diff options
| -rw-r--r-- | .SRCINFO | 6 | ||||
| -rw-r--r-- | PKGBUILD | 19 | ||||
| -rw-r--r-- | sagemath-matplotlib-3.4.patch | 12 | ||||
| -rw-r--r-- | sagemath-pari-2.13.patch | 3649 |
4 files changed, 8 insertions, 3678 deletions
@@ -1,6 +1,6 @@ pkgbase = sagemath-git pkgdesc = Open Source Mathematics Software, free alternative to Magma, Maple, Mathematica, and Matlab - pkgver = 9.4.beta2.r0.g46c5c53b4d + pkgver = 9.4.beta3.r0.ga60179ab6b pkgrel = 1 url = http://www.sagemath.org arch = x86_64 @@ -100,17 +100,13 @@ pkgbase = sagemath-git source = sagemath-optional-packages.patch source = latte-count.patch source = test-optional.patch - source = sagemath-pari-2.13.patch source = sagemath-lrcalc2.patch source = sagemath-eclib-20210310.patch - source = sagemath-matplotlib-3.4.patch sha256sums = SKIP sha256sums = c100a61c8dfade43bebc622a363abcb3d935a2f40958371ad87a9eb00689f8b0 sha256sums = 88e944f23c3b2391dc2e9f9be8e1131152d837dc8c829dfc714663869a272e81 sha256sums = af984186f852d2847d770a18fb6822296c50a652dbf55a1ed59d27517c3d3ee4 - sha256sums = 3797d5eb941b947968f6f118b92f7b1f309f3a27143785cdb6cab844402c0bdb sha256sums = 240ac4c29d96d56407a20e1b7f9846e342a7eb2bb4edd6e5c86b3b5a8ff462f9 sha256sums = e7b31f5e7ea88681c6eda41e5a74a2859a12dd128e75c00db3cfbd1d8ddf080d - sha256sums = 5e6f919a386e1a9e9caf7528088a3a3f3f3fc51b158a4daf435771afb1212384 pkgname = sagemath-git @@ -6,7 +6,7 @@ # Contributor: Stefan Husmann <stefan-husmann at t-online dot de> pkgname=sagemath-git -pkgver=9.4.beta2.r0.g46c5c53b4d +pkgver=9.4.beta3.r0.ga60179ab6b pkgrel=1 pkgdesc='Open Source Mathematics Software, free alternative to Magma, Maple, Mathematica, and Matlab' arch=(x86_64) @@ -41,18 +41,14 @@ source=(git://git.sagemath.org/sage.git#branch=develop sagemath-optional-packages.patch latte-count.patch test-optional.patch - sagemath-pari-2.13.patch sagemath-lrcalc2.patch - sagemath-eclib-20210310.patch - sagemath-matplotlib-3.4.patch) + sagemath-eclib-20210310.patch) sha256sums=('SKIP' 'c100a61c8dfade43bebc622a363abcb3d935a2f40958371ad87a9eb00689f8b0' '88e944f23c3b2391dc2e9f9be8e1131152d837dc8c829dfc714663869a272e81' 'af984186f852d2847d770a18fb6822296c50a652dbf55a1ed59d27517c3d3ee4' - '3797d5eb941b947968f6f118b92f7b1f309f3a27143785cdb6cab844402c0bdb' '240ac4c29d96d56407a20e1b7f9846e342a7eb2bb4edd6e5c86b3b5a8ff462f9' - 'e7b31f5e7ea88681c6eda41e5a74a2859a12dd128e75c00db3cfbd1d8ddf080d' - '5e6f919a386e1a9e9caf7528088a3a3f3f3fc51b158a4daf435771afb1212384') + 'e7b31f5e7ea88681c6eda41e5a74a2859a12dd128e75c00db3cfbd1d8ddf080d') pkgver() { cd sage @@ -63,14 +59,10 @@ prepare(){ cd sage # Upstream patches -# Port to PARI 2.13 https://trac.sagemath.org/ticket/30801 - patch -p1 -i ../sagemath-pari-2.13.patch # Replace lrcalc.pyx with a wrapper over lrcalc's python bindings https://trac.sagemath.org/ticket/31355 patch -p1 -i ../sagemath-lrcalc2.patch # Fix build with eclib 20210310 https://trac.sagemath.org/ticket/31443 patch -p1 -i ../sagemath-eclib-20210310.patch -# Fix deprecation warnings with matplotlib 3.4 https://trac.sagemath.org/ticket/31580 - patch -p1 -i ../sagemath-matplotlib-3.4.patch # Arch-specific patches # assume all optional packages are installed @@ -79,6 +71,9 @@ prepare(){ patch -p1 -i ../test-optional.patch # use correct latte-count binary name patch -p1 -i ../latte-count.patch + + cd build/pkgs/sagelib + ./bootstrap } build() { @@ -98,7 +93,7 @@ package() { # fix symlinks to assets _pythonpath=`python -c "from sysconfig import get_path; print(get_path('platlib'))"` - for _i in $(ls "$srcdir"/sage-$pkgver/src/sage/ext_data/notebook-ipython); do + for _i in $(ls "$srcdir"/sage/src/sage/ext_data/notebook-ipython); do rm "$pkgdir"/usr/share/jupyter/kernels/sagemath/$_i ln -s $_pythonpath/sage/ext_data/notebook-ipython/$_i "$pkgdir"/usr/share/jupyter/kernels/sagemath/ done diff --git a/sagemath-matplotlib-3.4.patch b/sagemath-matplotlib-3.4.patch deleted file mode 100644 index 3a0d4abd5783..000000000000 --- a/sagemath-matplotlib-3.4.patch +++ /dev/null @@ -1,12 +0,0 @@ -diff --git a/src/sage/plot/arrow.py b/src/sage/plot/arrow.py -index 0247872298..63de0ad5dd 100644 ---- a/src/sage/plot/arrow.py -+++ b/src/sage/plot/arrow.py -@@ -397,7 +397,6 @@ class Arrow(GraphicPrimitive): - self._n = n - - def get_paths(self, renderer): -- self._patch.set_dpi_cor(renderer.points_to_pixels(1.)) - paths, fillables = self._patch.get_path_in_displaycoord() - return paths - diff --git a/sagemath-pari-2.13.patch b/sagemath-pari-2.13.patch deleted file mode 100644 index e3a730f06f1d..000000000000 --- a/sagemath-pari-2.13.patch +++ /dev/null @@ -1,3649 +0,0 @@ -diff --git a/build/pkgs/pari/checksums.ini b/build/pkgs/pari/checksums.ini -index f10b432dbb..ec00516a1d 100644 ---- a/build/pkgs/pari/checksums.ini -+++ b/build/pkgs/pari/checksums.ini -@@ -1,5 +1,5 @@ - tarball=pari-VERSION.tar.gz --sha1=2b9ff51feb388664b834dc346a44867546c78618 --md5=fb2968d7805424518fe44a59a2024afd --cksum=1247903778 -+sha1=40731c850cc50fb4994148fac49fda4f68ce6106 -+md5=826064cf75af268be8a482ade6e27501 -+cksum=550849474 - 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 25cce6b355..94f15e9cc3 100644 ---- a/build/pkgs/pari/package-version.txt -+++ b/build/pkgs/pari/package-version.txt -@@ -1 +1 @@ --2.11.4.p1 -+2.13.1 -diff --git a/build/pkgs/pari/patches/pari-rnfdisc.patch b/build/pkgs/pari/patches/pari-rnfdisc.patch -new file mode 100644 -index 0000000000..39d325911e ---- /dev/null -+++ b/build/pkgs/pari/patches/pari-rnfdisc.patch -@@ -0,0 +1,35 @@ -+From 3edb98db78dd49bb8b4137b46781a7cd570c2556 Mon Sep 17 00:00:00 2001 -+From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> -+Date: Sun, 28 Mar 2021 13:27:24 +0200 -+Subject: [PATCH] rnfdisc_factored: remove spurious Q_primpart [#2284] -+ -+diff --git a/src/basemath/base2.c b/src/basemath/base2.c -+index b2b63ada5..531f5c558 100644 -+--- a/src/basemath/base2.c -++++ b/src/basemath/base2.c -+@@ -3582,7 +3582,7 @@ rnfdisc_factored(GEN nf, GEN pol, GEN *pd) -+ -+ nf = checknf(nf); -+ pol = rnfdisc_get_T(nf, pol, &lim); -+- disc = nf_to_scalar_or_basis(nf, nfX_disc(nf, Q_primpart(pol))); -++ disc = nf_to_scalar_or_basis(nf, nfX_disc(nf, pol)); -+ pol = nfX_to_monic(nf, pol, NULL); -+ fa = idealfactor_partial(nf, disc, lim); -+ P = gel(fa,1); l = lg(P); -+diff --git a/src/test/32/rnf b/src/test/32/rnf -+index 6bd4585..d24e1ce 100644 (file) -+--- a/src/test/32/rnf -++++ b/src/test/32/rnf -+@@ -832,9 +832,9 @@ error("inconsistent dimensions in idealtwoelt.") -+ 0 -+ 0 -+ 1 -+-[[7361, 3786, 318, 5823; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [-3, 6, -2, 0] -+-~] -+-[2, -1] -++[[433, 322, 318, 1318/17; 0, 1, 0, 12/17; 0, 0, 1, 5/17; 0, 0, 0, 1/17], [25 -++/17, -12/17, 12/17, 16/17]~] -++[1, -1] -+ *** at top-level: rnfdedekind(nf,P,pr2,1) -+ *** ^----------------------- -+ *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented. -diff --git a/build/pkgs/pari/patches/prot_none_cygwin.patch b/build/pkgs/pari/patches/prot_none_cygwin.patch -index 5cb7438b14..16340dd492 100644 ---- a/build/pkgs/pari/patches/prot_none_cygwin.patch -+++ b/build/pkgs/pari/patches/prot_none_cygwin.patch -@@ -3,10 +3,10 @@ Fix pari_mainstack_mreset() on Cygwin - Rejected upstream because Cygwin is considered a dead platform - - diff --git a/src/language/init.c b/src/language/init.c --index 2d13684..6ea2888 100644 -+index 8473a3b..d9993cc 100644 - --- a/src/language/init.c - +++ b/src/language/init.c --@@ -653,8 +653,8 @@ pari_mainstack_mfree(void *s, size_t size) -+@@ -884,8 +884,8 @@ pari_mainstack_mfree(void *s, size_t size) - /* Completely discard the memory mapped between the addresses "from" - * and "to" (which must be page-aligned). - * -@@ -17,7 +17,7 @@ index 2d13684..6ea2888 100644 - * still keep the mapping such that we can change the flags to - * PROT_READ|PROT_WRITE later. - * --@@ -662,7 +662,12 @@ pari_mainstack_mfree(void *s, size_t size) -+@@ -893,7 +893,12 @@ pari_mainstack_mfree(void *s, size_t size) - * calling mprotect(..., PROT_NONE) because the latter will keep the - * memory committed (this is in particular relevant on Linux with - * vm.overcommit = 2). This remains true even when calling -@@ -31,15 +31,17 @@ index 2d13684..6ea2888 100644 - static void - pari_mainstack_mreset(pari_sp from, pari_sp to) - { --@@ -671,9 +676,13 @@ pari_mainstack_mreset(pari_sp from, pari_sp to) -+@@ -902,11 +907,15 @@ pari_mainstack_mreset(pari_sp from, pari_sp to) - if (!s) return; - - addr = (void*)from; - +#ifdef __CYGWIN__ - + if (mprotect(addr, s, PROT_NONE)) pari_err(e_MEM); - +#else -+ BLOCK_SIGINT_START; - res = mmap(addr, s, PROT_NONE, - MAP_FIXED|MAP_PRIVATE|MAP_ANONYMOUS|MAP_NORESERVE, -1, 0); -+ BLOCK_SIGINT_END; - if (res != addr) pari_err(e_MEM); - +#endif - } -diff --git a/build/pkgs/pari/spkg-configure.m4 b/build/pkgs/pari/spkg-configure.m4 -index 9a1b0c7db8..d0fbb8f073 100644 ---- a/build/pkgs/pari/spkg-configure.m4 -+++ b/build/pkgs/pari/spkg-configure.m4 -@@ -1,6 +1,6 @@ - SAGE_SPKG_CONFIGURE([pari], [ - dnl See gp_version below on how the version is computed from MAJV.MINV.PATCHV -- m4_pushdef([SAGE_PARI_MINVER],["133889"]) -+ m4_pushdef([SAGE_PARI_MINVER],["134401"]) - SAGE_SPKG_DEPCHECK([gmp mpir readline], [ - AC_PATH_PROG([GP], [gp]) - if test x$GP = x; then dnl GP test -@@ -66,33 +66,11 @@ SAGE_SPKG_CONFIGURE([pari], [ - AC_MSG_NOTICE([Otherwise Sage will build its own pari/GP.]) - sage_spkg_install_pari=yes - fi -- AC_MSG_CHECKING([whether hyperellcharpoly bug is fixed]) -- bug_check=`echo "hyperellcharpoly(Mod(1,3)*(x^10 + x^9 + x^8 + x))" | $GP -qf 2>> config.log` -- expected="x^8 + 2*x^7 + 6*x^6 + 9*x^5 + 18*x^4 + 27*x^3 + 54*x^2 + 54*x + 81" -+ AC_MSG_CHECKING([whether rnfdisc bug of pari 2.13.1 is fixed]) -+ bug_check=`echo "K = nfinit(y^4-10*y^2+1); disc = rnfdisc(K,x^2-(y^3/2+y^2-5*y/2+1)); idealnorm(K,disc)" | $GP -qf 2>> config.log` -+ expected="2304" - if test x"$bug_check" = x"$expected"; then -- AC_MSG_RESULT([yes]) -- else -- AC_MSG_RESULT([no; cannot use system pari/GP with known bug]) -- AC_MSG_NOTICE([Upgrade your system package and reconfigure.]) -- AC_MSG_NOTICE([Otherwise Sage will build its own pari/GP.]) -- sage_spkg_install_pari=yes -- fi -- AC_MSG_CHECKING([whether bnfisunit bug of pari 2.11.3 is fixed]) -- bug_check=`echo "bnf = bnfinit(y^4-y-1); bnfisunit(bnf,-y^3+2*y^2-1)" | $GP -qf 2>> config.log` -- expected="[[0, 2, Mod(0, 2)]]~" -- if test x"$bug_check" = x"$expected"; then -- AC_MSG_RESULT([yes]) -- else -- AC_MSG_RESULT([no; cannot use system pari/GP with known bug]) -- AC_MSG_NOTICE([Upgrade your system package and reconfigure.]) -- AC_MSG_NOTICE([Otherwise Sage will build its own pari/GP.]) -- sage_spkg_install_pari=yes -- fi -- AC_MSG_CHECKING([whether qfisom bug of pari 2.11.2 is fixed]) -- bug_check=`echo "qfisom([[16,6;6,10]],[[4,3;3,10]])" | $GP -qf 2>> config.log` -- expected="0" -- if test x"$bug_check" = x"$expected"; then -- AC_MSG_RESULT([yes]) -+ AC_MSG_RESULT([yes]) - else - AC_MSG_RESULT([no; cannot use system pari/GP with known bug]) - AC_MSG_NOTICE([Upgrade your system package and reconfigure.]) -diff --git a/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst b/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst -index e1ed2b11f7..4832272f1c 100644 ---- a/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst -+++ b/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst -@@ -305,7 +305,7 @@ ideal classes containing :math:`(5,\sqrt{-30})` and - sage: category(C) - Category of finite enumerated commutative groups - sage: C.gens() -- (Fractional ideal class (2, a), Fractional ideal class (3, a)) -+ (Fractional ideal class (5, a), Fractional ideal class (3, a)) - - - Arithmetic in the class group -@@ -322,17 +322,17 @@ means "the product of the 0th and 1st generators of the class group - sage: K.<a> = QuadraticField(-30) - sage: C = K.class_group() - sage: C.0 -- Fractional ideal class (2, a) -+ Fractional ideal class (5, a) - sage: C.0.ideal() -- Fractional ideal (2, a) -+ Fractional ideal (5, a) - sage: I = C.0 * C.1 - sage: I -- Fractional ideal class (5, a) -+ Fractional ideal class (2, a) - - - Next we find that the class of the fractional ideal - :math:`(2,\sqrt{-30}+4/3)` is equal to the ideal class --:math:`C.0`. -+:math:`C.0*C.1`. - - .. link - -@@ -342,7 +342,7 @@ Next we find that the class of the fractional ideal - sage: J = C(A) - sage: J - Fractional ideal class (2/3, 1/3*a) -- sage: J == C.0 -+ sage: J == C.0*C.1 - True - - -diff --git a/src/doc/en/thematic_tutorials/sandpile.rst b/src/doc/en/thematic_tutorials/sandpile.rst -index 75ac904ec5..7dd7091415 100644 ---- a/src/doc/en/thematic_tutorials/sandpile.rst -+++ b/src/doc/en/thematic_tutorials/sandpile.rst -@@ -324,9 +324,9 @@ sink. - [1, 1, 3] - sage: S.reduced_laplacian().dense_matrix().smith_form() - ( -- [1 0 0] [ 0 0 1] [3 1 4] -- [0 1 0] [ 1 0 0] [4 1 6] -- [0 0 3], [ 0 1 -1], [4 1 5] -+ [1 0 0] [ 1 0 0] [1 3 5] -+ [0 1 0] [ 0 1 0] [1 4 6] -+ [0 0 3], [ 0 -1 1], [1 4 7] - ) - - Adding the identity to any recurrent configuration and stabilizing yields -@@ -687,7 +687,7 @@ Approximation to the zero set (setting ``x_0 = 1``):: - The zeros are generated as a group by a single vector:: - - sage: S.points() -- [[(1/2*I + 1/2)*sqrt(2), -(1/2*I + 1/2)*sqrt(2)]] -+ [[-(1/2*I + 1/2)*sqrt(2), (1/2*I + 1/2)*sqrt(2)]] - - - Resolutions -@@ -1384,12 +1384,12 @@ EXAMPLES:: - - sage: s = sandpiles.Cycle(5) - sage: s.group_gens() -- [{1: 1, 2: 1, 3: 1, 4: 0}] -+ [{1: 0, 2: 1, 3: 1, 4: 1}] - sage: s.group_gens()[0].order() - 5 - sage: s = sandpiles.Complete(5) - sage: s.group_gens(False) -- [[2, 2, 3, 2], [2, 3, 2, 2], [3, 2, 2, 2]] -+ [[2, 3, 2, 2], [2, 2, 3, 2], [2, 2, 2, 3]] - sage: [i.order() for i in s.group_gens()] - [5, 5, 5] - sage: s.invariant_factors() -@@ -2058,7 +2058,7 @@ single generator for the group of solutions. - - sage: S = sandpiles.Complete(4) - sage: S.points() -- [[1, I, -I], [I, 1, -I]] -+ [[-I, I, 1], [-I, 1, I]] - - --- - -@@ -4257,7 +4257,7 @@ EXAMPLES:: - sage: D.is_linearly_equivalent([0,1,1]) - True - sage: D.is_linearly_equivalent([0,1,1],True) -- (1, 0, 0) -+ (0, -1, -1) - sage: v = vector(D.is_linearly_equivalent([0,1,1],True)) - sage: vector(D.values()) - s.laplacian()*v - (0, 1, 1) -@@ -4983,8 +4983,8 @@ Other - - sage: P = matrix([[2,3,-7,-3],[5,2,-5,5],[8,2,5,4],[-5,-9,6,6]]) - sage: wilmes_algorithm(P) -- [ 1642 -13 -1627 -1] -- [ -1 1980 -1582 -397] -+ [ 3279 -79 -1599 -1600] -+ [ -1 1539 -136 -1402] - [ 0 -1 1650 -1649] - [ 0 0 -1658 1658] - -diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py -index b0861d9b20..a2096367ec 100644 ---- a/src/sage/arith/misc.py -+++ b/src/sage/arith/misc.py -@@ -1458,13 +1458,13 @@ def divisors(n): - - sage: K.<a> = QuadraticField(7) - sage: divisors(K.ideal(7)) -- [Fractional ideal (1), Fractional ideal (a), Fractional ideal (7)] -+ [Fractional ideal (1), Fractional ideal (-a), Fractional ideal (7)] - sage: divisors(K.ideal(3)) - [Fractional ideal (1), Fractional ideal (3), - Fractional ideal (-a + 2), Fractional ideal (-a - 2)] - sage: divisors(K.ideal(35)) -- [Fractional ideal (1), Fractional ideal (5), Fractional ideal (a), -- Fractional ideal (7), Fractional ideal (5*a), Fractional ideal (35)] -+ [Fractional ideal (1), Fractional ideal (5), Fractional ideal (-a), -+ Fractional ideal (7), Fractional ideal (-5*a), Fractional ideal (35)] - - TESTS:: - -diff --git a/src/sage/ext_data/pari/simon/ell.gp b/src/sage/ext_data/pari/simon/ell.gp -index 74f0786646..21cff9cbb3 100644 ---- a/src/sage/ext_data/pari/simon/ell.gp -+++ b/src/sage/ext_data/pari/simon/ell.gp -@@ -1038,7 +1038,7 @@ if( DEBUGLEVEL_ell >= 1, print(" trivial points on E(K) = "); - KS2gen = KS2gen[1]; - for( i = 1, #KS2gen, - KS2gen[i] = nfbasistoalg(bnf, KS2gen[i])); -- KS2gen = concat(Mod(lift(bnf.tufu),bnf.pol),KS2gen); -+ KS2gen = concat(Mod(lift(concat(bnf.tu[2], bnf.fu)),bnf.pol),KS2gen); - if( DEBUGLEVEL_ell >= 2, - print(" #K(b,2)gen = ",#KS2gen); - print(" K(b,2)gen = ",KS2gen)); -@@ -1072,7 +1072,7 @@ if( DEBUGLEVEL_ell >= 1, - KS2gen = KS2gen[1]; - for( i = 1, #KS2gen, - KS2gen[i] = nfbasistoalg(bnf, KS2gen[i])); -- KS2gen = concat(Mod(lift(bnf.tufu),bnf.pol),KS2gen); -+ KS2gen = concat(Mod(lift(concat(bnf.tu[2], bnf.fu)),bnf.pol),KS2gen); - if( DEBUGLEVEL_ell >= 2, - print(" #K(a^2-4b,2)gen = ",#KS2gen); - print(" K(a^2-4b,2)gen = ",KS2gen)); -@@ -1244,11 +1244,11 @@ if( DEBUGLEVEL_ell >= 4, print(" bbbnf.clgp = ",bbbnf.clgp)); - SL1 = idealmul(bbbnf,SL0,rnfeltup(rrrnf,bleg)); - SL = idealfactor(bbbnf,SL1)[,1]~; - sunL = bnfsunit(bbbnf,SL); -- fondsunL = concat(bbbnf.futu,vector(#sunL[1],i,nfbasistoalg(bbbnf,sunL[1][i]))); -+ fondsunL = concat(concat(bbbnf.fu, bbbnf.tu[2]),vector(#sunL[1],i,nfbasistoalg(bbbnf,sunL[1][i]))); - normfondsunL = vector(#fondsunL, i, norm(rnfeltabstorel(rrrnf,fondsunL[i]))); - SK = idealfactor(bnf,idealnorm(bbbnf,SL1))[,1]~; - sunK = bnfsunit(bnf,SK); -- fondsunK = concat(bnf.futu,vector(#sunK[1],i,nfbasistoalg(bnf,sunK[1][i]))); -+ fondsunK = concat(concat(bnf.fu, bnf.tu[2]),vector(#sunK[1],i,nfbasistoalg(bnf,sunK[1][i]))); - vecbleg = bnfissunit(bnf,sunK,bleg); - matnorm = matrix(#fondsunK,#normfondsunL,i,j,0); - for( i = 1, #normfondsunL, -@@ -1345,7 +1345,7 @@ if( DEBUGLEVEL_ell >= 4, print("on factorise bb = ",bb)); - sun = bnfsunit(bnf,idealfactor(bnf,bb)[,1]~); - fact = lift(bnfissunit(bnf,sun,bb)); - if( DEBUGLEVEL_ell >= 4, print("fact = ",fact)); -- suni = concat(bnf.futu,vector(#sun[1],i,nfbasistoalg(bnf,sun[1][i]))); -+ suni = concat(concat(bnf.fu, bnf.tu[2]),vector(#sun[1],i,nfbasistoalg(bnf,sun[1][i]))); - for( i = 1, #suni, - if( (f = fact[i]>>1), - test =0; -@@ -1554,7 +1554,7 @@ if( DEBUGLEVEL_ell >= 3, print(" KS2gen = ",KS2gen[1])); - - LS2gen = LS2gen[1]; - LS2 = vector(#LS2gen,i,lift(nfbasistoalg(Lrnf,LS2gen[i]))); -- LS2 = concat(lift(Lrnf.futu),LS2); -+ LS2 = concat(lift(concat(Lrnf.fu, Lrnf.tu[2])),LS2); - - LS2 = subst(LS2,'x,ttheta); - LS2 = LS2*Mod(1,polrel); -@@ -1992,7 +1992,7 @@ if( DEBUGLEVEL_ell >= 2, print(" Algorithm of complete 2-descent")); - KS2gen = KS2gen[1]; - for( i = 1, #KS2gen, - KS2gen[i] = nfbasistoalg(bnf, KS2gen[i])); -- KS2gen = concat(Mod(lift(bnf.tufu),bnf.pol),KS2gen); -+ KS2gen = concat(Mod(lift(concat(bnf.tu[2], bnf.fu)),bnf.pol),KS2gen); - if( DEBUGLEVEL_ell >= 2, - print(" #K(S,2)gen = ",#KS2gen); - print(" K(S,2)gen = ",KS2gen) -diff --git a/src/sage/ext_data/pari/simon/ellQ.gp b/src/sage/ext_data/pari/simon/ellQ.gp -index 1cfe6318f8..420af8f6a2 100644 ---- a/src/sage/ext_data/pari/simon/ellQ.gp -+++ b/src/sage/ext_data/pari/simon/ellQ.gp -@@ -1162,7 +1162,7 @@ if( DEBUGLEVEL_ell >= 4, print(" kerval = ",kerval)); - LS2gen[j]^kerval[j,i])); - - \\ Add the units -- LS2gen = concat(Mod(bnf[8][5],bnf.pol),LS2gen); \\ LS2gen = concat(bnf.fu,LS2gen); -+ LS2gen = concat(bnf.fu,LS2gen); \\ LS2gen = concat(bnf.fu,LS2gen); - \\ Add also the torsion unit if its order is divisible by p. - if( bnf[8][4][1]%p == 0, \\ if( bnf.tu[1]%p == 0, - LS2gen = concat( [Mod(bnf[8][4][2],bnf.pol)], LS2gen)); \\ LS2gen = concat( [Mod(bnf.tu[2],bnf.pol)], LS2gen)); -diff --git a/src/sage/geometry/cone.py b/src/sage/geometry/cone.py -index 79c75ad784..5b2326a8e7 100644 ---- a/src/sage/geometry/cone.py -+++ b/src/sage/geometry/cone.py -@@ -3504,8 +3504,8 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - - sage: K = Cone([(1,0,0), (0,1,0)]) - sage: K.solid_restriction().rays() -- N(1, 0), -- N(0, 1) -+ N(0, 1), -+ N(1, 0) - in 2-d lattice N - - The solid restriction of a single ray has the same -@@ -3624,7 +3624,7 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - sage: C2_Z2 = Cone([(1,0),(1,2)]) - sage: C2_Z2._split_ambient_lattice() - sage: C2_Z2._sublattice -- Sublattice <N(1, 2), N(0, -1)> -+ Sublattice <N(1, 0), N(0, 1)> - - Trivial cone:: - -@@ -3695,9 +3695,9 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - sage: cone.rays().basis().matrix().det() - -4 - sage: cone.sublattice() -- Sublattice <N(-1, -1, 1), N(1, 0, 0), N(1, 1, 0)> -+ Sublattice <N(1, 1, 1), N(0, -1, 0), N(-1, -1, 0)> - sage: matrix( cone.sublattice().gens() ).det() -- 1 -+ -1 - - Another example:: - -@@ -3709,7 +3709,7 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - N(4, -5, 1) - in 3-d lattice N - sage: c.sublattice() -- Sublattice <N(1, 2, 3), N(4, -5, 1)> -+ Sublattice <N(4, -5, 1), N(1, 2, 3)> - sage: c.sublattice(5, -3, 4) - N(5, -3, 4) - sage: c.sublattice(1, 0, 0) -@@ -3805,14 +3805,14 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - - sage: c = Cone([(1,2,3), (4,-5,1)]) - sage: c.sublattice() -- Sublattice <N(1, 2, 3), N(4, -5, 1)> -+ Sublattice <N(4, -5, 1), N(1, 2, 3)> - sage: c.sublattice_complement() -- Sublattice <N(0, -6, -5)> -+ Sublattice <N(2, -3, 0)> - sage: m = matrix( c.sublattice().gens() + c.sublattice_complement().gens() ) - sage: m -- [ 1 2 3] - [ 4 -5 1] -- [ 0 -6 -5] -+ [ 1 2 3] -+ [ 2 -3 0] - sage: m.det() - -1 - """ -@@ -3856,7 +3856,7 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - Sublattice <> - sage: c12 = Cone([(1,1,1), (1,-1,1)]) - sage: c12.sublattice() -- Sublattice <N(1, -1, 1), N(0, 1, 0)> -+ Sublattice <N(1, 1, 1), N(0, -1, 0)> - sage: c12.orthogonal_sublattice() - Sublattice <M(1, 0, -1)> - -@@ -3922,15 +3922,15 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - sage: sigma = Cone([(1,1,1,3),(1,-1,1,3),(-1,-1,1,3),(-1,1,1,3)]) - sage: rho = Cone([(-1, -1, 1, 3), (-1, 1, 1, 3)]) - sage: sigma.sublattice() -- Sublattice <N(-1, -1, 1, 3), N(1, 0, 0, 0), N(1, 1, 0, 0)> -+ Sublattice <N(1, 1, 1, 3), N(0, -1, 0, 0), N(-1, -1, 0, 0)> - sage: rho.sublattice() -- Sublattice <N(-1, 1, 1, 3), N(0, -1, 0, 0)> -+ Sublattice <N(-1, -1, 1, 3), N(0, 1, 0, 0)> - sage: sigma.relative_quotient(rho) - 1-d lattice, quotient -- of Sublattice <N(-1, -1, 1, 3), N(1, 0, 0, 0), N(1, 1, 0, 0)> -+ of Sublattice <N(1, 1, 1, 3), N(0, -1, 0, 0), N(-1, -1, 0, 0)> - by Sublattice <N(1, 0, -1, -3), N(0, 1, 0, 0)> - sage: sigma.relative_quotient(rho).gens() -- (N[1, 1, 0, 0],) -+ (N[1, 0, 0, 0],) - - More complicated example:: - -@@ -3938,12 +3938,12 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - sage: sigma = Cone([(1, 2, 3), (1, -1, 1), (-1, 1, 1), (-1, -1, 1)]) - sage: N_sigma = sigma.sublattice() - sage: N_sigma -- Sublattice <N(-1, 1, 1), N(1, 2, 3), N(0, 1, 1)> -+ Sublattice <N(1, 2, 3), N(1, -1, 1), N(-1, -1, -2)> - sage: N_rho = rho.sublattice() - sage: N_rho - Sublattice <N(1, -1, 1), N(1, 2, 3)> - sage: sigma.relative_quotient(rho).gens() -- (N[0, 1, 1],) -+ (N[-1, -1, -2],) - sage: N = rho.lattice() - sage: N_sigma == N.span(N_rho.gens() + tuple(q.lift() - ....: for q in sigma.relative_quotient(rho).gens())) -@@ -3958,12 +3958,12 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - Sublattice <N(1, -1, 1), N(1, 2, 3)> - sage: sigma1.relative_quotient(rho) - 1-d lattice, quotient -- of Sublattice <N(-1, 1, 1), N(1, 2, 3), N(0, 1, 1)> -+ of Sublattice <N(1, 2, 3), N(1, -1, 1), N(-1, -1, -2)> - by Sublattice <N(1, 2, 3), N(0, 3, 2)> - sage: sigma1.relative_quotient(rho).gens() -- (N[0, 1, 1],) -+ (N[-1, -1, -2],) - sage: sigma2.relative_quotient(rho).gens() -- (N[-1, 0, -2],) -+ (N[0, 2, 1],) - """ - try: - cached_values = self._relative_quotient -@@ -4263,9 +4263,9 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - sage: Cone([[1,0],[3,4]]).dual().Hilbert_basis() - M(0, 1), - M(4, -3), -- M(3, -2), -+ M(1, 0), - M(2, -1), -- M(1, 0) -+ M(3, -2) - in 2-d lattice M - sage: cone = Cone([[1,2,3,4],[0,1,0,7],[3,1,0,2],[0,0,1,0]]).dual() - sage: cone.Hilbert_basis() # long time -@@ -4275,16 +4275,16 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - M(15, -63, 25, 9), - M( 2, -3, 0, 1), - M( 1, -4, 1, 1), -- M(-1, 3, 0, 0), - M( 4, -4, 0, 1), -+ M(-1, 3, 0, 0), - M( 1, -5, 2, 1), - M( 3, -5, 1, 1), - M( 6, -5, 0, 1), - M( 3, -13, 5, 2), - M( 2, -6, 2, 1), - M( 5, -6, 1, 1), -- M( 0, 1, 0, 0), - M( 8, -6, 0, 1), -+ M( 0, 1, 0, 0), - M(-2, 8, 0, -1), - M(10, -42, 17, 6), - M( 7, -28, 11, 4), -@@ -4295,9 +4295,9 @@ class ConvexRationalPolyhedralCone(IntegralRayCollection, Container): - M( 4, -7, 2, 1), - M( 7, -7, 1, 1), - M( 0, 0, 1, 0), -- M(-3, 14, 0, -2), -+ M( 1, 0, 0, 0), - M(-1, 7, 0, -1), -- M( 1, 0, 0, 0) -+ M(-3, 14, 0, -2) - in 4-d lattice M - - Not a strictly convex cone:: -diff --git a/src/sage/geometry/fan.py b/src/sage/geometry/fan.py -index 4a28419762..df4c8174f4 100644 ---- a/src/sage/geometry/fan.py -+++ b/src/sage/geometry/fan.py -@@ -3087,8 +3087,8 @@ class RationalPolyhedralFan(IntegralRayCollection, Callable, Container): - - sage: f = Fan([Cone([(1,0,1,0), (0,1,1,0)])]) - sage: f.virtual_rays() -- N(0, 0, 0, 1), -- N(0, 0, 1, 0) -+ N(1, 0, 0, 0), -+ N(0, 0, 0, 1) - in 4-d lattice N - - sage: f.rays() -@@ -3097,14 +3097,14 @@ class RationalPolyhedralFan(IntegralRayCollection, Callable, Container): - in 4-d lattice N - - sage: f.virtual_rays([0]) -- N(0, 0, 0, 1) -+ N(1, 0, 0, 0) - in 4-d lattice N - - You can also give virtual ray indices directly, without - packing them into a list:: - - sage: f.virtual_rays(0) -- N(0, 0, 0, 1) -+ N(1, 0, 0, 0) - in 4-d lattice N - - Make sure that :trac:`16344` is fixed and one can compute -diff --git a/src/sage/geometry/fan_isomorphism.py b/src/sage/geometry/fan_isomorphism.py -index 04732ab0c2..18a6c9b199 100644 ---- a/src/sage/geometry/fan_isomorphism.py -+++ b/src/sage/geometry/fan_isomorphism.py -@@ -96,9 +96,9 @@ def fan_isomorphism_generator(fan1, fan2): - ....: Cone([m2*vector([-1,-14]), m2*vector([-100, -5])])]) - sage: sorted(fan_isomorphism_generator(fan1, fan2)) - [ -- [18 1 -5] -- [ 4 0 -1] -- [ 5 0 -1] -+ [-12 1 -5] -+ [ -4 0 -1] -+ [ -5 0 -1] - ] - - sage: m0 = identity_matrix(ZZ, 2) -@@ -125,15 +125,15 @@ def fan_isomorphism_generator(fan1, fan2): - ] - sage: sorted(fan_isomorphism_generator(fan1, fan2)) - [ -- [ 6 -3 7] [18 1 -5] -- [ 1 -1 2] [ 4 0 -1] -- [ 2 -1 2], [ 5 0 -1] -+ [-24 -3 7] [-12 1 -5] -+ [ -7 -1 2] [ -4 0 -1] -+ [ -8 -1 2], [ -5 0 -1] - ] - sage: sorted(fan_isomorphism_generator(fan2, fan1)) - [ -- [ 0 -1 1] [ 0 -1 1] -- [ 1 -7 2] [ 2 -2 -5] -- [ 0 -5 4], [ 1 0 -3] -+ [ 0 1 -1] [ 0 1 -1] -+ [ 1 -13 8] [ 2 -8 1] -+ [ 0 -5 4], [ 1 0 -3] - ] - """ - if not fan_isomorphic_necessary_conditions(fan1, fan2): -diff --git a/src/sage/geometry/integral_points.pyx b/src/sage/geometry/integral_points.pyx -index 765b0a5bb5..37e1d23339 100644 ---- a/src/sage/geometry/integral_points.pyx -+++ b/src/sage/geometry/integral_points.pyx -@@ -108,13 +108,13 @@ cpdef tuple parallelotope_points(spanning_points, lattice): - sage: from sage.geometry.integral_points import parallelotope_points - sage: rays = list(map(vector, [(2,0), (0,2)])) - sage: parallelotope_points(rays, ZZ^2) -- ((0, 0), (1, 0), (0, 1), (1, 1)) -+ ((0, 0), (0, 1), (1, 0), (1, 1)) - - The rays can also be toric lattice points:: - - sage: rays = list(map(ToricLattice(2), [(2,0), (0,2)])) - sage: parallelotope_points(rays, ToricLattice(2)) -- (N(0, 0), N(1, 0), N(0, 1), N(1, 1)) -+ (N(0, 0), N(0, 1), N(1, 0), N(1, 1)) - - A non-smooth cone:: - -diff --git a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py -index 4236419276..5bf4d59b14 100644 ---- a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py -+++ b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py -@@ -863,7 +863,7 @@ class LatticePolytope_PPL_class(C_Polyhedron): - sage: proj = poly.base_projection(fiber) - sage: proj_matrix = poly.base_projection_matrix(fiber) - sage: [ proj(p) for p in poly.integral_points() ] -- [(-1, -1), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (1, 0), (0, 1)] -+ [(-1, -1), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 1), (1, 0)] - sage: [ proj_matrix*p for p in poly.integral_points() ] - [(-1, -1), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 0), (0, 1), (1, 0)] - """ -diff --git a/src/sage/geometry/toric_lattice.py b/src/sage/geometry/toric_lattice.py -index 4444d662be..4d8ef3fba6 100644 ---- a/src/sage/geometry/toric_lattice.py -+++ b/src/sage/geometry/toric_lattice.py -@@ -425,7 +425,7 @@ class ToricLattice_generic(FreeModule_generic_pid): - sage: N3 = ToricLattice(3, 'N3') - sage: Q = N3 / N3.span([ N3(1,2,3) ]) - sage: Q.an_element() -- N3[0, 0, 1] -+ N3[1, 0, 0] - sage: N2 = ToricLattice(2, 'N2') - sage: N2( Q.an_element() ) - N2(1, 0) -@@ -1297,9 +1297,9 @@ class ToricLattice_quotient_element(FGP_Element): - sage: e == e2 - True - sage: e.vector() -- (4) -+ (-4) - sage: e2.vector() -- (4) -+ (-4) - """ - - def _latex_(self): -@@ -1407,7 +1407,7 @@ class ToricLattice_quotient(FGP_Module_class): - sage: Q - 1-d lattice, quotient of 3-d lattice N by Sublattice <N(1, 0, 1), N(0, 1, -1)> - sage: Q.gens() -- (N[0, 0, 1],) -+ (N[1, 0, 0],) - - Here, ``sublattice`` happens to be of codimension one in ``N``. If - you want to prescribe the sign of the quotient generator, you can -@@ -1416,15 +1416,15 @@ class ToricLattice_quotient(FGP_Module_class): - sage: Q = N.quotient(sublattice, positive_point=N(0,0,-1)); Q - 1-d lattice, quotient of 3-d lattice N by Sublattice <N(1, 0, 1), N(0, 1, -1)> - sage: Q.gens() -- (N[0, 0, -1],) -+ (N[1, 0, 0],) - - or:: - - sage: M = N.dual() -- sage: Q = N.quotient(sublattice, positive_dual_point=M(0,0,-1)); Q -+ sage: Q = N.quotient(sublattice, positive_dual_point=M(1,0,0)); Q - 1-d lattice, quotient of 3-d lattice N by Sublattice <N(1, 0, 1), N(0, 1, -1)> - sage: Q.gens() -- (N[0, 0, -1],) -+ (N[1, 0, 0],) - - TESTS:: - -diff --git a/src/sage/groups/abelian_gps/abelian_group.py b/src/sage/groups/abelian_gps/abelian_group.py -index 49e4192cc6..6567ac6c18 100644 ---- a/src/sage/groups/abelian_gps/abelian_group.py -+++ b/src/sage/groups/abelian_gps/abelian_group.py -@@ -1525,7 +1525,7 @@ class AbelianGroup_class(UniqueRepresentation, AbelianGroupBase): - generated by {f0, f0*f1^2} - sage: AbelianGroup([4,4]).subgroup_reduced( [ [1,0], [1,2] ]) - Multiplicative Abelian subgroup isomorphic to C2 x C4 -- generated by {f1^2, f0} -+ generated by {f0^2*f1^2, f0^3} - """ - from sage.matrix.constructor import matrix - d = self.ngens() -diff --git a/src/sage/groups/additive_abelian/additive_abelian_group.py b/src/sage/groups/additive_abelian/additive_abelian_group.py -index 3dcedeb7e3..2c76b75e0c 100644 ---- a/src/sage/groups/additive_abelian/additive_abelian_group.py -+++ b/src/sage/groups/additive_abelian/additive_abelian_group.py -@@ -43,7 +43,7 @@ def AdditiveAbelianGroup(invs, remember_generators = True): - sage: H = AdditiveAbelianGroup([0, 2, 3], remember_generators = False); H - Additive abelian group isomorphic to Z/6 + Z - sage: H.gens() -- ((0, 1, 2), (1, 0, 0)) -+ ((0, 1, 1), (1, 0, 0)) - - There are several ways to create elements of an additive abelian group. - Realize that there are two sets of generators: the "obvious" ones composed -diff --git a/src/sage/groups/fqf_orthogonal.py b/src/sage/groups/fqf_orthogonal.py -index 3c5190589b..ae9fc2fae2 100644 ---- a/src/sage/groups/fqf_orthogonal.py -+++ b/src/sage/groups/fqf_orthogonal.py -@@ -133,16 +133,16 @@ class FqfOrthogonalGroup(AbelianGroupAutomorphismGroup_subgroup): - sage: T - Finite quadratic module over Integer Ring with invariants (3, 3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0 0] -+ [2/3 0 0] - [ 0 2/3 0] -- [ 0 0 2/3] -+ [ 0 0 4/3] - sage: T.orthogonal_group() - Group of isometries of - Finite quadratic module over Integer Ring with invariants (3, 3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0 0] -+ [2/3 0 0] - [ 0 2/3 0] -- [ 0 0 2/3] -+ [ 0 0 4/3] - generated by 2 elements - sage: q = matrix.diagonal(QQ, [3/2, 1/4, 1/4]) - sage: T = TorsionQuadraticForm(q) -@@ -158,7 +158,7 @@ class FqfOrthogonalGroup(AbelianGroupAutomorphismGroup_subgroup): - sage: G = T.orthogonal_group() - sage: g = G(matrix(ZZ, 2, [8, 0, 0, 1])) - sage: Q.1 * g -- (0, 2) -+ (0, 1) - """ - Element = FqfIsometry - -@@ -225,8 +225,8 @@ class FqfOrthogonalGroup(AbelianGroupAutomorphismGroup_subgroup): - sage: f = OL(f) - sage: fbar = Oq(f) - sage: fbar -- [4 3] -- [3 1] -+ [1 3] -+ [3 4] - - Note that the following does not work since it may lead to ambiguities, see :trac:`30669`:: - -@@ -307,12 +307,12 @@ class FqfOrthogonalGroup(AbelianGroupAutomorphismGroup_subgroup): - Right action by Group of isometries of - Finite quadratic module over Integer Ring with invariants (3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0] -- [ 0 2/3] -+ [2/3 0] -+ [ 0 4/3] - generated by 2 elements on Finite quadratic module over Integer Ring with invariants (3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0] -- [ 0 2/3] -+ [2/3 0] -+ [ 0 4/3] - """ - import operator - if op == operator.mul and not self_on_left: -@@ -450,19 +450,19 @@ class ActionOnFqf(Action): - Right action by Group of isometries of - Finite quadratic module over Integer Ring with invariants (3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0] -- [ 0 2/3] -+ [2/3 0] -+ [ 0 4/3] - generated by 2 elements on Finite quadratic module over Integer Ring with invariants (3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0] -- [ 0 2/3] -+ [2/3 0] -+ [ 0 4/3] - sage: x = q.an_element() - sage: g = G.an_element() - sage: A(x, g).parent() - Finite quadratic module over Integer Ring with invariants (3, 3) - Gram matrix of the quadratic form with values in Q/2Z: -- [4/3 0] -- [ 0 2/3] -+ [2/3 0] -+ [ 0 4/3] - sage: q = TorsionQuadraticForm(matrix.diagonal([2/3, 2/3, 6/8, 1/4])) - sage: G = q.orthogonal_group() - sage: q2 = q.primary_part(2) -diff --git a/src/sage/homology/chain_complex.py b/src/sage/homology/chain_complex.py -index 49aaff1a85..47d14b4b9c 100644 ---- a/src/sage/homology/chain_complex.py -+++ b/src/sage/homology/chain_complex.py -@@ -1270,7 +1270,7 @@ class ChainComplex_class(Parent): - sage: C_k = ChainComplex({0:d0, 1:d1, 2:d2}, degree=-1) - sage: C_k.homology(generators=true, algorithm='no_chomp') - {0: [(Z, Chain(0:(1)))], -- 1: [(C2, Chain(1:(1, 0, 0))), (Z, Chain(1:(0, 0, 1)))], -+ 1: [(C2, Chain(1:(0, 1, -1))), (Z, Chain(1:(0, 1, 0)))], - 2: []} - - From a torus using a field:: -diff --git a/src/sage/homology/simplicial_complex.py b/src/sage/homology/simplicial_complex.py -index 8db479fd54..6c71bce482 100644 ---- a/src/sage/homology/simplicial_complex.py -+++ b/src/sage/homology/simplicial_complex.py -@@ -2305,7 +2305,7 @@ class SimplicialComplex(Parent, GenericCellComplex): - - sage: simplicial_complexes.Torus().homology(generators=True, algorithm='no_chomp') - {0: [], -- 1: [(Z, (1, 2) - (1, 6) + (2, 6)), (Z, (3, 4) - (3, 6) + (4, 6))], -+ 1: [(Z, (2, 4) - (2, 6) + (4, 6)), (Z, (1, 4) - (1, 6) + (4, 6))], - 2: [(Z, - (0, 1, 2) - (0, 1, 5) + (0, 2, 6) - (0, 3, 4) + (0, 3, 5) - (0, 4, 6) - (1, 2, 4) + (1, 3, 4) - (1, 3, 6) + (1, 5, 6) - (2, 3, 5) + (2, 3, 6) + (2, 4, 5) - (4, 5, 6))]} - """ -diff --git a/src/sage/lfunctions/pari.py b/src/sage/lfunctions/pari.py -index f810157b3e..f621b57c67 100644 ---- a/src/sage/lfunctions/pari.py -+++ b/src/sage/lfunctions/pari.py -@@ -421,7 +421,7 @@ class LFunction(SageObject): - sage: L.derivative(1,E.rank()) - 1.51863300057685 - sage: L.taylor_series(1,4) -- -3...e-19 + (...e-19)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) -+ ...e-19 + (...e-19)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) - - .. RUBRIC:: Number field - -diff --git a/src/sage/libs/pari/__init__.py b/src/sage/libs/pari/__init__.py -index 77eda66097..507b98c509 100644 ---- a/src/sage/libs/pari/__init__.py -+++ b/src/sage/libs/pari/__init__.py -@@ -161,12 +161,14 @@ exact object. Therefore, you should set the precision for each method - call individually:: - - sage: e = pari([0,0,0,-82,0]).ellinit() -- sage: eta1 = e.elleta(precision=100)[0] -+ sage: eta1 = e.elleta(precision=50)[0] - sage: eta1.sage() -- 3.6054636014326520859158205642077267748 -- sage: eta1 = e.elleta(precision=180)[0] -+ 3.6054636014326520859158205642077267748 # 64-bit -+ 3.605463601432652085915820564 # 32-bit -+ sage: eta1 = e.elleta(precision=150)[0] - sage: eta1.sage() -- 3.60546360143265208591582056420772677481026899659802474544 -+ 3.605463601432652085915820564207726774810268996598024745444380641429820491740 # 64-bit -+ 3.60546360143265208591582056420772677481026899659802474544 # 32-bit - - """ - -diff --git a/src/sage/libs/pari/tests.py b/src/sage/libs/pari/tests.py -index dd7f8e9bf8..f34b30146d 100644 ---- a/src/sage/libs/pari/tests.py -+++ b/src/sage/libs/pari/tests.py -@@ -135,7 +135,7 @@ Some more exotic examples:: - - sage: K.<a> = NumberField(polygen(QQ)^3 - 2) - sage: pari(K) -- [y^3 - 2, [1, 1], -108, 1, [[1, 1.25992104989487, 1.58740105196820; 1, -0.629960524947437 + 1.09112363597172*I, -0.793700525984100 - 1.37472963699860*I], [1, 1.25992104989487, 1.58740105196820; 1, 0.461163111024285, -2.16843016298270; 1, -1.72108416091916, 0.581029111014503], [1, 1, 2; 1, 0, -2; 1, -2, 1], [3, 0, 0; 0, 0, 6; 0, 6, 0], [6, 0, 0; 0, 6, 0; 0, 0, 3], [2, 0, 0; 0, 0, 1; 0, 1, 0], [2, [0, 0, 2; 1, 0, 0; 0, 1, 0]], []], [1.25992104989487, -0.629960524947437 + 1.09112363597172*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 2, 0, 2, 0; 0, 1, 0, 1, 0, 0, 0, 0, 2; 0, 0, 1, 0, 1, 0, 1, 0, 0]] -+ [y^3 - 2, [1, 1], -108, 1, [[1, 1.25992104989487, 1.58740105196820; 1, -0.629960524947437 + 1.09112363597172*I, -0.793700525984100 - 1.37472963699860*I], [1, 1.25992104989487, 1.58740105196820; 1, 0.461163111024285, -2.16843016298270; 1, -1.72108416091916, 0.581029111014503], [16, 20, 25; 16, 7, -35; 16, -28, 9], [3, 0, 0; 0, 0, 6; 0, 6, 0], [6, 0, 0; 0, 6, 0; 0, 0, 3], [2, 0, 0; 0, 0, 1; 0, 1, 0], [2, [0, 0, 2; 1, 0, 0; 0, 1, 0]], [2, 3]], [1.25992104989487, -0.629960524947437 + 1.09112363597172*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 2, 0, 2, 0; 0, 1, 0, 1, 0, 0, 0, 0, 2; 0, 0, 1, 0, 1, 0, 1, 0, 0]] - - sage: E = EllipticCurve('37a1') - sage: pari(E) -@@ -375,13 +375,13 @@ Constructors:: - sage: pari('["bc","ab","bc"]').Set() - ["ab", "bc"] - -- sage: pari([65,66,123]).Strchr() -+ sage: pari([65,66,123]).strchr() - "AB{" - sage: pari('"Sage"').Vecsmall() - Vecsmall([83, 97, 103, 101]) -- sage: _.Strchr() -+ sage: _.strchr() - "Sage" -- sage: pari([83, 97, 103, 101]).Strchr() -+ sage: pari([83, 97, 103, 101]).strchr() - "Sage" - - Basic functions:: -@@ -448,7 +448,7 @@ Basic functions:: - sage: pari('x').component(0) - Traceback (most recent call last): - ... -- PariError: non-existent component: index < 1 -+ PariError: nonexistent component: index < 1 - - sage: pari('x+1').conj() - x + 1 -@@ -767,7 +767,7 @@ Transcendental functions:: - sage: pari(2).besseli(3+i) - 1.12539407613913 + 2.08313822670661*I - sage: C.<i> = ComplexField() -- sage: pari(2+i).besseln(3) -+ sage: pari(2+i).bessely(3) - -0.280775566958244 - 0.486708533223726*I - - sage: pari(1.5).cos() -@@ -822,7 +822,7 @@ Transcendental functions:: - sage: pari(-1).gamma() - Traceback (most recent call last): - ... -- PariError: domain error in gamma: argument = non-positive integer -+ PariError: domain error in gamma: argument = nonpositive integer - - sage: pari(2).gammah() - 1.32934038817914 -@@ -1633,7 +1633,7 @@ General number fields:: - - sage: x = QQ['x'].0; nf = pari(x^2 + 2).nfinit() - sage: nf.nfgaloisconj() -- [x, -x]~ -+ [-x, x]~ - sage: nf = pari(x^3 + 2).nfinit() - sage: nf.nfgaloisconj() - [x]~ -@@ -1676,7 +1676,7 @@ General number fields:: - [[1, [7605, 4]~, [5610, 5]~, [7913, -6]~; 0, 1, 0, -1; 0, 0, 1, 0; 0, 0, 0, 1], [[19320, 13720; 0, 56], [2, 1; 0, 1], 1, 1]] - - sage: pari('x^3 - 17').nfinit() -- [x^3 - 17, [1, 1], -867, 3, [[1, 1.68006914259990, 2.57128159065824; 1, -0.340034571299952 - 2.65083754153991*I, -1.28564079532912 + 2.22679517779329*I], [1, 1.68006914259990, 2.57128159065824; 1, -2.99087211283986, 0.941154382464174; 1, 2.31080297023995, -3.51243597312241], [1, 2, 3; 1, -3, 1; 1, 2, -4], [3, 1, 0; 1, -11, 17; 0, 17, 0], [51, 0, 16; 0, 17, 3; 0, 0, 1], [17, 0, -1; 0, 0, 3; -1, 3, 2], [51, [-17, 6, -1; 0, -18, 3; 1, 0, -16]], [3, 17]], [2.57128159065824, -1.28564079532912 + 2.22679517779329*I], [3, x^2 - x + 1, 3*x], [1, 0, -1; 0, 0, 3; 0, 1, 1], [1, 0, 0, 0, -4, 6, 0, 6, -1; 0, 1, 0, 1, 1, -1, 0, -1, 3; 0, 0, 1, 0, 2, 0, 1, 0, 1]] -+ [x^3 - 17, [1, 1], -867, 3, [[1, 1.68006914259990, 2.57128159065824; 1, -0.340034571299952 - 2.65083754153991*I, -1.28564079532912 + 2.22679517779329*I], [1, 1.68006914259990, 2.57128159065824; 1, -2.99087211283986, 0.941154382464174; 1, 2.31080297023995, -3.51243597312241], [16, 27, 41; 16, -48, 15; 16, 37, -56], [3, 1, 0; 1, -11, 17; 0, 17, 0], [51, 0, 16; 0, 17, 3; 0, 0, 1], [17, 0, -1; 0, 0, 3; -1, 3, 2], [51, [-17, 6, -1; 0, -18, 3; 1, 0, -16]], [3, 17]], [2.57128159065824, -1.28564079532912 + 2.22679517779329*I], [3, x^2 - x + 1, 3*x], [1, 0, -1; 0, 0, 3; 0, 1, 1], [1, 0, 0, 0, -4, 6, 0, 6, -1; 0, 1, 0, 1, 1, -1, 0, -1, 3; 0, 0, 1, 0, 2, 0, 1, 0, 1]] - sage: pari('x^2 + 10^100 + 1').nfinit() - [...] - sage: pari('1.0').nfinit() -@@ -1737,7 +1737,7 @@ General number fields:: - sage: pari(-23).quadhilbert() - x^3 - x^2 + 1 - sage: pari(145).quadhilbert() -- x^4 - 6*x^2 - 5*x - 1 -+ x^4 - x^3 - 5*x^2 - x + 1 - sage: pari(-12).quadhilbert() # Not fundamental - Traceback (most recent call last): - ... -@@ -1760,13 +1760,14 @@ These are some doctests that used to be part of Sage and were removed from the c - library:: - - sage: e = pari([0,0,0,-82,0]).ellinit() -- sage: eta1 = e.elleta(precision=100)[0] -+ sage: eta1 = e.elleta(precision=50)[0] - sage: eta1.sage() -- 3.6054636014326520859158205642077267748 -- sage: eta1 = e.elleta(precision=180)[0] -+ 3.6054636014326520859158205642077267748 # 64-bit -+ 3.605463601432652085915820564 # 32-bit -+ sage: eta1 = e.elleta(precision=150)[0] - sage: eta1.sage() -- 3.60546360143265208591582056420772677481026899659802474544 -- -+ 3.605463601432652085915820564207726774810268996598024745444380641429820491740 # 64-bit -+ 3.60546360143265208591582056420772677481026899659802474544 # 32-bit - sage: from cypari2 import Pari - sage: pari = Pari() - -diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx -index 5c2d94bab2..2fdcf65ac6 100644 ---- a/src/sage/matrix/matrix_integer_dense.pyx -+++ b/src/sage/matrix/matrix_integer_dense.pyx -@@ -2400,13 +2400,13 @@ cdef class Matrix_integer_dense(Matrix_dense): - [0 3 0] - [0 0 0] - sage: U -- [ 0 1 0] -+ [ 0 2 -1] - [ 0 -1 1] -- [-1 2 -1] -+ [ 1 -2 1] - sage: V -- [-1 4 1] -- [ 1 -3 -2] - [ 0 0 1] -+ [-1 2 -2] -+ [ 1 -1 1] - sage: U*A*V - [1 0 0] - [0 3 0] -@@ -2421,12 +2421,12 @@ cdef class Matrix_integer_dense(Matrix_dense): - [0 2] - [0 0] - sage: U -- [ 0 1 0] -+ [ 0 2 -1] - [ 0 -1 1] -- [-1 2 -1] -+ [ 1 -2 1] - sage: V -- [-1 3] -- [ 1 -2] -+ [-1 1] -+ [ 1 0] - sage: U * A * V - [1 0] - [0 2] -@@ -2445,7 +2445,8 @@ cdef class Matrix_integer_dense(Matrix_dense): - - :meth:`elementary_divisors` - """ -- v = self.__pari__().matsnf(1).sage() -+ X = self.matrix_space()([self[i,j] for i in xrange(self._nrows-1,-1,-1) for j in xrange(self._ncols-1,-1,-1)]) -+ v = X.__pari__().matsnf(1).sage() - # need to reverse order of rows of U, columns of V, and both of D. - D = self.matrix_space()([v[2][i,j] for i in xrange(self._nrows-1,-1,-1) for j in xrange(self._ncols-1,-1,-1)]) - -@@ -2461,13 +2462,13 @@ cdef class Matrix_integer_dense(Matrix_dense): - # silly special cases for matrices with 0 columns (PARI has a unique empty matrix) - U = self.matrix_space(ncols = self._nrows)(1) - else: -- U = self.matrix_space(ncols = self._nrows)([v[0][i,j] for i in xrange(self._nrows-1,-1,-1) for j in xrange(self._nrows)]) -+ U = self.matrix_space(ncols = self._nrows)([v[0][i,j] for i in xrange(self._nrows-1,-1,-1) for j in xrange(self._nrows-1,-1,-1)]) - - if self._nrows == 0: - # silly special cases for matrices with 0 rows (PARI has a unique empty matrix) - V = self.matrix_space(nrows = self._ncols)(1) - else: -- V = self.matrix_space(nrows = self._ncols)([v[1][i,j] for i in xrange(self._ncols) for j in xrange(self._ncols-1,-1,-1)]) -+ V = self.matrix_space(nrows = self._ncols)([v[1][i,j] for i in xrange(self._ncols-1,-1,-1) for j in xrange(self._ncols-1,-1,-1)]) - - return D, U, V - -diff --git a/src/sage/matrix/matrix_integer_sparse.pyx b/src/sage/matrix/matrix_integer_sparse.pyx -index c53c92602e..8223fa8ab0 100644 ---- a/src/sage/matrix/matrix_integer_sparse.pyx -+++ b/src/sage/matrix/matrix_integer_sparse.pyx -@@ -611,13 +611,13 @@ cdef class Matrix_integer_sparse(Matrix_sparse): - [0 3 0] - [0 0 0] - sage: U -- [ 0 1 0] -+ [ 0 2 -1] - [ 0 -1 1] -- [-1 2 -1] -+ [ 1 -2 1] - sage: V -- [-1 4 1] -- [ 1 -3 -2] - [ 0 0 1] -+ [-1 2 -2] -+ [ 1 -1 1] - sage: U*A*V - [1 0 0] - [0 3 0] -@@ -632,12 +632,12 @@ cdef class Matrix_integer_sparse(Matrix_sparse): - [0 2] - [0 0] - sage: U -- [ 0 1 0] -+ [ 0 2 -1] - [ 0 -1 1] -- [-1 2 -1] -+ [ 1 -2 1] - sage: V -- [-1 3] -- [ 1 -2] -+ [-1 1] -+ [ 1 0] - sage: U * A * V - [1 0] - [0 2] -diff --git a/src/sage/modular/etaproducts.py b/src/sage/modular/etaproducts.py -index b656a0f7de..4a90b2cecf 100644 ---- a/src/sage/modular/etaproducts.py -+++ b/src/sage/modular/etaproducts.py -@@ -146,7 +146,7 @@ class EtaGroupElement(Element): - - sage: eta1, eta2 = EtaGroup(4).basis() # indirect doctest - sage: eta1 * eta2 -- Eta product of level 4 : (eta_1)^8 (eta_4)^-8 -+ Eta product of level 4 : (eta_1)^24 (eta_2)^-48 (eta_4)^24 - """ - newdict = {d: self._rdict.get(d, 0) + other._rdict.get(d, 0) - for d in union(self._rdict, other._rdict)} -@@ -161,7 +161,7 @@ class EtaGroupElement(Element): - - sage: eta1, eta2 = EtaGroup(4).basis() - sage: eta1 / eta2 # indirect doctest -- Eta product of level 4 : (eta_1)^-24 (eta_2)^48 (eta_4)^-24 -+ Eta product of level 4 : (eta_1)^-8 (eta_4)^8 - sage: (eta1 / eta2) * eta2 == eta1 - True - """ -@@ -509,16 +509,16 @@ class EtaGroup_class(UniqueRepresentation, Parent): - sage: EtaGroup(5).basis() - [Eta product of level 5 : (eta_1)^6 (eta_5)^-6] - sage: EtaGroup(12).basis() -- [Eta product of level 12 : (eta_1)^2 (eta_2)^1 (eta_3)^2 (eta_4)^-1 (eta_6)^-7 (eta_12)^3, -+ [Eta product of level 12 : (eta_1)^-3 (eta_2)^2 (eta_3)^1 (eta_4)^-1 (eta_6)^-2 (eta_12)^3, - Eta product of level 12 : (eta_1)^-4 (eta_2)^2 (eta_3)^4 (eta_6)^-2, -+ Eta product of level 12 : (eta_1)^6 (eta_2)^-9 (eta_3)^-2 (eta_4)^3 (eta_6)^3 (eta_12)^-1, - Eta product of level 12 : (eta_1)^-1 (eta_2)^3 (eta_3)^3 (eta_4)^-2 (eta_6)^-9 (eta_12)^6, -- Eta product of level 12 : (eta_1)^1 (eta_2)^-1 (eta_3)^-3 (eta_4)^-2 (eta_6)^7 (eta_12)^-2, -- Eta product of level 12 : (eta_1)^-6 (eta_2)^9 (eta_3)^2 (eta_4)^-3 (eta_6)^-3 (eta_12)^1] -+ Eta product of level 12 : (eta_1)^3 (eta_3)^-1 (eta_4)^-3 (eta_12)^1] - sage: EtaGroup(12).basis(reduce=False) # much bigger coefficients -- [Eta product of level 12 : (eta_2)^24 (eta_12)^-24, -- Eta product of level 12 : (eta_1)^-336 (eta_2)^576 (eta_3)^696 (eta_4)^-216 (eta_6)^-576 (eta_12)^-144, -- Eta product of level 12 : (eta_1)^-8 (eta_2)^-2 (eta_6)^2 (eta_12)^8, -- Eta product of level 12 : (eta_1)^1 (eta_2)^9 (eta_3)^13 (eta_4)^-4 (eta_6)^-15 (eta_12)^-4, -+ [Eta product of level 12 : (eta_1)^384 (eta_2)^-576 (eta_3)^-696 (eta_4)^216 (eta_6)^576 (eta_12)^96, -+ Eta product of level 12 : (eta_2)^24 (eta_12)^-24, -+ Eta product of level 12 : (eta_1)^-40 (eta_2)^116 (eta_3)^96 (eta_4)^-30 (eta_6)^-80 (eta_12)^-62, -+ Eta product of level 12 : (eta_1)^-4 (eta_2)^-33 (eta_3)^-4 (eta_4)^1 (eta_6)^3 (eta_12)^37, - Eta product of level 12 : (eta_1)^15 (eta_2)^-24 (eta_3)^-29 (eta_4)^9 (eta_6)^24 (eta_12)^5] - - ALGORITHM: An eta product of level `N` is uniquely -@@ -1030,7 +1030,7 @@ def _eta_relations_helper(eta1, eta2, degree, qexp_terms, labels, verbose): - sage: from sage.modular.etaproducts import _eta_relations_helper - sage: r,s = EtaGroup(4).basis() - sage: _eta_relations_helper(r,s,4,100,['a','b'],False) -- [a*b - a + 16] -+ [a + 1/16*b - 1/16] - sage: _eta_relations_helper(EtaProduct(26, {2:2,13:2,26:-2,1:-2}),EtaProduct(26, {2:4,13:2,26:-4,1:-2}),3,12,['a','b'],False) # not enough terms, will return rubbish - [1] - """ -diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py -index 91bfd2448d..f629bc659b 100644 ---- a/src/sage/modular/local_comp/liftings.py -+++ b/src/sage/modular/local_comp/liftings.py -@@ -222,9 +222,9 @@ def lift_for_SL(A, N=None): - TESTS:: - - sage: lift_for_SL(matrix(3,3,[1,2,0,3,4,0,0,0,1]),3) -- [10 14 3] -- [ 9 10 3] -- [ 3 3 1] -+ [-2 -1 0] -+ [ 0 1 -3] -+ [ 3 0 4] - - sage: A = matrix(Zmod(7), 2, [1,0,0,1]) - sage: L = lift_for_SL(A) -diff --git a/src/sage/modular/local_comp/local_comp.py b/src/sage/modular/local_comp/local_comp.py -index aa74ea7889..a00268ee91 100644 ---- a/src/sage/modular/local_comp/local_comp.py -+++ b/src/sage/modular/local_comp/local_comp.py -@@ -24,6 +24,7 @@ from sage.rings.all import ZZ, QQbar, PolynomialRing, polygen - from sage.misc.abstract_method import abstract_method - from sage.misc.cachefunc import cached_method - from sage.misc.verbose import verbose -+from sage.misc.flatten import flatten - from sage.modular.modform.element import Newform - from sage.structure.sequence import Sequence - -@@ -73,11 +74,9 @@ def LocalComponent(f, p, twist_factor=None): - Character of Q_7*, of level 0, mapping 7 |--> 1 - sage: Pi.species() - 'Supercuspidal' -- sage: Pi.characters() -- [ -- Character of unramified extension Q_7(s)* (s^2 + 6*s + 3 = 0), of level 1, mapping s |--> d, 7 |--> 1, -- Character of unramified extension Q_7(s)* (s^2 + 6*s + 3 = 0), of level 1, mapping s |--> -d, 7 |--> 1 -- ] -+ sage: set(Pi.characters()) -+ {Character of unramified extension Q_7(s)* (s^2 + 6*s + 3 = 0), of level 1, mapping s |--> -d, 7 |--> 1, -+ Character of unramified extension Q_7(s)* (s^2 + 6*s + 3 = 0), of level 1, mapping s |--> d, 7 |--> 1} - """ - p = ZZ(p) - if not p.is_prime(): -@@ -635,11 +634,9 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - - sage: f = Newform('50a') - sage: Pi = LocalComponent(f, 5) -- sage: chars = Pi.characters(); chars -- [ -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> d, 5 |--> 1, -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -d - 1, 5 |--> 1 -- ] -+ sage: chars = Pi.characters(); set(chars) -+ {Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -d - 1, 5 |--> 1, -+ Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> d, 5 |--> 1} - sage: chars[0].base_ring() - Number Field in d with defining polynomial x^2 + x + 1 - -@@ -653,13 +650,11 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - sage: f = Newforms(GammaH(25, [6]), 3, names='j')[0]; f - q + j0*q^2 + 1/3*j0^3*q^3 - 1/3*j0^2*q^4 + O(q^6) - sage: Pi = LocalComponent(f, 5) -- sage: Pi.characters() -- [ -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> d, 5 |--> 5, -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -d - 1/3*j0^3, 5 |--> 5 -- ] -+ sage: set(Pi.characters()) -+ {Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> 1/3*j0^2*d - 1/3*j0^3, 5 |--> 5, -+ Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -1/3*j0^2*d, 5 |--> 5} - sage: Pi.characters()[0].base_ring() -- Number Field in d with defining polynomial x^2 + 1/3*j0^3*x - 1/3*j0^2 over its base field -+ Number Field in d with defining polynomial x^2 - j0*x + 1/3*j0^2 over its base field - - .. warning:: - -@@ -672,11 +667,9 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - - sage: f = Newform('81a', names='j'); f - q + j0*q^2 + q^4 - j0*q^5 + O(q^6) -- sage: LocalComponent(f, 3).characters() # long time (12s on sage.math, 2012) -- [ -- Character of unramified extension Q_3(s)* (s^2 + 2*s + 2 = 0), of level 2, mapping -2*s |--> 2*d + j0, 4 |--> 1, 3*s + 1 |--> j0*d + 1, 3 |--> 1, -- Character of unramified extension Q_3(s)* (s^2 + 2*s + 2 = 0), of level 2, mapping -2*s |--> -2*d - j0, 4 |--> 1, 3*s + 1 |--> -j0*d - 2, 3 |--> 1 -- ] -+ sage: set(LocalComponent(f, 3).characters()) # long time (12s on sage.math, 2012) -+ {Character of unramified extension Q_3(s)* (s^2 + 2*s + 2 = 0), of level 2, mapping -2*s |--> -2*d + j0, 4 |--> 1, 3*s + 1 |--> -j0*d + 1, 3 |--> 1, -+ Character of unramified extension Q_3(s)* (s^2 + 2*s + 2 = 0), of level 2, mapping -2*s |--> 2*d - j0, 4 |--> 1, 3*s + 1 |--> j0*d - 2, 3 |--> 1} - - Some ramified examples:: - -@@ -706,11 +699,9 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - Character of unramified extension Q_2(s)* (s^2 + s + 1 = 0), of level 3, mapping s |--> 1, 2*s + 1 |--> 1/2*a0, 4*s + 1 |--> 1, -1 |--> 1, 2 |--> 1, - Character of unramified extension Q_2(s)* (s^2 + s + 1 = 0), of level 3, mapping s |--> 1, 2*s + 1 |--> 1/2*a0, 4*s + 1 |--> -1, -1 |--> 1, 2 |--> 1 - ] -- sage: Newform('243a',names='a').local_component(3).characters() # long time -- [ -- Character of ramified extension Q_3(s)* (s^2 - 6 = 0), of level 4, mapping -s - 1 |--> 1, 4 |--> 1, 3*s + 1 |--> d, s |--> 1, -- Character of ramified extension Q_3(s)* (s^2 - 6 = 0), of level 4, mapping -s - 1 |--> 1, 4 |--> 1, 3*s + 1 |--> -d - 1, s |--> 1 -- ] -+ sage: set(Newform('243a',names='a').local_component(3).characters()) # long time -+ {Character of ramified extension Q_3(s)* (s^2 - 6 = 0), of level 4, mapping -2*s - 1 |--> -d - 1, 4 |--> 1, 3*s + 1 |--> -d - 1, s |--> 1, -+ Character of ramified extension Q_3(s)* (s^2 - 6 = 0), of level 4, mapping -2*s - 1 |--> d, 4 |--> 1, 3*s + 1 |--> d, s |--> 1} - """ - T = self.type_space() - p = self.prime() -@@ -736,7 +727,9 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - F = self.coefficient_field().extension(theta_poly, "d") - G = G.base_extend(F) - -- gvals = [x[0] for x in theta_poly.roots(G.base_ring())] -+ # roots with repetitions allowed -+ gvals = flatten([[y[0]]*y[1] for y in theta_poly.roots(G.base_ring())]) -+ - if len(gs) == 1: - # This is always the case if p != 2 - chi1, chi2 = [G.extend_character(n, self.central_character(), [x]) for x in gvals] -@@ -747,18 +740,18 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - g0 = gs[0] - try: - G._reduce_Qp(1, g0) -- raise ZeroDivisionError -+ raise ArithmeticError("Bad generators returned") - except ValueError: - pass - - tr = (~T.rho(g0.matrix().list())).trace() - X = polygen(G.base_ring()) -- theta_poly = X**2 - (-1)**n*tr*X + self.central_character()(g0.norm()) -+ theta0_poly = X**2 - (-1)**n*tr*X + self.central_character()(g0.norm()) - verbose("theta_poly for %s is %s" % (g0, theta_poly), level=1) -- if theta_poly.is_irreducible(): -- F = theta_poly.base_ring().extension(theta_poly, "e") -+ if theta0_poly.is_irreducible(): -+ F = theta0_poly.base_ring().extension(theta_poly, "e") - G = G.base_extend(F) -- g0vals = [y[0] for y in theta_poly.roots(G.base_ring())] -+ g0vals = flatten([[y[0]]*y[1] for y in theta0_poly.roots(G.base_ring())]) - - pairA = [ [g0vals[0], gvals[0]], [g0vals[1], gvals[1]] ] - pairB = [ [g0vals[0], gvals[1]], [g0vals[1], gvals[0]] ] -@@ -774,26 +767,35 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - except ValueError: - B_fail = 1 - -+ if chisA == chisB or chisA == reversed(chisB): -+ # repeated roots -- break symmetry arbitrarily -+ B_fail = 1 -+ - # check the character relation from LW12 - if (not A_fail and not B_fail): - for x in G.ideal(n).invertible_residues(): - try: - # test if G mod p is in Fp -- G._reduce_Qp(1, x) -+ flag = G._reduce_Qp(1, x) - except ValueError: -- verbose("testing x = %s" % x, level=1) -- ti = (-1)**n * (~T.rho(x.matrix().list())).trace() -- verbose(" trace of matrix is %s" % ti, level=1) -- if ti != chisA[0](x) + chisA[1](x): -- verbose(" chisA FAILED", level=1) -- A_fail = 1 -- break -- if ti != chisB[0](x) + chisB[1](x): -- verbose(" chisB FAILED", level=1) -- B_fail = 1 -- break -- else: -- verbose(" Trace identity check works for both", level=1) -+ flag = None -+ if flag is not None: -+ verbose("skipping x=%s as congruent to %s mod p" % (x, flag)) -+ continue -+ -+ verbose("testing x = %s" % x, level=1) -+ ti = (-1)**n * (~T.rho(x.matrix().list())).trace() -+ verbose(" trace of matrix is %s" % ti, level=1) -+ if ti != chisA[0](x) + chisA[1](x): -+ verbose(" chisA FAILED", level=1) -+ A_fail = 1 -+ break -+ if ti != chisB[0](x) + chisB[1](x): -+ verbose(" chisB FAILED", level=1) -+ B_fail = 1 -+ break -+ else: -+ verbose(" Trace identity check works for both", level=1) - - if B_fail and not A_fail: - chi1, chi2 = chisA -@@ -851,7 +853,6 @@ class PrimitiveSupercuspidal(PrimitiveLocalComponent): - if theta_poly.is_irreducible(): - F = self.coefficient_field().extension(theta_poly, "d") - G = G.base_extend(F) -- from sage.misc.flatten import flatten - c1q, c2q = flatten([[x]*e for x,e in theta_poly.roots(G.base_ring())]) - - if len(qs) == 1: -diff --git a/src/sage/modular/local_comp/smoothchar.py b/src/sage/modular/local_comp/smoothchar.py -index e54d5ad1d4..92135f7f71 100644 ---- a/src/sage/modular/local_comp/smoothchar.py -+++ b/src/sage/modular/local_comp/smoothchar.py -@@ -1131,9 +1131,8 @@ class SmoothCharacterGroupQuadratic(SmoothCharacterGroupGeneric): - sage: from sage.modular.local_comp.smoothchar import SmoothCharacterGroupRamifiedQuadratic - sage: G = SmoothCharacterGroupRamifiedQuadratic(3, 1, QQ) - sage: s = G.number_field().gen() -- sage: G.discrete_log(4, 3 + 2*s) -- [1, 2, 2, 1] -- sage: gs = G.unit_gens(4); gs[0] * gs[1]^2 * gs[2]^2 * gs[3] - (3 + 2*s) in G.ideal(4) -+ sage: dl = G.discrete_log(4, 3 + 2*s) -+ sage: gs = G.unit_gens(4); gs[0]^dl[0] * gs[1]^dl[1] * gs[2]^dl[2] * gs[3]^dl[3] - (3 + 2*s) in G.ideal(4) - True - - An example with a custom generating set:: -@@ -1191,11 +1190,11 @@ class SmoothCharacterGroupQuadratic(SmoothCharacterGroupGeneric): - sage: from sage.modular.local_comp.smoothchar import SmoothCharacterGroupUnramifiedQuadratic - sage: G = SmoothCharacterGroupUnramifiedQuadratic(7,QQ) - sage: G.quotient_gens(1) -- [s] -+ [2*s - 2] - sage: G.quotient_gens(2) -- [23*s - 16] -+ [15*s + 21] - sage: G.quotient_gens(3) -- [-124*s - 2] -+ [-75*s + 33] - - A ramified case:: - -@@ -1208,11 +1207,11 @@ class SmoothCharacterGroupQuadratic(SmoothCharacterGroupGeneric): - - sage: G = SmoothCharacterGroupUnramifiedQuadratic(2,QQ) - sage: G.quotient_gens(1) -- [s] -+ [s + 1] - sage: G.quotient_gens(2) -- [-s + 1] -+ [-s + 2] - sage: G.quotient_gens(3) -- [7*s + 5, -s + 3] -+ [-17*s - 14, 3*s - 2] - """ - - # silly special case -@@ -1327,18 +1326,18 @@ class SmoothCharacterGroupQuadratic(SmoothCharacterGroupGeneric): - sage: G.extend_character(3, chi, [1]) - Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 0, mapping 5 |--> 7 - sage: K.<z> = CyclotomicField(6); G.base_extend(K).extend_character(1, chi, [z]) -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> z, 5 |--> 7 -+ Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -z + 1, 5 |--> 7 - - We extend the nontrivial quadratic character:: - - sage: chi = SmoothCharacterGroupQp(5, QQ).character(1, [-1, 7]) - sage: K.<z> = CyclotomicField(24); G.base_extend(K).extend_character(1, chi, [z^6]) -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> z^6, 5 |--> 7 -+ Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 1, mapping s |--> -z^6, 5 |--> 7 - - Extensions of higher level:: - - sage: K.<z> = CyclotomicField(20); rho = G.base_extend(K).extend_character(2, chi, [z]); rho -- Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 2, mapping 11*s - 10 |--> -z^5, 6 |--> 1, 5*s + 1 |--> z^4, 5 |--> 7 -+ Character of unramified extension Q_5(s)* (s^2 + 4*s + 2 = 0), of level 2, mapping 11*s - 10 |--> z^5, 6 |--> 1, 5*s + 1 |--> z^4, 5 |--> 7 - sage: rho(3) - -1 - -diff --git a/src/sage/modular/modform/find_generators.py b/src/sage/modular/modform/find_generators.py -index 18055ef00f..40f4f7c858 100644 ---- a/src/sage/modular/modform/find_generators.py -+++ b/src/sage/modular/modform/find_generators.py -@@ -400,8 +400,7 @@ class ModularFormsRing(SageObject): - sage: ModularFormsRing(Gamma0(13)).generators(maxweight=12, prec=4) - [(2, 1 + 2*q + 6*q^2 + 8*q^3 + O(q^4)), (4, 1 + O(q^4)), (4, q + O(q^4)), (4, q^2 + O(q^4)), (4, q^3 + O(q^4)), (6, 1 + O(q^4)), (6, q + O(q^4))] - sage: ModularFormsRing(Gamma0(13),base_ring=ZZ).generators(maxweight=12, prec=4) -- [(2, 1 + 2*q + 6*q^2 + 8*q^3 + O(q^4)), (4, O(q^4)), (4, q^3 + O(q^4)), (4, q^2 + O(q^4)), (4, q + O(q^4)), (6, O(q^4)), (6, O(q^4)), (12, O(q^4))] -- -+ [(2, 1 + 2*q + 6*q^2 + 8*q^3 + O(q^4)), (4, q + 4*q^2 + 10*q^3 + O(q^4)), (4, 2*q^2 + 5*q^3 + O(q^4)), (4, q^2 + O(q^4)), (4, -2*q^3 + O(q^4)), (6, O(q^4)), (6, O(q^4)), (12, O(q^4))] - sage: [k for k,f in ModularFormsRing(1, QQ).generators(maxweight=12)] - [4, 6] - sage: [k for k,f in ModularFormsRing(1, ZZ).generators(maxweight=12)] -diff --git a/src/sage/modular/modsym/p1list_nf.py b/src/sage/modular/modsym/p1list_nf.py -index 709a91035a..91f7efada6 100644 ---- a/src/sage/modular/modsym/p1list_nf.py -+++ b/src/sage/modular/modsym/p1list_nf.py -@@ -957,7 +957,7 @@ class P1NFList(SageObject): - sage: N = k.ideal(a + 1) - sage: P = P1NFList(N) - sage: u = k.unit_group().gens_values(); u -- [-1, a^3 + a^2 + a + 12, a^3 + 3*a^2 - 1] -+ [-1, -a^3 - a^2 - a - 12, -a^3 - 3*a^2 + 1] - sage: P.apply_J_epsilon(3, u[2]^2)==P.apply_J_epsilon(P.apply_J_epsilon(3, u[2]),u[2]) - True - """ -diff --git a/src/sage/modular/multiple_zeta.py b/src/sage/modular/multiple_zeta.py -index 67c46766c8..d1f1f55024 100644 ---- a/src/sage/modular/multiple_zeta.py -+++ b/src/sage/modular/multiple_zeta.py -@@ -458,7 +458,7 @@ class MultizetaValues(UniqueRepresentation): - """ - self.prec = int(prec) - self.max_weight = int(max_weight) -- self._data = pari.zetamultall(self.max_weight, self.prec) -+ self._data = pari.zetamultall(self.max_weight, precision=self.prec) - - def update(self, max_weight, prec): - """ -diff --git a/src/sage/modules/fg_pid/fgp_element.py b/src/sage/modules/fg_pid/fgp_element.py -index 53857d31a0..5a948b6152 100644 ---- a/src/sage/modules/fg_pid/fgp_element.py -+++ b/src/sage/modules/fg_pid/fgp_element.py -@@ -39,7 +39,7 @@ class FGP_Element(ModuleElement): - sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ); W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2]) - sage: Q = V/W - sage: x = Q(V.0-V.1); x #indirect doctest -- (0, 3) -+ (0, 9) - sage: isinstance(x, sage.modules.fg_pid.fgp_element.FGP_Element) - True - sage: type(x) -@@ -94,14 +94,14 @@ class FGP_Element(ModuleElement): - sage: Q.1 - (0, 1) - sage: Q.0.lift() -- (0, 0, 1) -+ (0, 6, 1) - sage: Q.1.lift() -- (0, 2, 0) -+ (0, -2, 0) - sage: x = Q(V.0); x -- (0, 4) -+ (0, 8) - sage: x.lift() - (1/2, 0, 0) -- sage: x == 4*Q.1 -+ sage: x == 8*Q.1 - True - sage: x.lift().parent() == V - True -@@ -158,9 +158,9 @@ class FGP_Element(ModuleElement): - We test canonical coercion from V and W. - - sage: Q.0 + V.0 -- (1, 4) -+ (1, 8) - sage: V.0 + Q.0 -- (1, 4) -+ (1, 8) - sage: W.0 + Q.0 - (1, 0) - sage: W.0 + Q.0 == Q.0 -@@ -291,7 +291,7 @@ class FGP_Element(ModuleElement): - sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ); W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2]) - sage: Q = V/W - sage: Q(V.1)._repr_() -- '(0, 1)' -+ '(0, 11)' - """ - return repr(self.vector()) - -diff --git a/src/sage/modules/fg_pid/fgp_module.py b/src/sage/modules/fg_pid/fgp_module.py -index 38b95d40a3..935d0ab5c0 100644 ---- a/src/sage/modules/fg_pid/fgp_module.py -+++ b/src/sage/modules/fg_pid/fgp_module.py -@@ -70,17 +70,17 @@ the technical note has a V that need not be equal to V0, in general. :: - sage: M0.optimized()[0].V() - Free module of degree 3 and rank 2 over Integer Ring - User basis matrix: -- [0 0 1] -- [0 2 0] -+ [ 0 8 1] -+ [ 0 -2 0] - - Create elements of M0 either by coercing in elements of V0, getting generators, - or coercing in a list or tuple or coercing in 0. Finally, one can express an - element as a linear combination of the smith form generators :: - - sage: M0(V0.0) -- (0, 14) -+ (0, 2) - sage: M0(V0.0 + W0.0) # no difference modulo W0 -- (0, 14) -+ (0, 2) - sage: M0.linear_combination_of_smith_form_gens([3,20]) - (3, 4) - sage: 3*M0.0 + 20*M0.1 -@@ -93,9 +93,9 @@ coerces to V0, then take the equivalence class modulo W0. :: - sage: x = M0.0 - M0.1; x - (1, 15) - sage: x.lift() -- (0, -2, 1) -+ (0, 10, 1) - sage: M0(vector([1/2,0,0])) -- (0, 14) -+ (0, 2) - sage: x.additive_order() - 16 - -@@ -142,9 +142,9 @@ You can explicitly coerce elements of the kernel into M0 though. :: - Finitely generated module V/W over Integer Ring with invariants (2, 16) - - sage: M0(K.0) -- (2, 0) -+ (2, 8) - sage: M0(K.1) -- (3, 1) -+ (1, 5) - sage: f(M0(K.0)) - (0) - sage: f(M0(K.1)) -@@ -180,7 +180,7 @@ TESTS:: - sage: Q.linear_combination_of_smith_form_gens([1,3]) - (1, 3) - sage: Q(V([1,3,4])) -- (0, 11) -+ (0, 1) - sage: Q(W([1,16,0])) - (0, 0) - sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],QQ) -@@ -632,7 +632,7 @@ class FGP_Module_class(Module): - sage: W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2]) - sage: Q = V/W - sage: x = Q(V.0-V.1); x # indirect doctest -- (0, 3) -+ (0, 9) - sage: type(x) - <class 'sage.modules.fg_pid.fgp_module.FGP_Module_class_with_category.element_class'> - sage: x is Q(x) -@@ -931,9 +931,9 @@ class FGP_Module_class(Module): - sage: Q = V/W - sage: Q._smith_form() - ( -- [ 1 0 0] [1 0 0] [ 1 0 -8] -- [ 0 4 0] [0 0 1] [ 0 0 1] -- [ 0 0 12], [0 1 0], [ 0 1 0] -+ [ 1 0 0] [ 1 0 0] [ 1 0 8] -+ [ 0 4 0] [ 0 1 1] [ 0 0 -1] -+ [ 0 0 12], [ 0 -1 0], [ 0 1 3] - ) - """ - return self._relative_matrix().smith_form() -@@ -1026,7 +1026,7 @@ class FGP_Module_class(Module): - sage: Q.smith_form_gens() - ((1, 0), (0, 1)) - sage: [x.lift() for x in Q.smith_form_gens()] -- [(0, 0, 1), (0, 1, 0)] -+ [(0, 3, 1), (0, -1, 0)] - """ - # Get the rightmost transformation in the Smith form - _, _, X = self._smith_form() -@@ -1069,15 +1069,15 @@ class FGP_Module_class(Module): - sage: D.gens_to_smith() - [0 3 0] - [0 0 3] -- [0 2 0] -- [1 0 0] -+ [0 4 0] -+ [1 2 0] - [0 0 4] - sage: T = D.gens_to_smith()*D.smith_to_gens() - sage: T -- [ 3 0 15 0 0] -+ [ 3 0 3 0 0] - [ 0 33 0 0 3] -- [ 2 0 10 0 0] -- [ 0 0 0 1 0] -+ [ 4 0 4 0 0] -+ [ 2 0 3 1 0] - [ 0 44 0 0 4] - - The matrix `T` now satisfies a certain congruence:: -@@ -1120,13 +1120,13 @@ class FGP_Module_class(Module): - [ 0 0 0 1/3 0] - [ 0 0 0 0 2/3] - sage: D.smith_to_gens() -- [ 0 0 0 1 0] -- [ 1 0 5 0 0] -+ [ 0 0 1 1 0] -+ [ 1 0 1 0 0] - [ 0 11 0 0 1] - sage: T = D.smith_to_gens()*D.gens_to_smith() - sage: T -- [ 1 0 0] -- [ 0 13 0] -+ [ 1 6 0] -+ [ 0 7 0] - [ 0 0 37] - - This matrix satisfies the congruence:: -@@ -1148,7 +1148,7 @@ class FGP_Module_class(Module): - of the user defined generators that is x:: - - sage: x.vector() * D.smith_to_gens() -- (2, 33, 10, 1, 3) -+ (2, 33, 3, 1, 3) - """ - if self.base_ring() != ZZ: - # it is not -@@ -1196,7 +1196,7 @@ class FGP_Module_class(Module): - sage: gens = [V(g) for g in gens] - sage: D = FGP_with_gens(V, W, gens) - sage: D.gens() -- ((0, 3, 0), (0, 0, 3), (0, 2, 0), (1, 0, 0), (0, 0, 8)) -+ ((0, 3, 0), (0, 0, 3), (0, 4, 0), (1, 2, 0), (0, 0, 8)) - - - We create some element of D:: -@@ -1209,12 +1209,12 @@ class FGP_Module_class(Module): - - sage: v = D.gens_vector(x) - sage: v -- (2, 9, 10, 1, 33) -+ (2, 9, 3, 1, 33) - - The output can be further reduced:: - - sage: D.gens_vector(x, reduce=True) -- (0, 1, 1, 1, 0) -+ (0, 1, 0, 1, 0) - - Let us check:: - -@@ -1262,9 +1262,9 @@ class FGP_Module_class(Module): - If x is not in self, it is coerced in:: - - sage: Q.coordinate_vector(V.0) -- (1, 0, -3) -+ (1, -3, 0) - sage: Q.coordinate_vector(Q(V.0)) -- (1, 0, -3) -+ (1, -3, 0) - - TESTS:: - -@@ -1278,28 +1278,28 @@ class FGP_Module_class(Module): - sage: O.V() - Free module of degree 3 and rank 2 over Integer Ring - User basis matrix: -- [0 0 1] -- [0 2 0] -+ [ 0 6 1] -+ [ 0 -2 0] - sage: phi = Q.hom([Q.0, 4*Q.1]) - sage: x = Q(V.0); x -- (0, 4) -+ (0, 8) - sage: Q.coordinate_vector(x, reduce=True) -- (0, 4) -+ (0, 8) - sage: Q.coordinate_vector(-x, reduce=False) # random -- (0, -4) -- sage: x == 4*Q.1 -+ (0, -8) -+ sage: x == 8*Q.1 - True - sage: x = Q(V.1); x -- (0, 1) -+ (0, 11) - sage: Q.coordinate_vector(x) -- (0, 1) -- sage: x == Q.1 -+ (0, -1) -+ sage: x == -Q.1 - True - sage: x = Q(V.2); x -- (1, 0) -+ (1, 3) - sage: Q.coordinate_vector(x) -- (1, 0) -- sage: x == Q.0 -+ (1, 3) -+ sage: x == Q.0 + 3*Q.1 - True - """ - try: -@@ -1407,8 +1407,8 @@ class FGP_Module_class(Module): - sage: O.V() - Free module of degree 3 and rank 2 over Integer Ring - User basis matrix: -- [0 0 1] -- [0 1 0] -+ [ 0 3 1] -+ [ 0 -1 0] - sage: O.W() - Free module of degree 3 and rank 2 over Integer Ring - Echelon basis matrix: -@@ -1699,7 +1699,7 @@ class FGP_Module_class(Module): - sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ); W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2]) - sage: Q = V/W - sage: Q.random_element() -- (1, 10) -+ (1, 5) - """ - return self(self._V.random_element(*args, **kwds)) - -diff --git a/src/sage/modules/fg_pid/fgp_morphism.py b/src/sage/modules/fg_pid/fgp_morphism.py -index fbbd479c6e..ce5df8df52 100644 ---- a/src/sage/modules/fg_pid/fgp_morphism.py -+++ b/src/sage/modules/fg_pid/fgp_morphism.py -@@ -258,20 +258,20 @@ class FGP_Morphism(Morphism): - sage: O.V() - Free module of degree 3 and rank 2 over Integer Ring - User basis matrix: -- [0 0 1] -- [0 2 0] -+ [ 0 6 1] -+ [ 0 -2 0] - sage: phi = Q.hom([Q.0, 4*Q.1]) - sage: x = Q(V.0); x -- (0, 4) -- sage: x == 4*Q.1 -+ (0, 8) -+ sage: x == 8*Q.1 - True - sage: x in O.V() - False - sage: phi(x) -- (0, 4) -- sage: phi(4*Q.1) -- (0, 4) -- sage: phi(4*Q.1) == phi(x) -+ (0, 8) -+ sage: phi(8*Q.1) -+ (0, 8) -+ sage: phi(8*Q.1) == phi(x) - True - """ - from .fgp_module import is_FGP_Module -diff --git a/src/sage/modules/free_quadratic_module_integer_symmetric.py b/src/sage/modules/free_quadratic_module_integer_symmetric.py -index 7de14e8d77..d09578682e 100644 ---- a/src/sage/modules/free_quadratic_module_integer_symmetric.py -+++ b/src/sage/modules/free_quadratic_module_integer_symmetric.py -@@ -549,8 +549,8 @@ def IntegralLatticeGluing(Lattices, glue, return_embeddings=False): - sage: [L, phi] = IntegralLatticeGluing([L1, L2], [[f1, g1], [f2, 2 * g2]], True) - sage: phi[0] - Free module morphism defined by the matrix -- [ 2 2 -1 -2] -- [ 0 2 0 -1] -+ [ 2 2 -2 -1] -+ [ 0 2 -1 0] - Domain: Lattice of degree 4 and rank 2 over Integer Ring - Basis matrix: - [1 1 0 0] -@@ -563,7 +563,7 @@ def IntegralLatticeGluing(Lattices, glue, return_embeddings=False): - Codomain: Lattice of degree 10 and rank 4 over Integer Ring - Basis matrix: - [ 1/2 0 -1/2 0 0 1/2 0 0 1/2 1/2] -- [ 0 1/2 1/2 0 0 0 0 0 1/2 1/2] -+ [ 0 1/2 1/2 0 0 1/2 0 0 0 0] - [ 0 0 0 0 0 1 0 0 0 0] - [ 0 0 0 0 0 0 0 0 1 1] - Inner product matrix: -@@ -784,7 +784,7 @@ class FreeQuadraticModule_integer_symmetric(FreeQuadraticModule_submodule_with_b - Finite quadratic module over Integer Ring with invariants (2, 10) - Gram matrix of the quadratic form with values in Q/2Z: - [ 1 1/2] -- [1/2 9/5] -+ [1/2 1/5] - sage: L.discriminant_group(2) - Finite quadratic module over Integer Ring with invariants (2, 2) - Gram matrix of the quadratic form with values in Q/2Z: -@@ -793,7 +793,7 @@ class FreeQuadraticModule_integer_symmetric(FreeQuadraticModule_submodule_with_b - sage: L.discriminant_group(5) - Finite quadratic module over Integer Ring with invariants (5,) - Gram matrix of the quadratic form with values in Q/2Z: -- [6/5] -+ [4/5] - - TESTS:: - -@@ -1463,8 +1463,8 @@ def local_modification(M, G, p, check=True): - sage: local_modification(M, L.gram_matrix(), 2) - Lattice of degree 4 and rank 4 over Integer Ring - Basis matrix: -- [1/3 0 1/3 2/3] -- [ 0 1/3 1/3 2/3] -+ [1/3 0 2/3 2/3] -+ [ 0 1/3 0 2/3] - [ 0 0 1 0] - [ 0 0 0 1] - Inner product matrix: -diff --git a/src/sage/modules/torsion_quadratic_module.py b/src/sage/modules/torsion_quadratic_module.py -index 27a019554e..f922c0c278 100644 ---- a/src/sage/modules/torsion_quadratic_module.py -+++ b/src/sage/modules/torsion_quadratic_module.py -@@ -62,7 +62,7 @@ def TorsionQuadraticForm(q): - - TESTS:: - -- sage: TorsionQuadraticForm(matrix.diagonal([3/8,3/8,3/4])) -+ sage: TorsionQuadraticForm(matrix.diagonal([3/4,3/8,3/8])) - Finite quadratic module over Integer Ring with invariants (4, 8, 8) - Gram matrix of the quadratic form with values in Q/2Z: - [3/4 0 0] -@@ -1030,10 +1030,10 @@ class TorsionQuadraticModule(FGP_Module_class, CachedRepresentation): - sage: T - Finite quadratic module over Integer Ring with invariants (6, 6, 12, 12) - Gram matrix of the quadratic form with values in Q/(1/3)Z: -- [1/18 5/36 0 0] -- [5/36 1/18 5/36 5/36] -- [ 0 5/36 1/36 1/72] -- [ 0 5/36 1/72 1/36] -+ [ 1/18 1/12 5/36 1/36] -+ [ 1/12 1/6 1/36 1/9] -+ [ 5/36 1/36 1/36 11/72] -+ [ 1/36 1/9 11/72 1/36] - sage: T.normal_form() - Finite quadratic module over Integer Ring with invariants (6, 6, 12, 12) - Gram matrix of the quadratic form with values in Q/(1/3)Z: -diff --git a/src/sage/quadratic_forms/extras.py b/src/sage/quadratic_forms/extras.py -index 37c30e9afa..2baa4e3cfa 100644 ---- a/src/sage/quadratic_forms/extras.py -+++ b/src/sage/quadratic_forms/extras.py -@@ -94,12 +94,12 @@ def extend_to_primitive(A_input): - - sage: A = Matrix(ZZ, 3, 2, range(6)) - sage: extend_to_primitive(A) -- [ 0 1 0] -+ [ 0 1 -1] - [ 2 3 0] -- [ 4 5 -1] -+ [ 4 5 0] - - sage: extend_to_primitive([vector([1,2,3])]) -- [(1, 2, 3), (0, 1, 0), (0, 0, 1)] -+ [(1, 2, 3), (0, 1, 1), (-1, 0, 0)] - - """ - ## Deal with a list of vectors -diff --git a/src/sage/quadratic_forms/genera/genus.py b/src/sage/quadratic_forms/genera/genus.py -index f0718593ea..35de7eea8d 100644 ---- a/src/sage/quadratic_forms/genera/genus.py -+++ b/src/sage/quadratic_forms/genera/genus.py -@@ -2897,18 +2897,18 @@ class GenusSymbol_global_ring(object): - sage: GS.discriminant_form() - Finite quadratic module over Integer Ring with invariants (2, 2, 4, 24) - Gram matrix of the quadratic form with values in Q/2Z: -- [ 1/2 0 0 0] -- [ 0 3/2 0 0] -- [ 0 0 7/4 0] -- [ 0 0 0 7/24] -+ [ 1/2 0 1/2 0] -+ [ 0 3/2 0 0] -+ [ 1/2 0 3/4 0] -+ [ 0 0 0 25/24] - sage: A = matrix.diagonal(ZZ, [1, -4, 6, 8]) - sage: GS = Genus(A) - sage: GS.discriminant_form() - Finite quadratic module over Integer Ring with invariants (2, 4, 24) - Gram matrix of the quadratic form with values in Q/Z: -- [ 1/2 0 0] -- [ 0 3/4 0] -- [ 0 0 7/24] -+ [ 1/2 1/2 0] -+ [ 1/2 3/4 0] -+ [ 0 0 1/24] - """ - from sage.modules.torsion_quadratic_module import TorsionQuadraticForm - qL = [] -diff --git a/src/sage/quadratic_forms/quadratic_form__split_local_covering.py b/src/sage/quadratic_forms/quadratic_form__split_local_covering.py -index 92102fcbd1..85abc20a86 100644 ---- a/src/sage/quadratic_forms/quadratic_form__split_local_covering.py -+++ b/src/sage/quadratic_forms/quadratic_form__split_local_covering.py -@@ -318,25 +318,25 @@ def complementary_subform_to_vector(self, v): - sage: Q1 = DiagonalQuadraticForm(ZZ, [1,3,5,7]) - sage: Q1.complementary_subform_to_vector([1,0,0,0]) - Quadratic form in 3 variables over Integer Ring with coefficients: -- [ 3 0 0 ] -+ [ 7 0 0 ] - [ * 5 0 ] -- [ * * 7 ] -+ [ * * 3 ] - - :: - - sage: Q1.complementary_subform_to_vector([1,1,0,0]) - Quadratic form in 3 variables over Integer Ring with coefficients: -- [ 12 0 0 ] -+ [ 7 0 0 ] - [ * 5 0 ] -- [ * * 7 ] -+ [ * * 12 ] - - :: - - sage: Q1.complementary_subform_to_vector([1,1,1,1]) - Quadratic form in 3 variables over Integer Ring with coefficients: -- [ 624 -480 -672 ] -- [ * 880 -1120 ] -- [ * * 1008 ] -+ [ 880 -480 -160 ] -+ [ * 624 -96 ] -+ [ * * 240 ] - - """ - n = self.dim() -@@ -417,8 +417,8 @@ def split_local_cover(self): - sage: Q1.split_local_cover() - Quadratic form in 3 variables over Integer Ring with coefficients: - [ 3 0 0 ] -- [ * 7 0 ] -- [ * * 5 ] -+ [ * 5 0 ] -+ [ * * 7 ] - - """ - ## 0. If a split local cover already exists, then return it. -diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx -index 9b029a4dd6..caff023cbd 100644 ---- a/src/sage/rings/finite_rings/finite_field_base.pyx -+++ b/src/sage/rings/finite_rings/finite_field_base.pyx -@@ -1638,14 +1638,14 @@ cdef class FiniteField(Field): - - We check that :trac:`23801` is resolved:: - -- sage: k.<a> = GF(3^240) -+ sage: k.<a> = GF(5^240) - sage: l, inc = k.subfield(3, 'z', map=True); l -- Finite Field in z of size 3^3 -+ Finite Field in z of size 5^3 - sage: inc - Ring morphism: -- From: Finite Field in z of size 3^3 -- To: Finite Field in a of size 3^240 -- Defn: z |--> a^239 + a^238 + ... + a^3 + 2 -+ From: Finite Field in z of size 5^3 -+ To: Finite Field in a of size 5^240 -+ Defn: z |--> 2*a^235 + a^231 + ... + a + 4 - - There is no coercion since we can't ensure compatibility with larger - fields in this case:: -@@ -1656,7 +1656,7 @@ cdef class FiniteField(Field): - But there is still a compatibility among the generators chosen for the subfields:: - - sage: ll, iinc = k.subfield(12, 'w', map=True) -- sage: x = iinc(ll.gen())^((3^12-1)/(3^3-1)) -+ sage: x = iinc(ll.gen())^((5^12-1)/(5^3-1)) - sage: x.minimal_polynomial() == l.modulus() - True - -diff --git a/src/sage/rings/finite_rings/finite_field_constructor.py b/src/sage/rings/finite_rings/finite_field_constructor.py -index e05b7fc9fa..219b4a778a 100644 ---- a/src/sage/rings/finite_rings/finite_field_constructor.py -+++ b/src/sage/rings/finite_rings/finite_field_constructor.py -@@ -285,14 +285,14 @@ class FiniteFieldFactory(UniqueFactory): - (a generator of the multiplicative group), use - ``modulus="primitive"`` if you need this:: - -- sage: K.<a> = GF(5^40) -+ sage: K.<a> = GF(5^45) - sage: a.multiplicative_order() -- 189478062869360049565633138 -+ 7105427357601001858711242675781 - sage: a.is_square() - True -- sage: K.<b> = GF(5^40, modulus="primitive") -+ sage: K.<b> = GF(5^45, modulus="primitive") - sage: b.multiplicative_order() -- 9094947017729282379150390624 -+ 28421709430404007434844970703124 - - The modulus must be irreducible:: - -diff --git a/src/sage/rings/finite_rings/integer_mod_ring.py b/src/sage/rings/finite_rings/integer_mod_ring.py -index 0dcef0d21a..8380acc653 100644 ---- a/src/sage/rings/finite_rings/integer_mod_ring.py -+++ b/src/sage/rings/finite_rings/integer_mod_ring.py -@@ -626,7 +626,7 @@ class IntegerModRing_generic(quotient_ring.QuotientRing_generic): - sage: Integers(5).multiplicative_subgroups() - ((2,), (4,), ()) - sage: Integers(15).multiplicative_subgroups() -- ((11, 7), (4, 11), (8,), (11,), (14,), (7,), (4,), ()) -+ ((11, 7), (11, 4), (2,), (11,), (14,), (7,), (4,), ()) - sage: Integers(2).multiplicative_subgroups() - ((),) - sage: len(Integers(341).multiplicative_subgroups()) -diff --git a/src/sage/rings/finite_rings/residue_field.pyx b/src/sage/rings/finite_rings/residue_field.pyx -index cd4c2212c3..007a68e4c0 100644 ---- a/src/sage/rings/finite_rings/residue_field.pyx -+++ b/src/sage/rings/finite_rings/residue_field.pyx -@@ -1055,7 +1055,7 @@ 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 -@@ -1268,7 +1268,7 @@ 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 in Number Field in a with defining polynomial x^5 - 5*x + 2 - sage: s(k.gen()) - a -@@ -1371,10 +1371,10 @@ cdef class LiftingMap(Section): - sage: F = K.factor(7)[0][0].residue_field() - sage: L = F.lift_map(); L - Lifting map: -- From: Residue field in abar of Fractional ideal (-2*a^4 + a^3 - 4*a^2 + 2*a - 1) -+ From: Residue field in abar of Fractional ideal (2*a^4 - a^3 + 4*a^2 - 2*a + 1) - To: Maximal Order in Number Field in a with defining polynomial x^5 + 2 - sage: L.domain() -- Residue field in abar of Fractional ideal (-2*a^4 + a^3 - 4*a^2 + 2*a - 1) -+ Residue field in abar of Fractional ideal (2*a^4 - a^3 + 4*a^2 - 2*a + 1) - - sage: K.<a> = CyclotomicField(7) - sage: F = K.factor(5)[0][0].residue_field() -@@ -1498,7 +1498,7 @@ 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 (-3*theta_12^2 + 1) -+ From: Residue field in tmod of Fractional ideal (theta_12^2 + 2) - To: Maximal Order in Cyclotomic Field of order 12 and degree 4 - """ - return "Lifting" -@@ -1515,7 +1515,7 @@ class ResidueFiniteField_prime_modn(ResidueField_generic, FiniteField_prime_modn - sage: P = K.ideal(29).factor()[1][0] - sage: k = ResidueField(P) - sage: k -- Residue field of Fractional ideal (a^2 + 2*a + 2) -+ Residue field of Fractional ideal (-a^2 - 2*a - 2) - sage: k.order() - 29 - sage: OK = K.maximal_order() -@@ -1597,7 +1597,7 @@ class ResidueFiniteField_prime_modn(ResidueField_generic, FiniteField_prime_modn - sage: P = K.ideal(29).factor()[1][0] - sage: k = ResidueField(P) - sage: k -- Residue field of Fractional ideal (a^2 + 2*a + 2) -+ Residue field of Fractional ideal (-a^2 - 2*a - 2) - sage: OK = K.maximal_order() - sage: c = OK(a) - sage: b = k(a); b -diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx -index 56cf1161d0..14eec0c8c3 100644 ---- a/src/sage/rings/integer.pyx -+++ b/src/sage/rings/integer.pyx -@@ -5483,7 +5483,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement): - sage: 3._bnfisnorm(QuadraticField(-1, 'i')) - (1, 3) - sage: 7._bnfisnorm(CyclotomicField(7)) -- (-zeta7^5 - zeta7^4 - 2*zeta7^3 - zeta7^2 - zeta7 - 1, 1) -+ (zeta7^5 - zeta7^2, 1) - """ - from sage.rings.rational_field import QQ - return QQ(self)._bnfisnorm(K, proof=proof, extra_primes=extra_primes) -diff --git a/src/sage/rings/number_field/S_unit_solver.py b/src/sage/rings/number_field/S_unit_solver.py -index 5c0a33eb74..ccd088d630 100644 ---- a/src/sage/rings/number_field/S_unit_solver.py -+++ b/src/sage/rings/number_field/S_unit_solver.py -@@ -24,10 +24,10 @@ EXAMPLES:: - sage: from sage.rings.number_field.S_unit_solver import solve_S_unit_equation, eq_up_to_order - sage: K.<xi> = NumberField(x^2+x+1) - sage: S = K.primes_above(3) -- sage: expected = [((2, 1), (4, 0), xi + 2, -xi - 1), -- ....: ((5, -1), (4, -1), 1/3*xi + 2/3, -1/3*xi + 1/3), -- ....: ((5, 0), (1, 0), -xi, xi + 1), -- ....: ((1, 1), (2, 0), -xi + 1, xi)] -+ sage: expected = [((0, 1), (4, 0), xi + 2, -xi - 1), -+ ....: ((1, -1), (0, -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)] - sage: sols = solve_S_unit_equation(K, S, 200) - sage: eq_up_to_order(sols, expected) - True -@@ -1780,20 +1780,20 @@ def sieve_ordering(SUK, q): - sage: SUK = K.S_unit_group(S=3) - sage: sieve_data = list(sieve_ordering(SUK, 19)) - sage: sieve_data[0] -- (Fractional ideal (-2*xi^2 + 3), -- Fractional ideal (xi - 3), -- Fractional ideal (2*xi + 1)) -+ (Fractional ideal (xi - 3), -+ Fractional ideal (-2*xi^2 + 3), -+ Fractional ideal (2*xi + 1)) - - sage: sieve_data[1] -- (Residue field of Fractional ideal (-2*xi^2 + 3), -- Residue field of Fractional ideal (xi - 3), -- Residue field of Fractional ideal (2*xi + 1)) -+ (Residue field of Fractional ideal (xi - 3), -+ Residue field of Fractional ideal (-2*xi^2 + 3), -+ Residue field of Fractional ideal (2*xi + 1)) - - sage: sieve_data[2] -- ([18, 9, 16, 8], [18, 7, 10, 4], [18, 3, 12, 10]) -+ ([18, 7, 16, 4], [18, 9, 12, 8], [18, 3, 10, 10]) - - sage: sieve_data[3] -- (972, 972, 3888) -+ (486, 648, 11664) - """ - - K = SUK.number_field() -@@ -2654,10 +2654,10 @@ def sieve_below_bound(K, S, bound=10, bump=10, split_primes_list=[], verbose=Fal - sage: S = SUK.primes() - sage: sols = sieve_below_bound(K, S, 10) - sage: expected = [ -- ....: ((5, -1), (4, -1), 1/3*xi + 2/3, -1/3*xi + 1/3), -- ....: ((2, 1), (4, 0), xi + 2, -xi - 1), -- ....: ((2, 0), (1, 1), xi, -xi + 1), -- ....: ((5, 0), (1, 0), -xi, xi + 1)] -+ ....: ((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), -+ ....: ((1, 0), (5, 0), xi + 1, -xi)] - sage: eq_up_to_order(sols, expected) - True - """ -@@ -2715,10 +2715,10 @@ def solve_S_unit_equation(K, S, prec=106, include_exponents=True, include_bound= - sage: S = K.primes_above(3) - sage: sols = solve_S_unit_equation(K, S, 200) - sage: expected = [ -- ....: ((2, 1), (4, 0), xi + 2, -xi - 1), -- ....: ((5, -1), (4, -1), 1/3*xi + 2/3, -1/3*xi + 1/3), -- ....: ((5, 0), (1, 0), -xi, xi + 1), -- ....: ((1, 1), (2, 0), -xi + 1, xi)] -+ ....: ((0, 1), (4, 0), xi + 2, -xi - 1), -+ ....: ((1, -1), (0, -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)] - sage: eq_up_to_order(sols, expected) - True - -@@ -2726,7 +2726,7 @@ 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 -- 6 -+ 7 - - You can omit the exponent vectors:: - -diff --git a/src/sage/rings/number_field/class_group.py b/src/sage/rings/number_field/class_group.py -index 46d0ca8c9d..1ad6d583a8 100644 ---- a/src/sage/rings/number_field/class_group.py -+++ b/src/sage/rings/number_field/class_group.py -@@ -157,7 +157,7 @@ class FractionalIdealClass(AbelianGroupWithValuesElement): - sage: C=K.class_group() - sage: c = C(2, a) - sage: c^2 -- Fractional ideal class (2, a^2 + 2*a - 1) -+ Fractional ideal class (4, a) - sage: c^3 - Trivial principal fractional ideal class - sage: c^1000 -@@ -467,7 +467,7 @@ class ClassGroup(AbelianGroupWithValues_class): - sage: CK = K.class_group() - sage: CL = L.class_group() - sage: [CL(I).exponents() for I in CK] -- [(0,), (4,), (2,)] -+ [(0,), (2,), (4,)] - """ - if isinstance(args[0], FractionalIdealClass): - return self.element_class(self, None, self._number_field.ideal(args[0].ideal())) -diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py -index fe02c6e824..ca6fee5532 100644 ---- a/src/sage/rings/number_field/number_field.py -+++ b/src/sage/rings/number_field/number_field.py -@@ -3592,7 +3592,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - 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 - -@@ -4760,7 +4760,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - 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] -+ -2/13*a^2 - 1/13*a + 755/13] - 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 -@@ -4802,8 +4802,8 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - sage: K.<a> = QuadraticField(-105) - sage: K._S_class_group_quotient_matrix((K.ideal(11, a + 4),)) - [0 0] -- [1 0] - [0 1] -+ [1 0] - - TESTS: - -@@ -4948,7 +4948,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - 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] -+ -2/13*a^2 - 1/13*a + 755/13] - 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) -@@ -6234,28 +6234,37 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - try: - return self._integral_basis_dict[v] - except (AttributeError, KeyError): -- f = self.pari_polynomial("y") -- if v: -- B = f.nfbasis(fa=v) -- elif self._assume_disc_small: -- B = f.nfbasis(1) -- elif not important: -- # Trial divide the discriminant with primes up to 10^6 -- m = self.pari_polynomial().poldisc().abs().factor(limit=10**6) -- # Since we only need a *squarefree* factorization for -- # primes with exponent 1, we need trial division up to D^(1/3) -- # instead of D^(1/2). -- trialdivlimit2 = pari(10**12) -- trialdivlimit3 = pari(10**18) -- if all(p < trialdivlimit2 or (e == 1 and p < trialdivlimit3) or p.isprime() for p, e in zip(m[0], m[1])): -- B = f.nfbasis(fa = m) -- else: -- raise RuntimeError("Unable to factor discriminant with trial division") -+ pass -+ -+ f = self.pari_polynomial("y") -+ if v: -+ # NOTE: here we make pari know about potentially big primes factors of -+ # the discriminant, see -+ # https://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=2257 -+ primelimit = pari.default("primelimit") -+ primes = [p for p in v if p > primelimit] -+ if primes: -+ pari.addprimes(primes) -+ B = f.nfbasis(fa=v) -+ elif self._assume_disc_small: -+ B = f.nfbasis(1) -+ elif not important: -+ # Trial divide the discriminant with primes up to 10^6 -+ m = self.pari_polynomial().poldisc().abs().factor(limit=10**6) -+ # Since we only need a *squarefree* factorization for -+ # primes with exponent 1, we need trial division up to D^(1/3) -+ # instead of D^(1/2). -+ trialdivlimit2 = pari(10**12) -+ trialdivlimit3 = pari(10**18) -+ if all(p < trialdivlimit2 or (e == 1 and p < trialdivlimit3) or p.isprime() for p, e in zip(m[0], m[1])): -+ B = f.nfbasis(fa = m) - else: -- B = f.nfbasis() -+ raise RuntimeError("Unable to factor discriminant with trial division") -+ else: -+ B = f.nfbasis() - -- self._integral_basis_dict[v] = B -- return B -+ self._integral_basis_dict[v] = B -+ return B - - def reduced_basis(self, prec=None): - r""" -@@ -6882,7 +6891,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - sage: A = x^4 - 10*x^3 + 20*5*x^2 - 15*5^2*x + 11*5^3 - sage: K = NumberField(A, 'a') - sage: K.units() -- (8/275*a^3 - 12/55*a^2 + 15/11*a - 3,) -+ (-1/275*a^3 - 4/55*a^2 + 5/11*a - 3,) - - For big number fields, provably computing the unit group can - take a very long time. In this case, one can ask for the -@@ -6893,14 +6902,14 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - sage: K.units(proof=True) # takes forever, not tested - ... - sage: K.units(proof=False) # result not independently verified -- (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^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, -+ (-a^9 - a + 1, -+ -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, -- 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 - 3*a^14 - 4*a^13 - 4*a^12 - 3*a^11 - a^10 + 2*a^9 + 4*a^8 + 5*a^7 + 4*a^6 + 2*a^5 - 2*a^4 - 6*a^3 - 9*a^2 - 9*a - 7, - 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, -- 5*a^16 - 6*a^14 + a^13 + 7*a^12 - 2*a^11 - 7*a^10 + 4*a^9 + 7*a^8 - 6*a^7 - 7*a^6 + 8*a^5 + 6*a^4 - 11*a^3 - 5*a^2 + 13*a + 4) -+ -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, -+ -a^14 - a^13 + a^12 + 2*a^10 + a^8 - 2*a^7 - 2*a^6 + 2*a^3 - a^2 + 2*a - 2) - - TESTS: - -@@ -6909,7 +6918,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - - sage: K.<a> = NumberField(1/2*x^2 - 1/6) - sage: K.units() -- (3*a - 2,) -+ (-3*a + 2,) - """ - proof = proof_flag(proof) - -@@ -6988,7 +6997,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - sage: U.gens() - (u0, u1, u2, u3, u4, u5, u6, u7, u8) - sage: U.gens_values() # result not independently verified -- [-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^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, 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 - 3*a^14 - 4*a^13 - 4*a^12 - 3*a^11 - a^10 + 2*a^9 + 4*a^8 + 5*a^7 + 4*a^6 + 2*a^5 - 2*a^4 - 6*a^3 - 9*a^2 - 9*a - 7, 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, 5*a^16 - 6*a^14 + a^13 + 7*a^12 - 2*a^11 - 7*a^10 + 4*a^9 + 7*a^8 - 6*a^7 - 7*a^6 + 8*a^5 + 6*a^4 - 11*a^3 - 5*a^2 + 13*a + 4] -+ [-1, -a^9 - a + 1, -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, -a^14 - a^13 + a^12 + 2*a^10 + a^8 - 2*a^7 - 2*a^6 + 2*a^3 - a^2 + 2*a - 2] - """ - proof = proof_flag(proof) - -@@ -7177,7 +7186,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField): - - sage: solutions, bound = K.S_unit_solutions(S, prec=100, include_bound=True) - sage: bound -- 6 -+ 7 - """ - from .S_unit_solver import solve_S_unit_equation - return solve_S_unit_equation(self, S, prec, include_exponents, include_bound, proof) -@@ -10997,9 +11006,9 @@ class NumberField_cyclotomic(NumberField_absolute): - EXAMPLES:: - - sage: k5.<z> = CyclotomicField(5) -- sage: gap('E(5)^7 + 3') -+ sage: w = libgap.eval('E(5)^7 + 3') -+ sage: w - -3*E(5)-2*E(5)^2-3*E(5)^3-3*E(5)^4 -- sage: w = gap('E(5)^7 + 3') - sage: z^7 + 3 - z^2 + 3 - sage: k5(w) # indirect doctest -@@ -11010,7 +11019,7 @@ class NumberField_cyclotomic(NumberField_absolute): - - sage: F = CyclotomicField(8) - sage: z = F.gen() -- sage: a = gap(z+1/z); a -+ sage: a = libgap(z+1/z); a - E(8)-E(8)^3 - sage: F(a) - -zeta8^3 + zeta8 -@@ -11024,6 +11033,7 @@ class NumberField_cyclotomic(NumberField_absolute): - - It also works with the old pexpect interface to GAP:: - -+ sage: a = gap(z + 1/z) - sage: b = gap(Matrix(F,[[z^2,1],[0,a+1]])); b - [ [ E(4), 1 ], [ 0, 1+E(8)-E(8)^3 ] ] - sage: b[1,2] -diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx -index 29932830f3..35e2857d96 100644 ---- a/src/sage/rings/number_field/number_field_element.pyx -+++ b/src/sage/rings/number_field/number_field_element.pyx -@@ -1632,7 +1632,7 @@ cdef class NumberFieldElement(FieldElement): - sage: Q.<X> = K[] - sage: L.<b> = NumberField(X^4 + a) - sage: t = (-a).is_norm(L, element=True); t -- (True, b^3 + 1) -+ (True, -b^3 - 1) - sage: t[1].norm(K) - -a - -@@ -1747,11 +1747,11 @@ cdef class NumberFieldElement(FieldElement): - sage: Q.<X> = K[] - sage: L.<b> = NumberField(X^4 + a) - sage: t = (-a)._rnfisnorm(L); t -- (b^3 + 1, 1) -+ (-b^3 - 1, 1) - sage: t[0].norm(K) - -a - sage: t = K(3)._rnfisnorm(L); t -- (-b^3 - a*b^2 - a^2*b + 1, 3*a^2 - 3*a + 6) -+ (b^3 + a*b^2 + a^2*b - 1, 3*a^2 - 3*a + 6) - sage: t[0].norm(K)*t[1] - 3 - -diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py -index 5277a9b06c..e75e61d161 100644 ---- a/src/sage/rings/number_field/number_field_ideal.py -+++ b/src/sage/rings/number_field/number_field_ideal.py -@@ -231,7 +231,7 @@ class NumberFieldIdeal(Ideal_generic): - 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 (-a))^2 * (Fractional ideal (5)) -+ (Fractional ideal (1/2*a + 3/2))^2 * (Fractional ideal (5)) - sage: (f[0][0] < f[1][0]) - True - sage: (f[0][0] == f[0][0]) -@@ -620,7 +620,7 @@ class NumberFieldIdeal(Ideal_generic): - - sage: K.<z> = CyclotomicField(7) - sage: I = K.factor(11)[0][0]; I -- Fractional ideal (-2*z^4 - 2*z^2 - 2*z + 1) -+ Fractional ideal (-3*z^4 - 2*z^3 - 2*z^2 - 2) - sage: A = I.free_module() - sage: A # warning -- choice of basis can be somewhat random - Free module of degree 6 and rank 6 over Integer Ring -@@ -780,7 +780,6 @@ class NumberFieldIdeal(Ideal_generic): - sage: P = EllipticCurve(L, '57a1').lift_x(z_x) * 3 - sage: ideal = L.fractional_ideal(P[0], P[1]) - sage: ideal.is_principal(proof=False) -- *** Warning: precision too low for generators, not given. - True - sage: len(ideal.gens_reduced(proof=False)) - 1 -@@ -789,7 +788,7 @@ class NumberFieldIdeal(Ideal_generic): - self._is_principal = True - self._reduced_generators = self.gens() - return self._reduced_generators -- self._cache_bnfisprincipal(proof=proof, gens_needed=True) -+ self._cache_bnfisprincipal(proof=proof, gens=True) - return self._reduced_generators - - def gens_two(self): -@@ -828,10 +827,13 @@ class NumberFieldIdeal(Ideal_generic): - try: - return self.__two_generators - except AttributeError: -- if self.is_zero(): -- self.__two_generators = (0,0) -- return self.__two_generators -- K = self.number_field() -+ pass -+ -+ K = self.number_field() -+ -+ if self.is_zero(): -+ self.__two_generators = (K.zero(), K.zero()) -+ else: - HNF = self.pari_hnf() - # Check whether the ideal is generated by an integer, i.e. - # whether HNF is a multiple of the identity matrix -@@ -841,7 +843,8 @@ class NumberFieldIdeal(Ideal_generic): - else: - a, alpha = K.pari_nf().idealtwoelt(HNF) - self.__two_generators = (K(a), K(alpha)) -- return self.__two_generators -+ -+ return self.__two_generators - - def integral_basis(self): - r""" -@@ -1031,7 +1034,7 @@ class NumberFieldIdeal(Ideal_generic): - raise ValueError("%s is not a prime ideal" % self) - return self._pari_prime - -- def _cache_bnfisprincipal(self, proof=None, gens_needed=False): -+ def _cache_bnfisprincipal(self, proof=None, gens=False): - r""" - This function is essentially the implementation of - :meth:`is_principal`, :meth:`gens_reduced` and -@@ -1043,9 +1046,8 @@ class NumberFieldIdeal(Ideal_generic): - - - ``proof`` -- proof flag. If ``proof=False``, assume GRH. - -- - ``gens_needed`` -- (default: True) if True, insist on computing -- the reduced generators of the ideal. With ``gens=False``, they -- may or may not be computed (depending on how big the ideal is). -+ - ``gens`` -- (default: False) if True, also computes the reduced -+ generators of the ideal. - - OUTPUT: - -@@ -1053,6 +1055,15 @@ class NumberFieldIdeal(Ideal_generic): - ``_ideal_class_log`` (see :meth:`ideal_class_log`), - ``_is_principal`` (see :meth:`is_principal`) and - ``_reduced_generators``. -+ -+ TESTS: -+ -+ Check that no warnings are triggered from PARI/GP (see :trac:`30801`):: -+ -+ sage: K.<a> = NumberField(x^2 - x + 112941801) -+ sage: I = K.ideal((112941823, a + 49942513)) -+ sage: I.is_principal() -+ False - """ - # Since pari_bnf() is cached, this call to pari_bnf() should not - # influence the run-time much. Also, this simplifies the handling -@@ -1064,29 +1075,33 @@ class NumberFieldIdeal(Ideal_generic): - - # If we already have _reduced_generators, no need to compute them again - if hasattr(self, "_reduced_generators"): -- gens_needed = False -+ gens = False - - # Is there something to do? -- if hasattr(self, "_ideal_class_log") and not gens_needed: -+ if hasattr(self, "_ideal_class_log") and not gens: - self._is_principal = not any(self._ideal_class_log) - return - -- # Call bnfisprincipal(). -- # If gens_needed, use flag=3 which will insist on computing -- # the generator. Otherwise, use flag=1, where the generator -- # may or may not be computed. -- v = bnf.bnfisprincipal(self.pari_hnf(), 3 if gens_needed else 1) -- self._ideal_class_log = list(v[0]) -- self._is_principal = not any(self._ideal_class_log) -- -- if self._is_principal: -- # Cache reduced generator if it was computed -- if v[1]: -- g = self.number_field()(v[1]) -- self._reduced_generators = (g,) -+ if not gens: -+ v = bnf.bnfisprincipal(self.pari_hnf(), 0) -+ self._ideal_class_log = list(v) -+ self._is_principal = not any(self._ideal_class_log) - else: -- # Non-principal ideal, compute two generators if asked for -- if gens_needed: -+ # TODO: this is a bit of a waste. We ask bnfisprincipal to compute the compact form and then -+ # convert this compact form back into an expanded form. -+ # (though calling with 3 instead of 5 most likely triggers an error with memory allocation failure) -+ v = bnf.bnfisprincipal(self.pari_hnf(), 5) -+ e = v[0] -+ t = v[1] -+ t = bnf.nfbasistoalg(bnf.nffactorback(t)) -+ self._ideal_class_log = list(e) -+ self._is_principal = not any(self._ideal_class_log) -+ -+ if self._is_principal: -+ g = self.number_field()(t) -+ self._reduced_generators = (g,) -+ elif gens: -+ # Non-principal ideal - self._reduced_generators = self.gens_two() - - def is_principal(self, proof=None): -@@ -2176,6 +2191,14 @@ class NumberFieldFractionalIdeal(MultiplicativeGroupElement, NumberFieldIdeal): - sage: len(list(K.primes_above(3)[0].invertible_residues())) - 80 - -+ TESTS: -+ -+ Check that the integrality is not lost, cf. :trac:`30801`:: -+ -+ sage: K.<a> = NumberField(x^2 + x + 1) -+ sage: list(K.ideal(8).invertible_residues())[:5] -+ [1, a - 1, -3*a, -2*a + 3, -a - 1] -+ - AUTHOR: John Cremona - """ - return self.invertible_residues_mod(subgp_gens=None, reduce=reduce) -@@ -2262,7 +2285,7 @@ class NumberFieldFractionalIdeal(MultiplicativeGroupElement, NumberFieldIdeal): - A, U, V = M.smith_form() - - V = V.inverse() -- new_basis = [prod([g[j]**V[i, j] for j in range(n)]) for i in range(n)] -+ new_basis = [prod([g[j]**(V[i, j] % invs[j]) for j in range(n)]) for i in range(n)] - - if reduce: - combo = lambda c: self.small_residue(prod(new_basis[i] ** c[i] -@@ -3121,7 +3144,7 @@ class NumberFieldFractionalIdeal(MultiplicativeGroupElement, NumberFieldIdeal): - sage: K.<a> = NumberField(x^5 + 2); K - Number Field in a with defining polynomial x^5 + 2 - sage: f = K.factor(19); f -- (Fractional ideal (a^2 + a - 3)) * (Fractional ideal (-2*a^4 - a^2 + 2*a - 1)) * (Fractional ideal (a^2 + a - 1)) -+ (Fractional ideal (a^2 + a - 3)) * (Fractional ideal (2*a^4 + a^2 - 2*a + 1)) * (Fractional ideal (a^2 + a - 1)) - sage: [i.residue_class_degree() for i, _ in f] - [2, 2, 1] - """ -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 37c20150ad..078682fa1f 100644 ---- a/src/sage/rings/number_field/number_field_ideal_rel.py -+++ b/src/sage/rings/number_field/number_field_ideal_rel.py -@@ -18,7 +18,7 @@ EXAMPLES:: - sage: G = [from_A(z) for z in I.gens()]; G - [7, -2*b*a - 1] - sage: K.fractional_ideal(G) -- Fractional ideal (2*b*a + 1) -+ Fractional ideal ((1/2*b + 2)*a - 1/2*b + 2) - sage: K.fractional_ideal(G).absolute_norm().factor() - 7^2 - """ -diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py -index e103bd8e59..3097a98002 100644 ---- a/src/sage/rings/number_field/number_field_rel.py -+++ b/src/sage/rings/number_field/number_field_rel.py -@@ -396,18 +396,18 @@ class NumberField_relative(NumberField_generic): - sage: K.<c> = F.extension(Y^2 - (1 + a)*(a + b)*a*b) - sage: K.subfields(2) - [ -- (Number Field in c0 with defining polynomial x^2 - 24*x + 72, Ring morphism: -- From: Number Field in c0 with defining polynomial x^2 - 24*x + 72 -+ (Number Field in c0 with defining polynomial x^2 - 24*x + 96, Ring morphism: -+ From: Number Field in c0 with defining polynomial x^2 - 24*x + 96 - To: Number Field in c with defining polynomial Y^2 + (-2*b - 3)*a - 2*b - 6 over its base field -- Defn: c0 |--> -6*a + 12, None), -+ Defn: c0 |--> -4*b + 12, None), - (Number Field in c1 with defining polynomial x^2 - 24*x + 120, Ring morphism: - From: Number Field in c1 with defining polynomial x^2 - 24*x + 120 - To: Number Field in c with defining polynomial Y^2 + (-2*b - 3)*a - 2*b - 6 over its base field - Defn: c1 |--> 2*b*a + 12, None), -- (Number Field in c2 with defining polynomial x^2 - 24*x + 96, Ring morphism: -- From: Number Field in c2 with defining polynomial x^2 - 24*x + 96 -+ (Number Field in c2 with defining polynomial x^2 - 24*x + 72, Ring morphism: -+ From: Number Field in c2 with defining polynomial x^2 - 24*x + 72 - To: Number Field in c with defining polynomial Y^2 + (-2*b - 3)*a - 2*b - 6 over its base field -- Defn: c2 |--> -4*b + 12, None) -+ Defn: c2 |--> -6*a + 12, None) - ] - sage: K.subfields(8, 'w') - [ -diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py -index b5cdeb2a96..be1548f7a2 100644 ---- a/src/sage/rings/number_field/order.py -+++ b/src/sage/rings/number_field/order.py -@@ -2180,7 +2180,7 @@ def EisensteinIntegers(names="omega"): - sage: R - Eisenstein Integers in Number Field in omega with defining polynomial x^2 + x + 1 with omega = -0.50000000000000000? + 0.866025403784439?*I - sage: factor(3 + omega) -- (omega) * (-3*omega - 2) -+ (-1) * (-omega - 3) - sage: CC(omega) - -0.500000000000000 + 0.866025403784439*I - sage: omega.minpoly() -diff --git a/src/sage/rings/number_field/unit_group.py b/src/sage/rings/number_field/unit_group.py -index d0508258a0..6dd6b68cb3 100644 ---- a/src/sage/rings/number_field/unit_group.py -+++ b/src/sage/rings/number_field/unit_group.py -@@ -15,12 +15,12 @@ The first generator is a primitive root of unity in the field:: - sage: UK.gens_values() # random - [-1/12*a^3 + 1/6*a, 1/24*a^3 + 1/4*a^2 - 1/12*a - 1] - sage: UK.gen(0).value() -- -1/12*a^3 + 1/6*a -+ 1/12*a^3 - 1/6*a - - sage: UK.gen(0) - u0 - sage: UK.gen(0) + K.one() # coerce abstract generator into number field -- -1/12*a^3 + 1/6*a + 1 -+ 1/12*a^3 - 1/6*a + 1 - - sage: [u.multiplicative_order() for u in UK.gens()] - [4, +Infinity] -@@ -37,18 +37,18 @@ as elements of an abstract multiplicative group:: - sage: UK(-1) - u0^2 - sage: [UK(u) for u in (x^4-1).roots(K, multiplicities=False)] -- [1, u0^2, u0^3, u0] -+ [1, u0^2, u0, u0^3] - - sage: UK.fundamental_units() # random - [1/24*a^3 + 1/4*a^2 - 1/12*a - 1] - sage: torsion_gen = UK.torsion_generator(); torsion_gen - u0 - sage: torsion_gen.value() -- -1/12*a^3 + 1/6*a -+ 1/12*a^3 - 1/6*a - sage: UK.zeta_order() - 4 - sage: UK.roots_of_unity() -- [-1/12*a^3 + 1/6*a, -1, 1/12*a^3 - 1/6*a, 1] -+ [1/12*a^3 - 1/6*a, -1, -1/12*a^3 + 1/6*a, 1] - - Exp and log functions provide maps between units as field elements and exponent - vectors with respect to the generators:: -@@ -82,7 +82,7 @@ S-unit groups may be constructed, where S is a set of primes:: - sage: SUK.rank() - 4 - sage: SUK.gens_values() -- [-1, a^2 + 1, a^5 + a^4 - a^2 - a - 1, a + 1, -a + 1] -+ [-1, a^2 + 1, -a^5 - a^4 + a^2 + a + 1, a + 1, a - 1] - sage: u = 9*prod(SUK.gens_values()); u - -18*a^5 - 18*a^4 - 18*a^3 - 9*a^2 + 9*a + 27 - sage: SUK.log(u) -@@ -100,29 +100,29 @@ A relative number field example:: - sage: UL.zeta_order() - 24 - sage: UL.roots_of_unity() -- [-b*a - b, -- b^2*a, -- b^3, -- a + 1, -- -b*a, -- -b^2, -- b^3*a + b^3, -- a, -- b, -+ [-b*a, - -b^2*a - b^2, -- b^3*a, -- -1, -- b*a + b, -- -b^2*a, - -b^3, -- -a - 1, -- b*a, -- b^2, -- -b^3*a - b^3, - -a, -+ -b*a - b, -+ -b^2, -+ b^3*a, -+ -a - 1, - -b, -+ b^2*a, -+ b^3*a + b^3, -+ -1, -+ b*a, - b^2*a + b^2, -+ b^3, -+ a, -+ b*a + b, -+ b^2, - -b^3*a, -+ a + 1, -+ b, -+ -b^2*a, -+ -b^3*a - b^3, - 1] - - A relative extension example, which worked thanks to the code review by F.W.Clarke:: -@@ -199,7 +199,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: UK.gen(5) - u5 - sage: UK.gen(5).value() -- z^7 + z -+ -z^7 - z - - An S-unit group:: - -@@ -216,7 +216,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: SUK.zeta_order() - 26 - sage: SUK.log(21*z) -- (12, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1) -+ (25, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1) - """ - # This structure is not a parent in the usual sense. The - # "elements" are NumberFieldElement_absolute. Instead, they should -@@ -250,7 +250,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: UK.gens() - (u0, u1) - sage: UK.gens_values() -- [-1, 6*a - 37] -+ [-1, -6*a + 37] - - sage: K.<a> = QuadraticField(-3) - sage: UK = K.unit_group(); UK -@@ -258,7 +258,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: UK.gens() - (u,) - sage: UK.gens_values() -- [1/2*a + 1/2] -+ [-1/2*a + 1/2] - - sage: K.<z> = CyclotomicField(13) - sage: UK = K.unit_group(); UK -@@ -329,28 +329,25 @@ class UnitGroup(AbelianGroupWithValues_class): - - # compute the additional S-unit generators: - if S: -- self.__S_unit_data = pK.bnfsunit(pS) -- su = [K(u, check=False) for u in self.__S_unit_data[0]] -+ self.__S_unit_data = pK.bnfunits(pS) - else: -- su = [] -- self.__nsu = len(su) -+ self.__S_unit_data = pK.bnfunits() -+ # TODO: converting the factored matrix representation of bnfunits into polynomial -+ # form is a *big* waste of time -+ su_fu_tu = [pK.nfbasistoalg(pK.nffactorback(z)) for z in self.__S_unit_data[0]] -+ -+ self.__nfu = len(pK.bnf_get_fu()) # number of fundamental units -+ self.__nsu = len(su_fu_tu) - self.__nfu - 1 # number of S-units -+ self.__ntu = pK.bnf_get_tu()[0] # order of torsion - self.__rank = self.__nfu + self.__nsu - -- # compute a torsion generator and pick the 'simplest' one: -- n, z = pK[7][3] # number of roots of unity and bnf.tu as in pari documentation -- n = ZZ(n) -- self.__ntu = n -- z = K(z, check=False) -- -- # If we replaced z by another torsion generator we would need -- # to allow for this in the dlog function! So we do not. -+ # Move the torsion unit first, then fundamental units then S-units -+ gens = [K(u, check=False) for u in su_fu_tu] -+ gens = [gens[-1]] + gens[self.__nsu:-1] + gens[:self.__nsu] - -- # Store the actual generators (torsion first): -- gens = [z] + fu + su -- values = Sequence(gens, immutable=True, universe=self, check=False) - # Construct the abstract group: -- gens_orders = tuple([ZZ(n)]+[ZZ(0)]*(self.__rank)) -- AbelianGroupWithValues_class.__init__(self, gens_orders, 'u', values, number_field) -+ gens_orders = tuple([ZZ(self.__ntu)]+[ZZ(0)]*(self.__rank)) -+ AbelianGroupWithValues_class.__init__(self, gens_orders, 'u', gens, number_field) - - def _element_constructor_(self, u): - """ -@@ -375,7 +372,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: UK.gens() - (u0, u1) - sage: UK.gens_values() -- [-1, 6*a - 37] -+ [-1, -6*a + 37] - sage: UK.ngens() - 2 - sage: [UK(u) for u in UK.gens()] -@@ -394,8 +391,8 @@ class UnitGroup(AbelianGroupWithValues_class): - except TypeError: - raise ValueError("%s is not an element of %s"%(u,K)) - if self.__S: -- m = pK.bnfissunit(self.__S_unit_data, pari(u)).mattranspose() -- if m.ncols()==0: -+ m = pK.bnfisunit(pari(u), self.__S_unit_data).mattranspose() -+ if m.ncols() == 0: - raise ValueError("%s is not an S-unit"%u) - else: - if not u.is_integral() or u.norm().abs() != 1: -@@ -405,9 +402,8 @@ class UnitGroup(AbelianGroupWithValues_class): - # convert column matrix to a list: - m = [ZZ(m[0,i].sage()) for i in range(m.ncols())] - -- # NB pari puts the torsion after the fundamental units, before -- # the extra S-units but we have the torsion first: -- m = [m[self.__nfu]] + m[:self.__nfu] + m[self.__nfu+1:] -+ # NOTE: pari ordering for the units is (S-units, fundamental units, torsion unit) -+ m = [m[-1]] + m[self.__nsu:-1] + m[:self.__nsu] - - return self.element_class(self, m) - -@@ -527,9 +523,9 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: U.zeta(2, all=True) - [-1] - sage: U.zeta(3) -- 1/2*z - 1/2 -+ -1/2*z - 1/2 - sage: U.zeta(3, all=True) -- [1/2*z - 1/2, -1/2*z - 1/2] -+ [-1/2*z - 1/2, 1/2*z - 1/2] - sage: U.zeta(4) - Traceback (most recent call last): - ... -@@ -645,7 +641,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: SUK = UnitGroup(K,S=2) - sage: v = (3,1,4,1,5,9,2) - sage: u = SUK.exp(v); u -- -8732*z^11 + 15496*z^10 + 51840*z^9 + 68804*z^8 + 51840*z^7 + 15496*z^6 - 8732*z^5 + 34216*z^3 + 64312*z^2 + 64312*z + 34216 -+ 8732*z^11 - 15496*z^10 - 51840*z^9 - 68804*z^8 - 51840*z^7 - 15496*z^6 + 8732*z^5 - 34216*z^3 - 64312*z^2 - 64312*z - 34216 - sage: SUK.log(u) - (3, 1, 4, 1, 5, 9, 2) - sage: SUK.log(u) == v -@@ -692,7 +688,7 @@ class UnitGroup(AbelianGroupWithValues_class): - sage: SUK = UnitGroup(K,S=2) - sage: v = (3,1,4,1,5,9,2) - sage: u = SUK.exp(v); u -- -8732*z^11 + 15496*z^10 + 51840*z^9 + 68804*z^8 + 51840*z^7 + 15496*z^6 - 8732*z^5 + 34216*z^3 + 64312*z^2 + 64312*z + 34216 -+ 8732*z^11 - 15496*z^10 - 51840*z^9 - 68804*z^8 - 51840*z^7 - 15496*z^6 + 8732*z^5 - 34216*z^3 - 64312*z^2 - 64312*z - 34216 - sage: SUK.log(u) - (3, 1, 4, 1, 5, 9, 2) - sage: SUK.log(u) == v -diff --git a/src/sage/rings/padics/relaxed_template.pxi b/src/sage/rings/padics/relaxed_template.pxi -index ba15d4f5d3..9ef4ea4e70 100644 ---- a/src/sage/rings/padics/relaxed_template.pxi -+++ b/src/sage/rings/padics/relaxed_template.pxi -@@ -2637,9 +2637,9 @@ cdef class RelaxedElement_random(RelaxedElementWithDigits): - - It is guaranteed that `a` and `b` are equal at any precision:: - -- sage: a[:30] -+ sage: a[:30] # random - ...?343214211432220241412003314311 -- sage: b[:30] -+ sage: b[:30] # random - ...?343214211432220241412003314311 - - sage: a == b -diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx -index 570c148e72..17f3ec8da9 100644 ---- a/src/sage/rings/polynomial/polynomial_element.pyx -+++ b/src/sage/rings/polynomial/polynomial_element.pyx -@@ -7619,7 +7619,7 @@ cdef class Polynomial(CommutativeAlgebraElement): - [(-3.5074662110434039?e451, 1)] - sage: p = bigc*x + 1 - sage: p.roots(ring=RR) -- [(0.000000000000000, 1)] -+ [(-2.85106096489671e-452, 1)] - sage: p.roots(ring=AA) - [(-2.8510609648967059?e-452, 1)] - sage: p.roots(ring=QQbar) -diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py -index bc65b286e8..315716afbc 100644 ---- a/src/sage/rings/polynomial/polynomial_quotient_ring.py -+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py -@@ -1324,7 +1324,7 @@ class PolynomialQuotientRing_generic(CommutativeRing): - `x^2 + 31` from 12 to 2, i.e. we lose a generator of order 6 (this was - fixed in :trac:`14489`):: - -- sage: S.S_class_group([K.ideal(a)]) -+ sage: S.S_class_group([K.ideal(a)]) # representation varies, not tested - [((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), 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), 2)] - - Note that all the returned values live where we expect them to:: -diff --git a/src/sage/sandpiles/sandpile.py b/src/sage/sandpiles/sandpile.py -index ad1cc56276..ce4e7fdc9b 100644 ---- a/src/sage/sandpiles/sandpile.py -+++ b/src/sage/sandpiles/sandpile.py -@@ -1494,12 +1494,12 @@ class Sandpile(DiGraph): - - sage: s = sandpiles.Cycle(5) - sage: s.group_gens() -- [{1: 1, 2: 1, 3: 1, 4: 0}] -+ [{1: 0, 2: 1, 3: 1, 4: 1}] - sage: s.group_gens()[0].order() - 5 - sage: s = sandpiles.Complete(5) - sage: s.group_gens(False) -- [[2, 2, 3, 2], [2, 3, 2, 2], [3, 2, 2, 2]] -+ [[2, 3, 2, 2], [2, 2, 3, 2], [2, 2, 2, 3]] - sage: [i.order() for i in s.group_gens()] - [5, 5, 5] - sage: s.invariant_factors() -@@ -2817,7 +2817,7 @@ class Sandpile(DiGraph): - - sage: S = sandpiles.Complete(4) - sage: S.points() -- [[1, I, -I], [I, 1, -I]] -+ [[-I, I, 1], [-I, 1, I]] - """ - return self._points - -@@ -5015,7 +5015,7 @@ class SandpileDivisor(dict): - sage: D.is_linearly_equivalent([0,1,1]) - True - sage: D.is_linearly_equivalent([0,1,1],True) -- (1, 0, 0) -+ (0, -1, -1) - sage: v = vector(D.is_linearly_equivalent([0,1,1],True)) - sage: vector(D.values()) - s.laplacian()*v - (0, 1, 1) -@@ -6646,8 +6646,8 @@ def wilmes_algorithm(M): - - sage: P = matrix([[2,3,-7,-3],[5,2,-5,5],[8,2,5,4],[-5,-9,6,6]]) - sage: wilmes_algorithm(P) -- [ 1642 -13 -1627 -1] -- [ -1 1980 -1582 -397] -+ [ 3279 -79 -1599 -1600] -+ [ -1 1539 -136 -1402] - [ 0 -1 1650 -1649] - [ 0 0 -1658 1658] - -diff --git a/src/sage/schemes/elliptic_curves/ell_finite_field.py b/src/sage/schemes/elliptic_curves/ell_finite_field.py -index 2aca9491af..76b111b423 100644 ---- a/src/sage/schemes/elliptic_curves/ell_finite_field.py -+++ b/src/sage/schemes/elliptic_curves/ell_finite_field.py -@@ -785,11 +785,13 @@ class EllipticCurve_finite_field(EllipticCurve_field, HyperellipticCurve_finite_ - sage: len(E.gens()) - 2 - sage: E.cardinality() -- 867361737988403547207212930746733987710588 -- sage: E.gens()[0].order() -- 433680868994201773603606465373366993855294 -- sage: E.gens()[1].order() -- 433680868994201773603606465373366993855294 -+ 867361737988403547206134229616487867594472 -+ sage: a = E.gens()[0].order(); a # random -+ 433680868994201773603067114808243933797236 -+ sage: b = E.gens()[1].order(); b # random -+ 30977204928157269543076222486303138128374 -+ sage: lcm(a,b) -+ 433680868994201773603067114808243933797236 - """ - G = self.__pari__().ellgroup(flag=1) - return tuple(self.point(list(pt)) for pt in G[2]) -diff --git a/src/sage/schemes/elliptic_curves/ell_generic.py b/src/sage/schemes/elliptic_curves/ell_generic.py -index 7b02e8f663..a1a48d2397 100644 ---- a/src/sage/schemes/elliptic_curves/ell_generic.py -+++ b/src/sage/schemes/elliptic_curves/ell_generic.py -@@ -527,7 +527,7 @@ class EllipticCurve_generic(WithEqualityById, plane_curve.ProjectivePlaneCurve): - sage: E = EllipticCurve([0,0,0,-49,0]) - sage: T = E.torsion_subgroup() - sage: [E(t) for t in T] -- [(0 : 1 : 0), (-7 : 0 : 1), (0 : 0 : 1), (7 : 0 : 1)] -+ [(0 : 1 : 0), (0 : 0 : 1), (-7 : 0 : 1), (7 : 0 : 1)] - - :: - -@@ -2951,8 +2951,8 @@ class EllipticCurve_generic(WithEqualityById, plane_curve.ProjectivePlaneCurve): - Mod(-928, y^2 - 2), Mod(3456/29, y^2 - 2), Vecsmall([5]), - [[y^2 - 2, [2, 0], 8, 1, [[1, -1.41421356237310; - 1, 1.41421356237310], [1, -1.41421356237310; 1, 1.41421356237310], -- [1, -1; 1, 1], [2, 0; 0, 4], [4, 0; 0, 2], [2, 0; 0, 1], -- [2, [0, 2; 1, 0]], []], [-1.41421356237310, 1.41421356237310], -+ [16, -23; 16, 23], [2, 0; 0, 4], [4, 0; 0, 2], [2, 0; 0, 1], -+ [2, [0, 2; 1, 0]], [2]], [-1.41421356237310, 1.41421356237310], - [1, y], [1, 0; 0, 1], [1, 0, 0, 2; 0, 1, 1, 0]]], [0, 0, 0, 0, 0]] - - PARI no longer requires that the `j`-invariant has negative `p`-adic valuation:: -diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py -index 29316bebeb..ccfa33915a 100644 ---- a/src/sage/schemes/elliptic_curves/ell_number_field.py -+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py -@@ -214,9 +214,9 @@ class EllipticCurve_number_field(EllipticCurve_field): - sage: E == loads(dumps(E)) - True - sage: E.simon_two_descent() -- (2, 2, [(0 : 0 : 1), (1/8*a + 5/8 : -3/16*a - 7/16 : 1)]) -- sage: E.simon_two_descent(lim1=3, lim3=20, limtriv=5, maxprob=7, limbigprime=10) -- (2, 2, [(-1 : 0 : 1), (-1/8*a + 5/8 : -3/16*a - 9/16 : 1)]) -+ (2, 2, [(0 : 0 : 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)]) - - :: - -@@ -238,35 +238,7 @@ class EllipticCurve_number_field(EllipticCurve_field): - K = bnfinit(y^2 + 7); - a = Mod(y,K.pol); - bnfellrank(K, [0, 0, 0, 1, a], [[Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)]]); -- elliptic curve: Y^2 = x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7) -- A = Mod(0, y^2 + 7) -- B = Mod(1, y^2 + 7) -- C = Mod(y, y^2 + 7) -- <BLANKLINE> -- Computing L(S,2) -- L(S,2) = [Mod(Mod(-1/2*y + 1/2, y^2 + 7)*x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + Mod(-y - 1, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(-x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(-1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(x^2 + 2, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(x + Mod(1/2*y + 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(x + Mod(1/2*y - 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))] -- <BLANKLINE> -- Computing the Selmer group -- #LS2gen = 2 -- LS2gen = [Mod(Mod(-1/2*y + 1/2, y^2 + 7)*x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + Mod(-y - 1, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(x^2 + Mod(1/2*y + 1/2, y^2 + 7)*x - 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))] -- Search for trivial points on the curve -- Trivial points on the curve = [[Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)], [1, 1, 0], [Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7), 1]] -- zc = Mod(Mod(-1/2*y + 1/2, y^2 + 7)*x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + Mod(-y - 1, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)) -- Hilbert symbol (Mod(1, y^2 + 7),Mod(-2*y + 2, y^2 + 7)) = -- sol of quadratic equation = [1, 1, 0]~ -- zc*z1^2 = Mod(4*x + Mod(-2*y + 6, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)) -- quartic: (-1)*Y^2 = x^4 + (3*y - 9)*x^2 + (-8*y + 16)*x + (9/2*y - 11/2) -- reduced: Y^2 = -x^4 + (-3*y + 9)*x^2 + (-8*y + 16)*x + (-9/2*y + 11/2) -- not ELS at [2, [0, 1]~, 1, 1, [1, -2; 1, 0]] -- zc = Mod(Mod(1, y^2 + 7)*x^2 + Mod(1/2*y + 1/2, y^2 + 7)*x + Mod(-1, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)) -- comes from the trivial point [Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)] -- m1 = 1 -- m2 = 1 -- #S(E/K)[2] = 2 -- #E(K)/2E(K) = 2 -- #III(E/K)[2] = 1 -- rank(E/K) = 1 -- listpoints = [[Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)]] -+ ... - v = [1, 1, [[Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)]]] - sage: v - (1, 1, [(1/2*a + 3/2 : -a - 2 : 1)]) -@@ -298,8 +270,8 @@ class EllipticCurve_number_field(EllipticCurve_field): - sage: E.simon_two_descent() # long time (4s on sage.math, 2013) - (3, - 3, -- [(0 : 0 : 1), -- (-1/2*zeta43_0^2 - 1/2*zeta43_0 + 7 : -3/2*zeta43_0^2 - 5/2*zeta43_0 + 18 : 1)...) -+ [(5/8*zeta43_0^2 + 17/8*zeta43_0 - 9/4 : -27/16*zeta43_0^2 - 103/16*zeta43_0 + 39/8 : 1), -+ (0 : 0 : 1)]) - """ - verbose = int(verbose) - if known_points is None: -@@ -2228,29 +2200,29 @@ class EllipticCurve_number_field(EllipticCurve_field): - sage: EK = E.base_extend(K) - sage: EK.torsion_points() # long time (1s on sage.math, 2014) - [(0 : 1 : 0), -- (16 : 60 : 1), -- (5 : 5 : 1), -- (5 : -6 : 1), -- (16 : -61 : 1), - (t : 1/11*t^3 + 6/11*t^2 + 19/11*t + 48/11 : 1), -- (-3/55*t^3 - 7/55*t^2 - 2/55*t - 133/55 : 6/55*t^3 + 3/55*t^2 + 25/11*t + 156/55 : 1), -- (-9/121*t^3 - 21/121*t^2 - 127/121*t - 377/121 : -7/121*t^3 + 24/121*t^2 + 197/121*t + 16/121 : 1), -- (5/121*t^3 - 14/121*t^2 - 158/121*t - 453/121 : -49/121*t^3 - 129/121*t^2 - 315/121*t - 207/121 : 1), -- (10/121*t^3 + 49/121*t^2 + 168/121*t + 73/121 : 32/121*t^3 + 60/121*t^2 - 261/121*t - 807/121 : 1), - (1/11*t^3 - 5/11*t^2 + 19/11*t - 40/11 : -6/11*t^3 - 3/11*t^2 - 26/11*t - 321/11 : 1), -- (14/121*t^3 - 15/121*t^2 + 90/121*t + 232/121 : 16/121*t^3 - 69/121*t^2 + 293/121*t - 46/121 : 1), -- (3/55*t^3 + 7/55*t^2 + 2/55*t + 78/55 : 7/55*t^3 - 24/55*t^2 + 9/11*t + 17/55 : 1), -- (-5/121*t^3 + 36/121*t^2 - 84/121*t + 24/121 : 34/121*t^3 - 27/121*t^2 + 305/121*t + 708/121 : 1), -- (-26/121*t^3 + 20/121*t^2 - 219/121*t - 995/121 : 15/121*t^3 + 156/121*t^2 - 232/121*t + 2766/121 : 1), - (1/11*t^3 - 5/11*t^2 + 19/11*t - 40/11 : 6/11*t^3 + 3/11*t^2 + 26/11*t + 310/11 : 1), -- (-26/121*t^3 + 20/121*t^2 - 219/121*t - 995/121 : -15/121*t^3 - 156/121*t^2 + 232/121*t - 2887/121 : 1), -- (-5/121*t^3 + 36/121*t^2 - 84/121*t + 24/121 : -34/121*t^3 + 27/121*t^2 - 305/121*t - 829/121 : 1), -- (3/55*t^3 + 7/55*t^2 + 2/55*t + 78/55 : -7/55*t^3 + 24/55*t^2 - 9/11*t - 72/55 : 1), -- (14/121*t^3 - 15/121*t^2 + 90/121*t + 232/121 : -16/121*t^3 + 69/121*t^2 - 293/121*t - 75/121 : 1), - (t : -1/11*t^3 - 6/11*t^2 - 19/11*t - 59/11 : 1), -+ (16 : 60 : 1), -+ (-3/55*t^3 - 7/55*t^2 - 2/55*t - 133/55 : 6/55*t^3 + 3/55*t^2 + 25/11*t + 156/55 : 1), -+ (14/121*t^3 - 15/121*t^2 + 90/121*t + 232/121 : 16/121*t^3 - 69/121*t^2 + 293/121*t - 46/121 : 1), -+ (-26/121*t^3 + 20/121*t^2 - 219/121*t - 995/121 : -15/121*t^3 - 156/121*t^2 + 232/121*t - 2887/121 : 1), - (10/121*t^3 + 49/121*t^2 + 168/121*t + 73/121 : -32/121*t^3 - 60/121*t^2 + 261/121*t + 686/121 : 1), -+ (5 : 5 : 1), -+ (-9/121*t^3 - 21/121*t^2 - 127/121*t - 377/121 : -7/121*t^3 + 24/121*t^2 + 197/121*t + 16/121 : 1), -+ (3/55*t^3 + 7/55*t^2 + 2/55*t + 78/55 : 7/55*t^3 - 24/55*t^2 + 9/11*t + 17/55 : 1), -+ (-5/121*t^3 + 36/121*t^2 - 84/121*t + 24/121 : -34/121*t^3 + 27/121*t^2 - 305/121*t - 829/121 : 1), - (5/121*t^3 - 14/121*t^2 - 158/121*t - 453/121 : 49/121*t^3 + 129/121*t^2 + 315/121*t + 86/121 : 1), -+ (5 : -6 : 1), -+ (5/121*t^3 - 14/121*t^2 - 158/121*t - 453/121 : -49/121*t^3 - 129/121*t^2 - 315/121*t - 207/121 : 1), -+ (-5/121*t^3 + 36/121*t^2 - 84/121*t + 24/121 : 34/121*t^3 - 27/121*t^2 + 305/121*t + 708/121 : 1), -+ (3/55*t^3 + 7/55*t^2 + 2/55*t + 78/55 : -7/55*t^3 + 24/55*t^2 - 9/11*t - 72/55 : 1), - (-9/121*t^3 - 21/121*t^2 - 127/121*t - 377/121 : 7/121*t^3 - 24/121*t^2 - 197/121*t - 137/121 : 1), -+ (16 : -61 : 1), -+ (10/121*t^3 + 49/121*t^2 + 168/121*t + 73/121 : 32/121*t^3 + 60/121*t^2 - 261/121*t - 807/121 : 1), -+ (-26/121*t^3 + 20/121*t^2 - 219/121*t - 995/121 : 15/121*t^3 + 156/121*t^2 - 232/121*t + 2766/121 : 1), -+ (14/121*t^3 - 15/121*t^2 + 90/121*t + 232/121 : -16/121*t^3 + 69/121*t^2 - 293/121*t - 75/121 : 1), - (-3/55*t^3 - 7/55*t^2 - 2/55*t - 133/55 : -6/55*t^3 - 3/55*t^2 - 25/11*t - 211/55 : 1)] - - :: -diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py -index 1ce8323e1b..5a6bcdf7ee 100644 ---- a/src/sage/schemes/elliptic_curves/ell_rational_field.py -+++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py -@@ -4082,7 +4082,7 @@ class EllipticCurve_rational_field(EllipticCurve_number_field): - sage: G.1 - (282 : 0 : 1) - sage: list(G) -- [(0 : 1 : 0), (147 : 12960 : 1), (2307 : 97200 : 1), (-933 : 29160 : 1), (1011 : 0 : 1), (-933 : -29160 : 1), (2307 : -97200 : 1), (147 : -12960 : 1), (282 : 0 : 1), (8787 : 816480 : 1), (-285 : 27216 : 1), (1227 : 22680 : 1), (-1293 : 0 : 1), (1227 : -22680 : 1), (-285 : -27216 : 1), (8787 : -816480 : 1)] -+ [(0 : 1 : 0), (147 : -12960 : 1), (2307 : -97200 : 1), (-933 : -29160 : 1), (1011 : 0 : 1), (-933 : 29160 : 1), (2307 : 97200 : 1), (147 : 12960 : 1), (-1293 : 0 : 1), (1227 : 22680 : 1), (-285 : 27216 : 1), (8787 : 816480 : 1), (282 : 0 : 1), (8787 : -816480 : 1), (-285 : -27216 : 1), (1227 : -22680 : 1)] - """ - try: - G = self.__torsion_subgroup -@@ -5405,10 +5405,10 @@ class EllipticCurve_rational_field(EllipticCurve_number_field): - EXAMPLES:: - - sage: E = EllipticCurve('37a1') -- sage: E.eval_modular_form([1.5+I,2.0+I,2.5+I],100) # abs tol 1e-20 -- [-0.0018743978548152085771342944989052703431, -- 0.0018604485340371083710285594393397945456, -- -0.0018743978548152085771342944989052703431] -+ sage: E.eval_modular_form([1.5+I,2.0+I,2.5+I],100) -+ [-0.0018743978548152085..., -+ 0.0018604485340371083..., -+ -0.0018743978548152085...] - - sage: E.eval_modular_form(2.1+I, 100) # abs tol 1e-16 - [0.00150864362757267079 + 0.00109100341113449845*I] -diff --git a/src/sage/schemes/elliptic_curves/ell_torsion.py b/src/sage/schemes/elliptic_curves/ell_torsion.py -index 7f6f0f9701..33265f11d7 100644 ---- a/src/sage/schemes/elliptic_curves/ell_torsion.py -+++ b/src/sage/schemes/elliptic_curves/ell_torsion.py -@@ -84,7 +84,7 @@ class EllipticCurveTorsionSubgroup(groups.AdditiveAbelianGroupWrapper): - sage: E = EllipticCurve([0,0,0,-49,0]) - sage: T = E.torsion_subgroup() - sage: [E(t) for t in T] -- [(0 : 1 : 0), (-7 : 0 : 1), (0 : 0 : 1), (7 : 0 : 1)] -+ [(0 : 1 : 0), (0 : 0 : 1), (-7 : 0 : 1), (7 : 0 : 1)] - - An example where the torsion subgroup is trivial:: - -@@ -256,7 +256,7 @@ class EllipticCurveTorsionSubgroup(groups.AdditiveAbelianGroupWrapper): - sage: E = EllipticCurve(K,[0,0,0,1,0]) - sage: tor = E.torsion_subgroup() - sage: tor.points() -- [(0 : 1 : 0), (-i : 0 : 1), (0 : 0 : 1), (i : 0 : 1)] -+ [(0 : 1 : 0), (0 : 0 : 1), (-i : 0 : 1), (i : 0 : 1)] - """ - return [x.element() for x in self] - -diff --git a/src/sage/schemes/elliptic_curves/isogeny_small_degree.py b/src/sage/schemes/elliptic_curves/isogeny_small_degree.py -index 7178da3685..8342d92ed3 100644 ---- a/src/sage/schemes/elliptic_curves/isogeny_small_degree.py -+++ b/src/sage/schemes/elliptic_curves/isogeny_small_degree.py -@@ -801,8 +801,8 @@ def isogenies_5_0(E, minimal_models=True): - sage: K.<a> = NumberField(x**6-320*x**3-320) - sage: E = EllipticCurve(K,[0,0,1,0,0]) - sage: isogenies_5_0(E) -- [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 + (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 + (-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] -+ [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 + (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) 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) over Number Field in a with defining polynomial x^6 - 320*x^3 - 320] - """ - F = E.base_field() - if E.j_invariant() != 0: -diff --git a/src/sage/schemes/elliptic_curves/period_lattice.py b/src/sage/schemes/elliptic_curves/period_lattice.py -index 0f1d17f995..fe1899f647 100644 ---- a/src/sage/schemes/elliptic_curves/period_lattice.py -+++ b/src/sage/schemes/elliptic_curves/period_lattice.py -@@ -1625,7 +1625,7 @@ class PeriodLattice_ell(PeriodLattice): - sage: P,Q = T[2] - sage: embs = K.embeddings(CC) - sage: Lambda = E.period_lattice(embs[0]) -- sage: Lambda.elliptic_logarithm(P+3*Q, 100) -+ sage: Lambda.elliptic_logarithm(P, 100) - 4.7100131126199672766973600998 - sage: R.<x> = QQ[] - sage: K.<a> = NumberField(x^2 + x + 5) -diff --git a/src/sage/schemes/toric/chow_group.py b/src/sage/schemes/toric/chow_group.py -index 89e82467b0..84d32fe373 100644 ---- a/src/sage/schemes/toric/chow_group.py -+++ b/src/sage/schemes/toric/chow_group.py -@@ -62,7 +62,7 @@ EXAMPLES:: - 7 - sage: a = sum( A.gen(i) * (i+1) for i in range(A.ngens()) ) # an element of A - sage: a # long time (2s on sage.math, 2011) -- ( 3 | 1 mod 7 | 0 mod 2, 1 mod 2, 4, 5, 6, 7, 8 | 9 ) -+ ( 9 | 1 mod 7 | 1 mod 2, 0 mod 2, 4, 5, 6, 7, 8 | 3 ) - - The Chow group elements are printed as ``( a0 | a1 mod 7 | a2 mod 2, - a3 mod 2, a4, a5, a6, a7, a8 | a9 )``, which denotes the element of -@@ -93,13 +93,13 @@ Cones of toric varieties can determine their own Chow cycle:: - sage: cone = X.fan(dim=2)[3]; cone - 2-d cone of Rational polyhedral fan in 3-d lattice N - sage: A_cone = A(cone); A_cone -- ( 0 | 1 mod 7 | 0 mod 2, 0 mod 2, 0, 0, 0, 0, 0 | 0 ) -+ ( 0 | 6 mod 7 | 0 mod 2, 0 mod 2, 0, 0, 0, 0, 0 | 0 ) - sage: A_cone.degree() - 1 - sage: 2 * A_cone -- ( 0 | 2 mod 7 | 0 mod 2, 0 mod 2, 0, 0, 0, 0, 0 | 0 ) -+ ( 0 | 5 mod 7 | 0 mod 2, 0 mod 2, 0, 0, 0, 0, 0 | 0 ) - sage: A_cone + A.gen(0) -- ( 0 | 1 mod 7 | 0 mod 2, 1 mod 2, 0, 0, 0, 0, 0 | 0 ) -+ ( 0 | 6 mod 7 | 1 mod 2, 0 mod 2, 0, 0, 0, 0, 0 | 0 ) - - Chow cycles can be of mixed degrees:: - -@@ -151,7 +151,7 @@ class ChowCycle(FGP_Element): - sage: P2 = toric_varieties.P2() - sage: A = P2.Chow_group() - sage: A.gens() -- (( 1 | 0 | 0 ), ( 0 | 1 | 0 ), ( 0 | 0 | 1 )) -+ (( 0 | 0 | 1 ), ( 0 | 1 | 0 ), ( 1 | 0 | 0 )) - sage: cone = P2.fan(1)[0] - sage: A(cone) - ( 0 | 1 | 0 ) -@@ -199,7 +199,7 @@ class ChowCycle(FGP_Element): - sage: A.degree() - (Z, Z, Z) - sage: A.an_element()._repr_() -- '( 1 | 0 | 0 )' -+ '( 0 | 0 | 1 )' - - A more complicated example with torsion:: - -@@ -208,7 +208,7 @@ class ChowCycle(FGP_Element): - sage: A.degree() - (Z, 0, C2 x Z^5, Z) - sage: sum( A.gen(i) * (i+1) for i in range(A.ngens()) ) -- ( 2 || 1 mod 2, 3, 4, 5, 6, 7 | 8 ) -+ ( 8 || 1 mod 2, 3, 4, 5, 6, 7 | 2 ) - """ - A = self.parent() - s = '(' -@@ -245,7 +245,7 @@ class ChowCycle(FGP_Element): - sage: P2 = toric_varieties.P2() - sage: A = P2.Chow_group() - sage: [ a.degree() for a in A.gens() ] -- [0, 1, 2] -+ [2, 1, 0] - """ - if '_dim' in self.__dict__: - return self._dim -@@ -279,9 +279,9 @@ class ChowCycle(FGP_Element): - sage: A = toric_varieties.P2().Chow_group() - sage: cycle = 10*A.gen(0) + 11*A.gen(1) + 12*A.gen(2) - sage: cycle -- ( 10 | 11 | 12 ) -+ ( 12 | 11 | 10 ) - sage: cycle.project_to_degree(2) -- ( 0 | 0 | 12 ) -+ ( 0 | 0 | 10 ) - """ - ambient_dim = self.parent()._variety.dimension() - v = list(self.lift()) -@@ -307,7 +307,7 @@ class ChowCycle(FGP_Element): - - sage: P2 = toric_varieties.P2() - sage: A = P2.Chow_group() -- sage: a = 5*A.gen(0) + 7*A.gen(1); a -+ sage: a = 5*A.gen(2) + 7*A.gen(1); a - ( 5 | 7 | 0 ) - sage: a.count_points() - 5 -@@ -373,7 +373,7 @@ class ChowCycle(FGP_Element): - V(y) - sage: A = dP6.Chow_group() - sage: A(cone) -- ( 0 | 0, 0, 0, 1 | 0 ) -+ ( 0 | 0, 0, 1, 0 | 0 ) - sage: intersection = A(cone).intersection_with_divisor(D); intersection - ( -1 | 0, 0, 0, 0 | 0 ) - sage: intersection.count_points() -@@ -405,8 +405,8 @@ class ChowCycle(FGP_Element): - ( 0 | 0, 0, 0, 0 | 0 ), ( 0 | 0, 0, 0, 0 | 0 ), - ( 0 | 0, 0, 0, 0 | 0 )] - sage: [ r.intersection_with_divisor(D).lift() for r in dP6.Chow_group().relation_gens() ] -- [(0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0), -- (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), -+ [(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), -+ (0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0), - (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), - (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), - (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), -@@ -504,13 +504,13 @@ class ChowCycle(FGP_Element): - sage: HH = WP4.cohomology_ring() - sage: cone3d = Cone([(0,0,1,0), (0,0,0,1), (-9,-6,-1,-1)]) - sage: A(cone3d) -- ( 0 | 1 | 0 | 0 | 0 ) -+ ( 0 | -1 | 0 | 0 | 0 ) - sage: HH(cone3d) - [3*z4^3] - - sage: D = -WP4.K() # the anticanonical divisor - sage: A(D) -- ( 0 | 0 | 0 | 18 | 0 ) -+ ( 0 | 0 | 0 | -18 | 0 ) - sage: HH(D) - [18*z4] - -@@ -605,7 +605,7 @@ class ChowGroup_class(FGP_Module_class, WithEqualityById): - sage: A = ChowGroup_class(P2,ZZ,True); A - Chow group of 2-d CPR-Fano toric variety covered by 3 affine patches - sage: A.an_element() -- ( 1 | 0 | 0 ) -+ ( 0 | 0 | 1 ) - """ - - Element = ChowCycle -@@ -627,7 +627,7 @@ class ChowGroup_class(FGP_Module_class, WithEqualityById): - - sage: A_ZZ = P2.Chow_group() - sage: 2 * A_ZZ.an_element() * 3 -- ( 6 | 0 | 0 ) -+ ( 0 | 0 | 6 ) - sage: 1/2 * A_ZZ.an_element() * 1/3 - Traceback (most recent call last): - ... -@@ -705,9 +705,9 @@ class ChowGroup_class(FGP_Module_class, WithEqualityById): - sage: A = dP6.Chow_group() - sage: cone = dP6.fan(dim=1)[4] - sage: A(cone) -- ( 0 | 0, 1, 0, 0 | 0 ) -+ ( 0 | 1, 1, 0, -1 | 0 ) - sage: A(Cone(cone)) # isomorphic but not identical to a cone of the fan! -- ( 0 | 0, 1, 0, 0 | 0 ) -+ ( 0 | 1, 1, 0, -1 | 0 ) - sage: A( dP6.K() ) - ( 0 | -1, -2, -2, -1 | 0 ) - """ -@@ -1003,7 +1003,7 @@ class ChowGroup_class(FGP_Module_class, WithEqualityById): - - sage: A = toric_varieties.P2().Chow_group() - sage: A.gens() -- (( 1 | 0 | 0 ), ( 0 | 1 | 0 ), ( 0 | 0 | 1 )) -+ (( 0 | 0 | 1 ), ( 0 | 1 | 0 ), ( 1 | 0 | 0 )) - sage: A.gens(degree=1) - (( 0 | 1 | 0 ),) - """ -diff --git a/src/sage/schemes/toric/divisor.py b/src/sage/schemes/toric/divisor.py -index e03b724ae6..eddbda0d21 100644 ---- a/src/sage/schemes/toric/divisor.py -+++ b/src/sage/schemes/toric/divisor.py -@@ -113,7 +113,7 @@ The (rational) divisor class group is where the Kaehler cone lives:: - in Basis lattice of The toric rational divisor class group - of a 2-d CPR-Fano toric variety covered by 6 affine patches - sage: Kc.ray(1).lift() -- V(y) + V(v) -+ V(x) + V(w) - - Given a divisor `D`, we have an associated line bundle (or a reflexive - sheaf, if `D` is not Cartier) `\mathcal{O}(D)`. Its sections are:: -@@ -1011,10 +1011,10 @@ class ToricDivisor_generic(Divisor_generic): - sage: Cartier - 2*V(z0) + 2*V(z1) + V(z2) + V(z3) + V(z4) - sage: Cartier.move_away_from(line_cone) -- -V(z2) - V(z3) + V(z4) -+ 3*V(z2) + 3*V(z3) - V(z4) - sage: QQ_Weil = X.divisor([1,0,1,1,0]) - sage: QQ_Weil.move_away_from(line_cone) -- V(z2) -+ 2*V(z2) + V(z3) - 1/2*V(z4) - """ - m = self.m(cone) - X = self.parent().scheme() -@@ -1112,9 +1112,9 @@ class ToricDivisor_generic(Divisor_generic): - EXAMPLES:: - - sage: dP6 = toric_varieties.dP6() -- sage: cone = dP6.fan(1)[0] -+ sage: cone = dP6.fan(1)[5] - sage: D = dP6.divisor(cone); D -- V(x) -+ V(w) - sage: D.Chow_cycle() - ( 0 | -1, 0, 1, 1 | 0 ) - sage: dP6.Chow_group()(cone) -@@ -1959,11 +1959,11 @@ class ToricRationalDivisorClassGroup(FreeModule_ambient_field, UniqueRepresentat - [1 1 0 0 0] - [0 2 1 1 1] - sage: Cl._lift_matrix -- [1 0] -- [0 0] -- [0 0] -- [0 1] -- [0 0] -+ [ 0 0] -+ [ 1 0] -+ [ 0 0] -+ [-2 1] -+ [ 0 0] - sage: Cl._lift_matrix.base_ring() - Integer Ring - """ -diff --git a/src/sage/schemes/toric/divisor_class.pyx b/src/sage/schemes/toric/divisor_class.pyx -index f0e6eeca7e..52874594a5 100644 ---- a/src/sage/schemes/toric/divisor_class.pyx -+++ b/src/sage/schemes/toric/divisor_class.pyx -@@ -39,9 +39,9 @@ The only special method is :meth:`~ToricRationalDivisorClass.lift` to get a - divisor representing a divisor class:: - - sage: D.lift() -- V(x) - 2*V(u) + 3*V(y) - 4*V(v) -+ -3*V(x) - 9*V(u) + 7*V(z) + 3*V(w) - sage: E.lift() -- 1/2*V(x) - 2/3*V(u) + 3/4*V(y) - 4/5*V(v) -+ -3/10*V(x) - 133/60*V(u) + 31/20*V(z) + 3/4*V(w) - """ - - -@@ -279,7 +279,7 @@ cdef class ToricRationalDivisorClass(Vector_rational_dense): - sage: D.divisor_class() - Divisor class [29, 6, 8, 10, 0] - sage: Dequiv = D.divisor_class().lift(); Dequiv -- 6*V(z1) - 17*V(z2) - 22*V(z3) - 7*V(z4) + 25*V(z6) + 32*V(z7) -+ 15*V(z1) - 11*V(z2) - 9*V(z5) + 19*V(z6) + 10*V(z7) - sage: Dequiv == D - False - sage: Dequiv.divisor_class() == D.divisor_class() -diff --git a/src/sage/schemes/toric/homset.py b/src/sage/schemes/toric/homset.py -index 4bff92bcb0..f13482bae0 100644 ---- a/src/sage/schemes/toric/homset.py -+++ b/src/sage/schemes/toric/homset.py -@@ -641,7 +641,7 @@ class SchemeHomset_points_subscheme_toric_field(SchemeHomset_points_toric_base): - sage: P2.<x,y,z> = toric_varieties.P2(base_ring=GF(5)) - sage: cubic = P2.subscheme([x^3 + y^3 + z^3]) - sage: list(cubic.point_set()) -- [[0 : 1 : 4], [1 : 0 : 4], [1 : 4 : 0], [1 : 2 : 1], [1 : 1 : 2], [1 : 3 : 3]] -+ [[0 : 1 : 4], [1 : 0 : 4], [1 : 4 : 0], [1 : 1 : 2], [1 : 2 : 1], [1 : 3 : 3]] - sage: cubic.point_set().cardinality() - 6 - """ -@@ -661,7 +661,7 @@ class SchemeHomset_points_subscheme_toric_field(SchemeHomset_points_toric_base): - sage: P2.<x,y,z> = toric_varieties.P2(base_ring=GF(5)) - sage: cubic = P2.subscheme([x^3 + y^3 + z^3]) - sage: list(cubic.point_set()) -- [[0 : 1 : 4], [1 : 0 : 4], [1 : 4 : 0], [1 : 2 : 1], [1 : 1 : 2], [1 : 3 : 3]] -+ [[0 : 1 : 4], [1 : 0 : 4], [1 : 4 : 0], [1 : 1 : 2], [1 : 2 : 1], [1 : 3 : 3]] - sage: cubic.point_set().cardinality() - 6 - """ -diff --git a/src/sage/schemes/toric/morphism.py b/src/sage/schemes/toric/morphism.py -index 94be447f9c..0d8ed6f20d 100644 ---- a/src/sage/schemes/toric/morphism.py -+++ b/src/sage/schemes/toric/morphism.py -@@ -1692,7 +1692,7 @@ class SchemeMorphism_fan_fiber_component_toric_variety(SchemeMorphism): - From: 2-d toric variety covered by 4 affine patches - To: 4-d toric variety covered by 23 affine patches - Defn: Defined on coordinates by sending [z0 : z1 : z2 : z3] to -- [1 : 1 : 1 : 1 : z3 : 0 : 1 : z2 : 1 : 1 : 1 : z1 : z0 : 1 : 1] -+ [1 : 1 : 1 : 1 : z2 : 0 : 1 : z3 : 1 : 1 : 1 : z1 : z0 : 1 : 1] - sage: type(fiber_component.embedding_morphism()) - <class 'sage.schemes.toric.morphism.SchemeMorphism_fan_fiber_component_toric_variety'> - """ -@@ -1775,7 +1775,7 @@ class SchemeMorphism_fan_fiber_component_toric_variety(SchemeMorphism): - From: 2-d toric variety covered by 4 affine patches - To: 4-d toric variety covered by 23 affine patches - Defn: Defined on coordinates by sending [z0 : z1 : z2 : z3] to -- [1 : 1 : 1 : 1 : z3 : 0 : 1 : z2 : 1 : 1 : 1 : z1 : z0 : 1 : 1] -+ [1 : 1 : 1 : 1 : z2 : 0 : 1 : z3 : 1 : 1 : 1 : z1 : z0 : 1 : 1] - - sage: primitive_cone = Cone([(-1, 2, -1, 0)]) - sage: f = fibration.fiber_component(primitive_cone).embedding_morphism() -@@ -1949,11 +1949,11 @@ class SchemeMorphism_fan_fiber_component_toric_variety(SchemeMorphism): - sage: f = fc.embedding_morphism() - sage: for r in fc.fan().rays(): - ....: print("{} {}".format(r, f._image_ray_multiplicity(r))) -- N(-1, 2) (11, 1) -+ N(-1, -1) (9, 2) - N(0, 1) (5, 1) -- N(1, -3) (9, 2) -+ N(1, 0) (11, 1) - sage: f._ray_index_map -- {N(-3, 4): 10, N(-1, 2): 11, N(0, 1): 5, N(1, 0): 4, N(2, -6): 9} -+ {N(-2, -2): 9, N(-1, 2): 4, N(0, 1): 5, N(1, 0): 11, N(3, -2): 10} - """ - try: - image_ray_index = self._ray_index_map[fiber_ray] -@@ -1997,7 +1997,7 @@ class SchemeMorphism_fan_fiber_component_toric_variety(SchemeMorphism): - V(z0) + V(z1) + 3*V(z2) + 4*V(z3) - sage: fc = f.fiber_component(Cone([(1,1,0)])) - sage: fc.embedding_morphism().pullback_divisor(D) -- 2*V(z0) + 3*V(z1) -+ 4*V(z0) + V(z1) + 4*V(z2) - sage: fc = f.fiber_component(Cone([(1,0,0)])) - sage: fc.embedding_morphism().pullback_divisor(D) - -V(z0) - 3*V(z1) - 3*V(z2) -diff --git a/src/sage/schemes/toric/points.py b/src/sage/schemes/toric/points.py -index 31e7769ede..2ea3067e8a 100644 ---- a/src/sage/schemes/toric/points.py -+++ b/src/sage/schemes/toric/points.py -@@ -986,7 +986,7 @@ class FiniteFieldSubschemePointEnumerator(NaiveSubschemePointEnumerator): - sage: point_set = X.point_set() - sage: ffe = point_set._enumerator() - sage: list(ffe) # indirect doctest -- [(1, 4, 3), (1, 1, 6), (1, 2, 5)] -+ [(1, 1, 6), (1, 2, 5), (1, 4, 3)] - """ - for cone, nonzero_coordinates, cokernel in self.ambient.cone_points_iter(): - R = PolynomialRing(self.ambient.ring, cokernel.ngens(), 't') -diff --git a/src/sage/schemes/toric/variety.py b/src/sage/schemes/toric/variety.py -index 1bcfd27f82..5650488045 100644 ---- a/src/sage/schemes/toric/variety.py -+++ b/src/sage/schemes/toric/variety.py -@@ -1498,7 +1498,7 @@ class ToricVariety_field(AmbientSpace): - in Basis lattice of The toric rational divisor class group - of a 2-d CPR-Fano toric variety covered by 4 affine patches - sage: [ divisor_class.lift() for divisor_class in Kc.rays() ] -- [V(x), V(s)] -+ [V(y), V(t)] - sage: Kc.lattice() - Basis lattice of The toric rational divisor class group of a - 2-d CPR-Fano toric variety covered by 4 affine patches -@@ -1654,7 +1654,7 @@ class ToricVariety_field(AmbientSpace): - sage: A = toric_varieties.P2().Chow_group(); A - Chow group of 2-d CPR-Fano toric variety covered by 3 affine patches - sage: A.gens() -- (( 1 | 0 | 0 ), ( 0 | 1 | 0 ), ( 0 | 0 | 1 )) -+ (( 0 | 0 | 1 ), ( 0 | 1 | 0 ), ( 1 | 0 | 0 )) - """ - from sage.schemes.toric.chow_group import ChowGroup - return ChowGroup(self,base_ring) -diff --git a/src/sage/structure/factorization.py b/src/sage/structure/factorization.py -index 1d32db0842..7636f1a9ba 100644 ---- a/src/sage/structure/factorization.py -+++ b/src/sage/structure/factorization.py -@@ -133,17 +133,17 @@ Factorizations can involve fairly abstract mathematical objects:: - 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 (-a))^2 * (Fractional ideal (5)) -+ (Fractional ideal (1/2*a + 3/2))^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 (-a))^4 -+ (Fractional ideal (1/2*a + 3/2))^4 - sage: f.lcm(g) -- (Fractional ideal (-a))^4 * (Fractional ideal (5)) -+ (Fractional ideal (1/2*a + 3/2))^4 * (Fractional ideal (5)) - sage: f.gcd(g) -- (Fractional ideal (-a))^2 -+ (Fractional ideal (1/2*a + 3/2))^2 - sage: f.is_integral() - True - -diff --git a/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py b/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py -index d67a33e7c4..e3c78e6620 100644 ---- a/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py -+++ b/src/sage/tests/books/computational-mathematics-with-sagemath/linalg_doctest.py -@@ -233,11 +233,11 @@ Sage example in ./linalg.tex, line 1640:: - ....: [-1,-1,-1,-2,-2,-2,1,1,-1,2,2,2,2,2,-1,2,2,2,2,2]) - sage: S,U,V = A.smith_form(); S,U,V - ( -- [ 0 -2 -1 -5 0] -- [1 0 0 0 0] [ 1 0 0 0] [ 1 0 1 -1 -1] -- [0 1 0 0 0] [ 0 0 1 0] [ 0 0 0 0 1] -- [0 0 3 0 0] [-2 1 0 0] [-1 2 0 5 0] -- [0 0 0 6 0], [ 0 0 -2 -1], [ 0 -1 0 -2 0] -+ [ 3 1 2 -1 0] -+ [1 0 0 0 0] [ 0 0 1 0] [ 0 0 0 0 1] -+ [0 1 0 0 0] [ 0 1 0 0] [ 1 1 1 1 -1] -+ [0 0 3 0 0] [ 1 -2 -4 1] [-3 -2 -3 -1 0] -+ [0 0 0 6 0], [ 0 0 4 -1], [ 1 0 0 -2 0] - ) - - Sage example in ./linalg.tex, line 1674:: -diff --git a/src/sage/tests/books/judson-abstract-algebra/galois-sage.py b/src/sage/tests/books/judson-abstract-algebra/galois-sage.py -index ac15dad7a9..6996d34012 100644 ---- a/src/sage/tests/books/judson-abstract-algebra/galois-sage.py -+++ b/src/sage/tests/books/judson-abstract-algebra/galois-sage.py -@@ -414,18 +414,18 @@ r""" - To: Number Field in c with defining polynomial x^8 + 28*x^4 + 2500 - Defn: c4 |--> 2*c^2, - None), -- (Number Field in c5 with defining polynomial x^4 + 648, -- Ring morphism: -- From: Number Field in c5 with defining polynomial x^4 + 648 -- To: Number Field in c with defining polynomial x^8 + 28*x^4 + 2500 -- Defn: c5 |--> 1/80*c^5 + 79/40*c, -- None), -- (Number Field in c6 with defining polynomial x^4 + 8, -+ (Number Field in c5 with defining polynomial x^4 + 8, - Ring morphism: -- From: Number Field in c6 with defining polynomial x^4 + 8 -+ From: Number Field in c5 with defining polynomial x^4 + 8 - To: Number Field in c with defining polynomial x^8 + 28*x^4 + 2500 -- Defn: c6 |--> -1/80*c^5 + 1/40*c, -+ Defn: c5 |--> -1/80*c^5 + 1/40*c, - None), -+ (Number Field in c6 with defining polynomial x^4 + 648, -+ Ring morphism: -+ From: Number Field in c6 with defining polynomial x^4 + 648 -+ To: Number Field in c with defining polynomial x^8 + 28*x^4 + 2500 -+ Defn: c6 |--> 1/80*c^5 + 79/40*c, -+ None), - (Number Field in c7 with defining polynomial x^4 - 512, - Ring morphism: - From: Number Field in c7 with defining polynomial x^4 - 512 -diff --git a/src/sage/tests/parigp.py b/src/sage/tests/parigp.py -index c118b6eb37..4692b613de 100644 ---- a/src/sage/tests/parigp.py -+++ b/src/sage/tests/parigp.py -@@ -6,9 +6,7 @@ Check that :trac:`9876` has been fixed, this test comes from PARI's - self-test :pari:`rnfkummer` but was modified such that the answer is - canonical:: - -- sage: pari('addprimes([31438243, 238576291, 18775387483, 24217212463267, 1427657500359111961, 135564809928627323997297867381959])') -- [31438243, 238576291, 18775387483, 24217212463267, 1427657500359111961, 135564809928627323997297867381959] -- sage: pari('K = bnfinit(y^4-52*y^2+26,1); pol = rnfkummer(bnrinit(K,3,1),Mat(5)); L = rnfinit(K, pol); polredabs(polredbest(L.polabs))') # long time -+ sage: pari('K = bnfinit(y^4-52*y^2+26,1); pol = rnfkummer(bnrinit(K,3,1),Mat(5)); L = rnfinit(K, [pol, 10^6]); polredabs(polredbest(L.polabs))') # long time - x^20 - 112*x^18 + 5108*x^16 - 123460*x^14 + 1724337*x^12 - 14266996*x^10 + 69192270*x^8 - 188583712*x^6 + 260329852*x^4 - 141461008*x^2 + 19860776 - - Check that :trac:`10195` (PARI bug 1153) has been fixed:: |