Sage 9.1 Release Tour

released May 20, 2020

Python 3 transition

SageMath 9.0 was the first version of Sage running on Python 3 by default. Sage 9.1 continues to support both Python 2 and Python 3.

In Sage 9.1, we have made some further improvements regarding Python 3 support. In particular, SageMath now supports underscored numbers PEP 515 (py3); the fix was done in Trac #28490:

sage: 1_000_000 + 3_000

The next release, SageMath 9.2, will remove support for Python 2. See Python3-Switch for more details.

Portability improvements, increased use of system packages

The SageMath distribution continues to vendor versions of required software packages ("SPKGs") that work well together.

In order to reduce compilation times and the size of the Sage installation, a development effort ongoing since the 8.x release series has made it possible to use many system packages provided by the OS distribution (or by the Homebrew or conda-forge distributions) instead of building SageMath's own copies.

This so-called "spkg-configure" mechanism runs at the beginning of a build from source, during the ./configure phase.

(See the sage-devel threads "Brainstorming about Sage dependencies from system packages" (May 2017) and "conditionalise installation of many spkg's?" (Nov 2017) for its origins and Trac #24919 for its initial implementation.)

Sage 9.1 is adding many packages to this mechanism, including openblas, gsl, r, boost, libatomic, cddlib, tachyon, nauty, sqlite, planarity, fplll, brial, flintqs, ppl, libbraiding, cbc, gfan, and python3. As to the latter, SageMath will now make use of a suitable installation of Python 3.7.x in your system by setting up a venv (Python 3 virtual environment).

New in Sage 9.1 is also a database of system packages equivalent to our SPKGs. At the end of a ./configure run, you will see messages like the following:

  configure: notice: the following SPKGs did not find equivalent system packages: arb boost boost_cropped bzip2 ... yasm zeromq zlib
  checking for the package system in use... debian
  configure: hint: installing the following system packages is recommended and may avoid building some of the above SPKGs from source:
  configure:   $ sudo apt-get install libflint-arb-dev ... yasm libzmq3-dev libz-dev
  configure: After installation, re-run configure using:
  configure:   $ ./config.status --recheck && ./config.status

We also use the same database to update our installation manual automatically.

Status of Cygwin support

Thanks to the hard work of our Cygwin maintainers, in particular during the 8.x release cycles, building Sage on Windows using Cygwin64 is fully supported. Sage 9.1 reflects this by integrating the instructions for building from source on Cygwin into its documentation.

For developers

For developers who wish to help improve the portability of SageMath, there is a new power tool: A tox configuration that automatically builds and tests Sage within Docker containers running various Linux distributions (ubuntu-trusty through -focal, debian-jessie through -sid, linuxmint-17 through -19.3, fedora-26 through -32, centos-7 and -8, archlinux, slackware-14.2), each in several configurations regarding what system packages are installed. Thus, it is no longer necessary for developers to have access to a machine running fedora-29, say, to verify whether the Sage distribution works there; instead, you just type:

  tox -e docker-fedora-29-standard -- build ptest

The Dockerfiles are generated automatically on the fly using the same database of system packages that provides information to users. See the tutorial for developers: Portability testing of the Sage distribution using Docker and the Sage distro-package database from the Global Virtual SageDays 109 and the new section on "testing on multiple platforms" in the Developer's Guide for details.

An entry point for developers who wish to improve the testing infrastructure is the Meta-Ticket #29060: Add Dockerfiles and CI scripts for integration testing. See also the broader Meta-Meta-Ticket #29133.

For packagers

Although we now have continuous integration environments for testing the interaction of the Sage distribution with most major Linux distributions, we are still missing a few. Adding them will enable all Sage developers to check that their changes do not break things on your distribution.

Package updates

We have only made minor updates to standard packages:

We expect to make larger package updates in the 9.2 release.

For developers

Preparing and testing package updates has become easier. The new optional field upstream_url in checksums.ini holds an URL to the upstream package archive, see for example build/pkgs/numpy/checksums.ini. Note that, like the tarball field, the upstream_url is a template; the word VERSION is substituted with the actual version. The package can be updated by simply typing ./sage -package update numpy 3.14.59; this will automatically download the archive and update the build/pkgs/ information.

Developers who wish to test a package update from a Trac branch before the archive is available on a Sage mirror can do so by configuring their Sage tree using ./configure --enable-download-from-upstream-url.

Every Sage developer now has easy access to "their own" set of 20 (40 for GitHub Pro accounts) two-core virtual machines running Linux, macOS, and Windows through GitHub Actions. To automatically test a branch on a multitude of our supported platforms, it suffices to create a fork of the sagemath/sage repository on GitHub, enable GitHub Actions, add the repository as a remote, create a tag and push the tag to the remote. After ... a ... while, your test results will be available — like the ones at sagemath/sage Actions. We hope that this new testing infrastructure will reduce the FUD in the process of upgrading packages.

Polyhedral geometry

There is now a catalog for common polyhedral cones, e.g.

sage: cones.nonnegative_orthant(5)
5-d cone in 5-d lattice N

New features for polyhedra:

sage: P = polytopes.cube(intervals='zero_one') # obtain others than the standard cube
sage: P = matrix([[0,1,0],[0,1,1],[1,0,0]])*P  # linear transformations
sage: it = P.face_generator()                  # a (fast and efficient) face generator
sage: next(it)
A 3-dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 8 vertices
sage: next(it)
A -1-dimensional face of a Polyhedron in ZZ^3
sage: f = next(it)
sage: f.normal_cone()                          # normal cone for faces
A 1-dimensional polyhedron in ZZ^3 defined as the convex hull of 1 vertex and 1 ray
sage: P.an_affine_basis()                      # an_affine_basis and a_maximal_chain
[A vertex at (0, 0, 0),
 A vertex at (1, 1, 0),
 A vertex at (0, 0, 1),
 A vertex at (0, 1, 0)]
sage: P = polytopes.hypercube(4)
sage: P.flag_f_vector(0,3)                     # flag_f_vector is exposed

Regarding the optional package normaliz there are some news as well:

sage: P = polytopes.cube(intervals=[[0,1],[0,2],[0,3]], backend='normaliz')
sage: save(P, '/tmp/this_takes_very_long_so_we_save_it')   # saving works now
sage: sage: P.h_star_vector()                              # compute the h_star_vector with normaliz
[1, 20, 15]

There are also some bug fixes and other improvements. For more details see the presentation on combinatorial polyhedra and development of geometric polyhedra from the Global Virtual SageDays 109 and the release notes for optimization and polyhedral geometry software interactions in Sage.

Improvements in the three.js 3D viewer

Three.js has become the default 3D viewer in SageMath 9.0. In this release, some improvements have been performed:

Integral curves over finite fields

A dream has come true! The integral curves over finite fields are now attached with the global function field machinery of Sage. This is a short tour:

sage: A.<x,y> = AffineSpace(GF(16),2)
sage: C = Curve(y^3 + x^3*y + x); C  # Klein quartic
Affine Plane Curve over Finite Field in z4 of size 2^4 defined by x^3*y + y^3 + x
sage: C.function_field()
Function field in y defined by y^3 + x^3*y + x
sage: C.genus()
sage: C.closed_points()
[Point (x, y),
 Point (x + (z4), y + (z4^3 + z4^2)),
 Point (x + (z4^2), y + (z4^3 + z4^2 + z4 + 1)),
 Point (x + (z4^3), y + (z4^2 + z4)),
 Point (x + (z4 + 1), y + (z4^3 + z4)),
 Point (x + (z4^2 + z4), y + (z4^2 + z4 + 1)),
 Point (x + (z4^2 + z4), y + (z4^3 + 1)),
 Point (x + (z4^2 + z4), y + (z4^3 + z4^2 + z4)),
 Point (x + (z4^3 + z4^2), y + (z4^2 + z4 + 1)),
 Point (x + (z4^2 + 1), y + (z4^3)),
 Point (x + (z4^3 + z4), y + (z4^2 + z4 + 1)),
 Point (x + (z4^2 + z4 + 1), y + (z4^2 + z4)),
 Point (x + (z4^2 + z4 + 1), y + (z4^3 + z4 + 1)),
 Point (x + (z4^2 + z4 + 1), y + (z4^3 + z4^2 + 1)),
 Point (x + (z4^3 + z4^2 + z4 + 1), y + (z4^2 + z4))]
sage: p1, p2 = _[:2]
sage: P1 =
sage: P2 =
sage: D = 5 * P1 - P2
sage: D.basis_function_space()  # Riemann-Roch space
[(x + z4)/x, 1/x^2*y + (z4^2 + z4)/x]
sage: D.dimension()
sage: f1, f2 = D.basis_function_space()
sage: f1.zeros()
[Place (x + z4, y^2 + (z4^3 + z4^2)*y + z4^2 + z4 + 1),
 Place (x + z4, y + z4^3 + z4^2)]
sage: Q1, Q2 = _
sage: q1 = C.place_to_closed_point(Q1); q1
Point (y^2 + (z4^3 + z4^2)*y + (z4^2 + z4 + 1), x + (z4))
sage: q2 = C.place_to_closed_point(Q2); q2
Point (x + (z4), y + (z4^3 + z4^2))
sage: q2.rational_point()
(z4, z4^3 + z4^2)
sage: _ in C

For an extended tour of the new (and newer) functionality, see the presentation on integral curves from the Global Virtual SageDays 109.


Puiseux series

After 11 years Trac #4618 has come to an end. Thus, Puiseux series are available, right now:

sage: R.<x> = PuiseuxSeriesRing(QQ)
sage: p = x^(-7/2) + 3 + 5*x^(1/2) - 7*x^3
sage: 1/p
x^(7/2) - 3*x^7 - 5*x^(15/2) + 7*x^10 + 9*x^(21/2) + 30*x^11 + 25*x^(23/2) + O(x^(27/2))

See also the reference manual.


Integral domains can be localized at finite sets of their non invertible elements:

sage: L = ZZ.localization(45); L
Integer Ring localized at (3, 5)
sage: [1/l in L for l in range(1,6)]
[True, False, True, False, True]

sage: P.<x,y,z> = QQ[]
sage: d = x^2+y^2+z^2
sage: Ld = P.localization(d); Ld
Multivariate Polynomial Ring in x, y, z over Rational Field localized at (x^2 + y^2 + z^2,)
sage: (x + y + z)/d in Ld

See also the reference manual.

Ariki–Koike algebras

An Ariki–Koike algebra (aka cyclotomic Hecke algebra) is a generalization of the Iwahori–Hecke algebra to the complex reflection group G(r,1,n) instead of a Coxeter group. These have now been implemented in Sage:

sage: H = algebras.ArikiKoike(3, 4)
sage: LT = H.LT()
sage: LT.dimension()
sage: LT.inject_variables()
Defining L1, L2, L3, L4, T1, T2, T3
sage: L1^3
u0*u1*u2 + ((-u0*u1-u0*u2-u1*u2))*L1 + ((u0+u1+u2))*L1^2
sage: T1 * L2
-(1-q)*L2 + L1*T[1]
sage: T2 * L3 * L1
-(1-q)*L1*L3 + L1*L2*T[2]
sage: T2 * T1 * T2 * L3 * L2
-(q-q^2)*L2*L3 + (1-2*q+q^2)*L2*L3*T[2] - (1-q)*L1*L3*T[1,2] + L1*L2*T[2,1,2]

See also the reference manual.

normal_basis for positive-dimensional ideals

The computation of a normal basis of an ideal can now be restricted to monomials of a particular degree. This allows to compute a (partial) basis for quotient rings that are not finite-dimensional. #29543 #29625

sage: R.<x,y,z> = QQ[]
sage: I = R.ideal(x^2 + y^2 - 1)
sage: [I.normal_basis(d) for d in (0..3)]
 [z, y, x],
 [z^2, y*z, x*z, y^2, x*y],
 [z^3, y*z^2, x*z^2, y^2*z, x*y*z, y^3, x*y^2]]

Graph theory


The arboricity of a graph can now be computed using the arboricity function (#19053).

MCS traversal and clique separators

Ticket #28473 introduced the following methods to the Graph class:


Checking whether a uniform hypergraph has a Berge-cycle can be done using the is_berge_cyclic method of ticket #21931.

Generator for cube-connected cycles

There is now a generator for cube-connected cycles (#21423):

sage: g = graphs.CubeConnectedCycle(3)
Cube-Connected Cycle of dimension 3: Graph on 24 vertices

The cube-connected-cycles graph of dim 3

Enumeration of minimal dominating sets

The minimal_dominating_sets method of a Graph is a generator of its minimal dominating sets (#27424):

   1 sage: g = graphs.PathGraph(5)
   2 sage: list(g.minimal_dominating_sets())
   3 [{0, 2, 4}, {1, 4}, {0, 3}, {1, 3}]


Degenerate manifolds and submanifolds

Manifolds endowed with a degenerate metric have been introduced in this release (tickets #26355, #29080 and #29440). See the documentation and well as these Jupyter notebooks: example 1 and example 2.

More functionalities in index notation for tensors

Index notation to indicate operations like contractions has been enhanced (ticket #28787). For instance, a sum can be introduced in a contraction:

sage: E.<x,y> = EuclideanSpace()
sage: v = E.vector_field(-y, x)
sage: t = E.tensor_field(0, 2, [[1, x], [-2*y, x^2]])
sage: v['j']*(t['_ij'] + t['_ji']) == v.contract(2*t.symmetrize())

Applying a function to all components of a tensor field

The new method apply_map() of tensor fields (ticket #29244) allows one to perform operations like factorization, expansion, simplification or substitution on all components of a tensor field:

sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: v = M.vector_field(x^2 - y^2, x*(y^2 - y), name='v')
sage: v.display()
v = (x^2 - y^2) d/dx + (y^2 - y)*x d/dy
sage: v.apply_map(factor)
sage: v.display()
v = (x + y)*(x - y) d/dx + x*(y - 1)*y d/dy

Other changes

Some improvements and bug fixes have been introduced in this release. See the full change log.

Configuration changes

Easier installation of optional linear and mixed integer linear optimization backends

It is no longer necessary to recompile sagelib if you wish to use one of the state-of-the-art LP/MIP solvers COIN-OR CBC, CPLEX, or Gurobi, instead of the default (GLPK). The simplified new installation procedure is explained in the section on solvers (backends) in the Thematic Tutorial on Linear Programming.

(If you cannot update to 9.1 just yet, you can retroactively get the same feature in your installation of Sage too by pip-installing one of the packages sage-numerical-backends-cplex, sage-numerical-backends-coin, sage-numerical-backends-gurobi.)

New way to install optional and experimental packages

It is now possible to use ./configure options to request the installation of optional and experimental packages at the next run of make. For example, type

    $ ./configure --enable-4ti2 --enable-lrslib

to request these two packages to be installed. Check ./configure --help for a list of all options. (The traditional way of installing optional packages, sage -i, still works.)

Likewise, optional and experimental packages can be requested to be uninstalled at the next run of make by using --disable-SPKG options.

For developers and packagers

Happy news! The configuration file

(introduced 4 years ago in Trac #21479) finally has some company. Two new configuration files, also generated by the Sage distribution's ./configure script, are taking over some of its duties.

See Meta-ticket #21707: Split sage-env into 5 to clean up sage configuration for details and planned future work.

Spring cleaning

Availability of Sage 9.1 and installation help

Source code

Sage 9.1 has been tagged in the sage git repository, and the self-contained source tarballs are available for download.

Sage 9.1 has been tested to compile from source on a wide variety of platforms, including:


Binary distributions are available for some Linux systems and for macOS, as well as a Windows installer package.

Availability in distributions

Sage 9.1 is already available in some rolling Linux distributions and as a Homebrew Cask, see sagemath

Installation FAQ

See in the source distribution for installation instructions; for more details, see the SageMath Installation Guide (updated for 9.1).

See sage-release, sage-devel.

More details

ReleaseTours/sage-9.1 (last edited 2021-09-29 20:17:44 by soehms)