (source (origin
               (method git-fetch)
               (uri (git-reference
@@ -369,8 +369,7 @@ database.")
               (file-name (git-file-name name version))
               (sha256
                (base32
-                "1lr9v38w5ljvrgywyr3hfvw4dmbzqv1cr67dmrfxj3zplrp3qzvy"))
-              (patches (search-patches "sage-update-pari-gp.patch"))))
+                "0hj882wbyax5w7kilh6gwczz0gy0gnhpkz0608sn2yzc4r484w2d"))))
     (build-system pyproject-build-system)
     (native-inputs
       (list autoconf automake m4 pkg-config ; for ./bootstrap