-
Notifications
You must be signed in to change notification settings - Fork 0
ReleaseTours sage 9.8
This is the Trac macro PageOutline that was inherited from the migration
Current development cycle (2022)
The method FiniteRankFreeModule.tensor_module now accepts optional arguments sym, antisym; if given, a submodule of the tensor module spanned by the tensors with these prescribed symmetries is created. #30229
The new methods symmetric_power and dual_symmetric_power provide two important special cases.
Standard bases of tensor modules (and of their new submodules) are now explicit objects. The basis method now works for tensor modules, not just the base module, and returns an instance of a new class TensorFreeSubmoduleBasis_sym, which represents the standard basis of a tensor module associated with a basis of the base module. #30229
The method FiniteRankFreeModule.isomorphism_with_fixed_basis now also works for tensor modules (and their submodules). #34427
For example, we can now send (1,1)-tensors to matrices:
sage: V = FiniteRankFreeModule(QQ, 3, start_index=1); V
3-dimensional vector space over the Rational Field
sage: basis = e = V.basis("e"); basis
Basis (e_1,e_2,e_3) on the 3-dimensional vector space over the Rational Field
sage: T11 = V.tensor_module(1, 1); T11
Free module of type-(1,1) tensors on the 3-dimensional vector space over the Rational Field
sage: e_T11 = T11.basis("e"); e_T11
Standard basis on the
Free module of type-(1,1) tensors on the 3-dimensional vector space over the Rational Field
induced by Basis (e_1,e_2,e_3) on the 3-dimensional vector space over the Rational Field
sage: W = MatrixSpace(QQ, 3)
sage: phi_e_T11 = T11.isomorphism_with_fixed_basis(e_T11, codomain=W); phi_e_T11
Generic morphism:
From: Free module of type-(1,1) tensors on the 3-dimensional vector space over the Rational Field
To: Full MatrixSpace of 3 by 3 dense matrices over Rational Field
sage: t = T11.an_element(); t.display()
1/2 e_1⊗e^1
sage: phi_e_T11(t)
[1/2 0 0]
[ 0 0 0]
[ 0 0 0]
Or we can send symmetric bilinear forms to matrices:
sage: V = FiniteRankFreeModule(QQ, 3, start_index=1); V
3-dimensional vector space over the Rational Field
sage: basis = e = V.basis("e"); basis
Basis (e_1,e_2,e_3) on the 3-dimensional vector space over the Rational Field
sage: T02 = V.tensor_module(0, 2); T02
Free module of type-(0,2) tensors on the 3-dimensional vector space over the Rational Field
sage: e_T02 = T02.basis("e"); e_T02
Standard basis on the
Free module of type-(0,2) tensors on the 3-dimensional vector space over the Rational Field
induced by Basis (e_1,e_2,e_3) on the 3-dimensional vector space over the Rational Field
sage: W = MatrixSpace(QQ, 3)
sage: phi_e_T02 = T02.isomorphism_with_fixed_basis(e_T02, codomain=W); phi_e_T02
Generic morphism:
From: Free module of type-(0,2) tensors on the 3-dimensional vector space over the Rational Field
To: Full MatrixSpace of 3 by 3 dense matrices over Rational Field
sage: a = V.sym_bilinear_form()
sage: a[1,1], a[1,2], a[1,3] = 1, 2, 3
sage: a[2,2], a[2,3] = 4, 5
sage: a[3,3] = 6
sage: a.display()
e^1⊗e^1 + 2 e^1⊗e^2 + 3 e^1⊗e^3 + 2 e^2⊗e^1 + 4 e^2⊗e^2 + 5 e^2⊗e^3 + 3 e^3⊗e^1 + 5 e^3⊗e^2 + 6 e^3⊗e^3
sage: phi_e_T02(a)
[1 2 3]
[2 4 5]
[3 5 6]
A new interface to the msolve library (now available as an optional package) provides efficient tools for solving large polynomial systems. #31664, #33734, #34519
In particular:
- The
groebner_basismethod of polynomial ideals now supports using msolve to compute Gröbner bases over prime fields (with some cardinality constraints). - The
varietymethod supports computing real or complex solutions of zero-dimensional polynomial systems over the rational numbers using msolve.
(Some of these features use probabilistic algorithms.)
The Polyhedron constructor offers a new option backend='number_field'. #34479
It accepts any input data that Sage can convert to a common real embedded algebraic number field. The new backend uses this embedded number field internally for the polyhedral representation conversion, but the results are converted back to the (common) base ring of the input.
sage: polytopes.icosahedron(exact=True, backend='number_field')
A 3-dimensional polyhedron
in (Number Field in sqrt5 with defining polynomial x^2 - 5
with sqrt5 = 2.236067977499790?)^3
defined as the convex hull of 12 vertices
sage: x = polygen(ZZ); P = Polyhedron(
....: vertices=[[sqrt(2)], [AA.polynomial_root(x^3-2, RIF(0,3))]],
....: backend='number_field')
sage: P
A 1-dimensional polyhedron
in (Symbolic Ring)^1 defined as the convex hull of 2 vertices
sage: P.vertices()
(A vertex at (sqrt(2)), A vertex at (2^(1/3)))
The same was previously only possible with backend='normaliz'. The new backend does not require the installation of an optional package; but note that backend='normaliz' is much faster than backend='number_field'.
The Polyhedron constructor now can also convert from convex polyhedra represented by some other classes. #14222
For example:
sage: quadrant = Cone([(1,0), (0,1)])
sage: Polyhedron(quadrant)
A 2-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 2 rays
sage: Polyhedron(quadrant, base_ring=QQ)
A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 1 vertex and 2 rays
sage: H.<x,y> = HyperplaneArrangements(QQ)
sage: h = x + y - 1; h
Hyperplane x + y - 1
sage: Polyhedron(h, base_ring=ZZ)
A 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 1 line
sage: Polyhedron(h)
A 1-dimensional polyhedron in QQ^2 defined as the convex hull of 1 vertex and 1 line
-
CRT_list()now uses a binary tree instead of folding the input from one side, which can be much faster. #34512
The new optional package msolve is an open source C library implementing computer algebra algorithms for solving polynomial systems (with rational coefficients or coefficients in a prime field) using Gröbner bases. msolve has been initiated in 2019 and is mainly authored by Jérémy Berthomieu, Christian Eder, and Mohab Safey El Din. The optional package provides version 0.4.4 of msolve. #31664, #34519
Normaliz, the package for computations in affine monoids, vector configurations, lattice polytopes, and rational cones, has been upgraded to version 3.9.4, which brings new algorithms and many improvements (release notes). For computations with algebraic polyhedra, Normaliz uses e-antic, a library for real embedded number fields, which has been upgraded to the 1.x series. The new version of e-antic has been refactored and now depends on ANTIC, an algebraic number theory library. #31588
TOPCOM, the package for computing triangulations of point configurations and oriented matroids, has been upgraded to 1.1.2. #31531
NumPy has been updated from 1.22.x to 1.23.5 (release notes for 1.23). #34110, #34658
SciPy has been updated from 1.8.1 to 1.9.3 (release notes for 1.9). #34081, #34658
Updated sympy to 1.11.1. #34118
Updated igraph, python_igraph to 0.10.x. #34491, #34498, #34680
Matplotlib has been updated to 3.6. #34796
The rpy2 package has been upgraded to version 3.4.5. It provides an interface to a suitable system installation of R, versions 3.5 or newer. Sage 9.8 no longer offers a package for installing R itself from source. #34268
Python has been upgraded to 3.10.8; Sage continues to support system Python 3.8.x, 3.9.x, 3.10.x. #34271
Sphinx has been upgraded from 4.4.x to 5.2.3. #34615
For a list of all packages and their versions, see
This does an incremental build of Sage on top of a prebuilt image published at ghcr.io (https://github.com/orgs/sagemath/packages?tab=packages). #34228
For example:
$ tox -e docker-fedora-31-standard-incremental
This new option ensures that venv/var/lib/sage/wheels/ contains up-to-date wheels for all Python packages, including sagemath-standard (the Sage library). #32874
The option can be used with or without --disable-editable, so there are now 4 modes of installation:
-
./configure(or./configure --enable-editable --disable-wheels): The Sage library (sagemath-standard) and other distribution packages whose source trees are part of the Sage monorepo (sage-conf, sage-docbuild, sage-setup, sage-sws2rst) are installed in editable mode. Changes to Python source files take immediate effect after restarting Sage. Runningsage -bormake buildis only necessary if you make changes (or switch to a branch that makes changes) to Cython sources or external packages. No wheels are available for these distributions; to build wheels once, usemake wheels. -
./configure --enable-wheels: When runningsage -bormake build, in addition to updating the editable install, Sage also builds/updates wheels for sagemath-standard and the other distribution packages whose source trees are part of the Sage monorepo. -
./configure --disable-editable: Sage installs sagemath-standard using the legacysetup.py installcommand. For any source changes to take effect, usesage -bormake build. No wheel is available; to build a wheel once, usemake wheels. -
./configure --disable-editable --enable-wheels: Sage builds a wheel for sagemath-standard and installs the wheel.
When Sage is installed from source, it will make use of various system packages; in particular, it will link to shared libraries provided by the system. Indiscriminate upgrades of system packages can break a Sage installation.
This can always be fixed by a full rebuild (make distclean && make build), but this time-consuming step can often be avoided by just reinstalling a few packages. The new command make -j list-broken-packages assists with this. #34203
$ make -j list-broken-packages
make --no-print-directory auditwheel_or_delocate-no-deps
...
# Checking .../local/var/lib/sage/installed/bliss-0.73+debian-1+sage-2016-08-02.p0
...
Checking shared library file '.../local/lib/libumfpack.dylib'
Checking shared library file '.../local/var/tmp/sage/build/suitesparse-5.10.1/src/lib/libsliplu.1.0.2.dylib'
Error during installcheck of 'suitesparse': .../local/var/tmp/sage/build/suitesparse-5.10.1/src/lib/libsliplu.1.0.2.dylib
...
Uninstall broken packages by typing:
make lcalc-SAGE_LOCAL-uninstall;
make ratpoints-SAGE_LOCAL-uninstall;
make r-SAGE_LOCAL-uninstall;
make suitesparse-SAGE_LOCAL-uninstall;
real 2m25.787s
user 4m54.270s
sys 4m0.796s
Sage 9.8 now requires GCC >= 8 (or a recent version of clang). This enables upgrades of various packages to versions that require C++17 language or library features. Developers can now also use C++17 features in the Sage library (this requires use of the directive # distutils: extra_compile_args = -std=c++17). #34266
Users of older Linux distributions (in particular, ubuntu-xenial
or older, debian-stretch or older, linuxmint-18 or older, fedora-28 or older)
should upgrade their systems before attempting to install Sage from
source.
Users of ubuntu-bionic, linuxmint-19.x, and
opensuse-15.x can install a versioned gcc system package
and then use ./configure CC=gcc-8 CXX=g++-8 FC=gfortran-8
or similar. See SAGE_ROOT/build/pkgs/_gcc8, _gcc9, ... for distribution-specific information.
Users on ubuntu can also install a modern compiler
toolchain using the ubuntu-toolchain-r ppa.
On ubuntu-trusty, also the package binutils-2.26 is required;
after installing it, make it available using export PATH="/usr/lib/binutils-2.26/bin:$PATH".
Instead of upgrading their distribution, users of centos-7 or RHEL can install a modern compiler
toolchain using Redhat's devtoolset.
On other old distributions, if an upgrade to a newer distribution is not possible, users can try to use ./configure --without-system-gcc. Then Sage will attempt to build its own copy of GCC using the available system GCC. We no longer test such system configurations, so this may or may not work.
Sage 9.8 ships a copy of GCC 12.x with Apple Silicon support, so it can now be built from source on macOS systems without Homebrew. #33816
The first development release, 9.8.beta0, was tagged on 2022-09-25. The current development release is 9.8.beta5, tagged on 2022-12-11.
The Sage source code is available in the sage git repository.