Sage 9.1 Release Tour
released May 20, 2020
Contents

Sage 9.1 Release Tour
 Python 3 transition
 Portability improvements, increased use of system packages
 Package updates
 Polyhedral geometry
 Improvements in the three.js 3D viewer
 Integral curves over finite fields
 Algebra
 Graph theory
 Manifolds
 Configuration changes
 Spring cleaning
 Availability of Sage 9.1 and installation help
 More details
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 1003000
The next release, SageMath 9.2, will remove support for Python 2. See Python3Switch 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 condaforge distributions) instead of building SageMath's own copies.
This socalled "spkgconfigure" mechanism runs at the beginning of a build from source, during the ./configure phase.
(See the sagedevel 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 aptget install libflintarbdev ... yasm libzmq3dev libzdev configure: After installation, rerun 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 (ubuntutrusty through focal, debianjessie through sid, linuxmint17 through 19.3, fedora26 through 32, centos7 and 8, archlinux, slackware14.2), 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 fedora29, say, to verify whether the Sage distribution works there; instead, you just type:
tox e dockerfedora29standard  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 distropackage 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 MetaTicket #29060: Add Dockerfiles and CI scripts for integration testing. See also the broader MetaMetaTicket #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:
 dateutil – 2.8.1 (from 2.5.3)
 fplll – 5.3.2 (from 5.2.1)
 fpylll – 0.5.1.dev (from 0.4.1dev)
 freetype – 2.10.1
 m4ri – 20200115
 m4rie – 20200115
 matplotlib – 2.2.5 (from 2.2.4)
 ntl – 11.4.3 (from 11.3.2)
 numpy – 1.16.6 (from 1.16.1)
 openblas – 0.3.9
 pkgconfig – 1.5.1 (from 1.4.0)
 pyzmq – 19.0.0 (from 18.1)
 sage_brial – 1.2.5 (this is the python module of the brial package)
 scipy – 1.2.3 (from 1.2.0)
 sympy – 1.5 (from 1.4)
 traitlets – 4.3.3
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 enabledownloadfromupstreamurl.
Every Sage developer now has easy access to "their own" set of 20 (40 for GitHub Pro accounts) twocore 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) 5d cone in 5d 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 3dimensional face of a Polyhedron in ZZ^3 defined as the convex hull of 8 vertices sage: next(it) A 1dimensional face of a Polyhedron in ZZ^3 sage: f = next(it) sage: f.normal_cone() # normal cone for faces A 1dimensional 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 64
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:
bug fixes: plot of vectors (Trac ticket #29206), plot of a single text (#29227), method plot3d transforming a 2D object into a 3D one (#29251)
code cleanup to prepare for camera viewpoint option (#29250)
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() 3 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 = p1.place() sage: P2 = p2.place() sage: D = 5 * P1  P2 sage: D.basis_function_space() # RiemannRoch space [(x + z4)/x, 1/x^2*y + (z4^2 + z4)/x] sage: D.dimension() 2 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: q1.degree() 2 sage: q2 = C.place_to_closed_point(Q2); q2 Point (x + (z4), y + (z4^3 + z4^2)) sage: q2.degree() 1 sage: q2.rational_point() (z4, z4^3 + z4^2) sage: _ in C True
For an extended tour of the new (and newer) functionality, see the presentation on integral curves from the Global Virtual SageDays 109.
Algebra
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.
Localization
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 True
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() 1944 sage: LT.inject_variables() Defining L1, L2, L3, L4, T1, T2, T3 sage: L1^3 u0*u1*u2 + ((u0*u1u0*u2u1*u2))*L1 + ((u0+u1+u2))*L1^2 sage: T1 * L2 (1q)*L2 + L1*T[1] sage: T2 * L3 * L1 (1q)*L1*L3 + L1*L2*T[2] sage: T2 * T1 * T2 * L3 * L2 (qq^2)*L2*L3 + (12*q+q^2)*L2*L3*T[2]  (1q)*L1*L3*T[1,2] + L1*L2*T[2,1,2]
See also the reference manual.
normal_basis for positivedimensional 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 finitedimensional. #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)] [[1], [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
Arboricity
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:
maximum_cardinality_search for the Maximal Cardinality Search (MCS) graph traversal (in O(n+m) time),
maximum_cardinality_search_M, an extension of MCS that also returns a minimal triangulation (in O(n.m) time), and
atoms_and_clique_separators, a method that decomposes the graph according clique minimal separators and returns the atoms and the clique minimal separators (in O(n.m) time).
Hypergraphs
Checking whether a uniform hypergraph has a Bergecycle can be done using the is_berge_cyclic method of ticket #21931.
Generator for cubeconnected cycles
There is now a generator for cubeconnected cycles (#21423):
sage: g = graphs.CubeConnectedCycle(3) CubeConnected Cycle of dimension 3: Graph on 24 vertices
Enumeration of minimal dominating sets
The minimal_dominating_sets method of a Graph is a generator of its minimal dominating sets (#27424):
Manifolds
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()) True
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 stateoftheart LP/MIP solvers COINOR 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 pipinstalling one of the packages sagenumericalbackendscplex, sagenumericalbackendscoin, sagenumericalbackendsgurobi.)
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 enable4ti2 enablelrslib
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 disableSPKG options.
For developers and packagers
Happy news! The configuration file
src/bin/sageenvconfig (installed as $SAGE_LOCAL/bin/sageenvconfig)
(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.
build/bin/sagebuildenvconfig (not installed) provides configuration variables that are used only while building packages.
build/pkgs/sage_conf/src/sage_conf.py (installed as Python module sage_conf) provides configuration variables that are needed by the Sage library runtime, but are not needed in the form of environment variables. (They are available to the Sage library even when it is imported into a Python running outside of the environment set up by sageenv.)
See Metaticket #21707: Split sageenv into 5 to clean up sage configuration for details and planned future work.
Spring cleaning
Trac #29406: Remove documentation on creating oldstyle SPKGs, Trac #29383: Remove related scripts
Remove numerous deprecated items, fix coding style, refactoring
Availability of Sage 9.1 and installation help
Source code
Sage 9.1 has been tagged in the sage git repository, and the selfcontained source tarballs are available for download.
Sage 9.1 has been tested to compile from source on a wide variety of platforms, including:
 Linux 64bit (x86_64)
 ubuntu{trusty,xenial,bionic,eoan,focal},
 debian{jessie,stretch,buster,bullseye,sid},
 linuxmint{17,18,19,19.3},
 fedora{26,27,28,29,30,31,32},
 centos{7,8},
 archlinux,
 slackware14.2.
 Linux 32bit (i386)
 debianbuster
 ubuntueoan
 macOS
 Windows (Cygwin64).
Binaries
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 repology.org: sagemath
Installation FAQ
See README.md in the source distribution for installation instructions; for more details, see the SageMath Installation Guide (updated for 9.1).
See sagerelease, sagedevel.