Sage 9.6 Release Tour

Current development cycle (2022)

Linear Algebra

The new classes Matrix_numpy_integer_dense and Vector_numpy_integer_dense implement matrices and vectors with 64-bit integer entries backed by numpy arrays. #32465.

As a first application, several methods of GenericGraph that return matrices, such as adjacency_matrix, now accept keyword arguments that can select the matrix implementation. #33377, #33387, #33388, #33389

sage: graphs.PathGraph(5).adjacency_matrix(sparse=False, implementation='numpy')
[0 1 0 0 0]
[1 0 1 0 0]
[0 1 0 1 0]
[0 0 1 0 1]
[0 0 0 1 0]
sage: type(_)
<class 'sage.matrix.matrix_numpy_integer_dense.Matrix_numpy_integer_dense'>

Symbolics

ImageSet

Sage 9.6 defines a new class ImageSet. #32121

sage: ImageSet(sin, RealSet.open(0, pi/4))
Image of (0, 1/4*pi) by The map sin from (0, 1/4*pi)
sage: _.an_element()
1/2*sqrt(-sqrt(2) + 2)

sage: sos(x,y) = x^2 + y^2; sos
(x, y) |--> x^2 + y^2
sage: ImageSet(sos, ZZ^2)
Image of
 Ambient free module of rank 2 over the principal ideal domain Integer Ring by
 The map (x, y) |--> x^2 + y^2 from Vector space of dimension 2 over Symbolic Ring
sage: _.an_element()
1
sage: ImageSet(sos, Set([(3, 4), (3, -4)]))
Image of {...(3, -4)...} by
 The map (x, y) |--> x^2 + y^2 from Vector space of dimension 2 over Symbolic Ring
sage: _.an_element()
25

The new class mirrors and translates to SymPy's ImageSet:

sage: from sage.sets.image_set import ImageSet
sage: S = ImageSet(sin, RealSet.open(0, pi/4)); S
Image of (0, 1/4*pi) by The map sin from (0, 1/4*pi)
sage: S._sympy_()
ImageSet(Lambda(x, sin(x)), Interval.open(0, pi/4))

Most methods of ImageSet are actually provided by its base class, the new class ImageSubobject. For all morphisms in the Sets category, there is now a default method image, which constructs an instance of either ImageSubobject or ImageSet.

Manifolds

The structure parameter of the Manifold constructor has new, more convenient defaulting behavior. #33001

When parameters such as diff_degree or metric_name are given, the implied structure is selected:

sage: M = Manifold(3, 'M', diff_degree=0); M
3-dimensional topological manifold M
sage: M = Manifold(3, 'M', diff_degree=2); M
3-dimensional differentiable manifold M
sage: M = Manifold(3, 'M', metric_name='g'); M
3-dimensional Riemannian manifold M

Symplectic manifolds

Symplectic structures have been added to Sage (#30362).

Projective spaces

Real projective spaces have been added to the manifold catalog (#33221).

Algebra

• Ideal membership over quotient rings can now be decided (by reducing to ideal membership in the parent ring). #33237

• Iterating over (some) infinite modules (including ℤ^n) now enumerates the entire module, in a "natural" order. #33287

• BinaryQF.solve_integer() now also works for quadratic forms of square discriminant. #33026

• Quaternion fractional ideals (including orders) now support the usual operations (e.g., a*I, I*a, I+J). #32264

• AdditiveAbelianGroupWrapper now exposes .discrete_log() for (multi-dimensional) logarithms in finite abelian groups. #32384

Number theory

Elliptic curves

• Elliptic-curve DLP and Weil pairings over finite fields are now much faster (thanks to PARI). #33121

• Scalar multiplication on elliptic curves over finite fields is now significantly faster (thanks to PARI). #33147

• Computing the Weierstraß ℘ function of an elliptic curve is now significantly faster (thanks to PARI). #33223

Package upgrades

For a list of all packages and their versions, see

• https://repology.org/projects/?inrepo=sagemath_develop

Python 3.10

Sage 9.6 continues to support system Python 3.7.x to 3.10.x. If no suitable version of Python is installed in the system, Sage will install its own copy of Python. Sage now ships Python 3.10.2 for this purpose. #30767

FLINT and arb

FLINT from 2.7.1 to 2.8.4, arb to 2.22.1 #32211, #33189

The FLINT 2.8 series brings major new algorithms and general speedups. https://github.com/wbhart/flint2/blob/flint-2.8/NEWS#L1262 Note that Sage accepts system installations of FLINT >= 2.6.x. Users on older distributions who want to benefit from the speed ups in FLINT 2.8.x may want to use ./configure --without-system-flint.

Meta-ticket #31408 tracks the effort to make use of new features added in recent FLINT releases in the Sage library.

lrcalc

lrcalc, Anders Buch's Littlewood-Richardson Calculator, has been upgraded to the major new version 2.1 changelog. #31355

SymPy

SymPy has been upgraded to version 1.10 (release notes). #33398

polymake

polymake, a comprehensive system for computations in polyhedral geometry, tropical geometry, etc., has been upgraded to version 4.6 (release notes). #33251

New developer tools

Pre-built Docker containers on ghcr.io

Our portability CI on GitHub Actions builds Docker images for all tested Linux platforms (and system package configurations) and makes them available on GitHub Packages (ghcr.io). #39033

Since 9.6.beta1, the image version corresponding to the latest development release receives the additional Docker tag dev, see for example the Docker image for ubuntu-impish-standard. Thus, for example, the following command will work:

$ docker run -it ghcr.io/sagemath/sage/sage-docker-ubuntu-impish-standard-with-targets-optional:dev bash

Images whose names end with the suffix -with-targets-optional are the results of full builds and a run of make ptest. They also contain a copy of the source tree and the full logs of the build and test.

Smaller images corresponding to earlier build stages are also available:

• -with-system-packages provides a system installation with system packages installed, no source tree,

• -configured contains a partial source tree and has completed bootstrap and the configure,

• -with-targets-pre contains the full source tree and a full installation of all non-Python packages,

• -with-targets contains the full source tree and a full installation of Sage, including the HTML documentation, but make ptest has not been run yet.

Gitpod

Gitpod is a service that provides a development environment in the cloud based on VS Code. It is free to use for up to 50 hours per month. Sage now includes a configuration for Gitpod; see the new section Setting up your workspace in the Sage Developer's Guide. #33103

To launch Gitpod on a branch of a Trac ticket, you can use the new Gitpod badge in the ticket box.

New status badges on Trac tickets

We have now:

1. Linter that checks that the code of the current branch adheres to the style guidelines. In order to see details when it fails, you can click on it and then select the most recent workflow run.

2. Build & test that builds sage for the current branch (incrementally on top of the system packages of the develop branch) and runs the test. Details are again available by clicking on the badge. (This is currently still gray until #33263 is merged.)

3. Build documentation workflow that builds the HTML documentation for the current branch. If you click on it, you get the HTML output of the successful run. The idea is to use this to easily inspect changes to the documentation without the need to locally rebuild the docs yourself. If the doc build fails, you can go to the Actions tab of sagemath/sagetrac-mirror repo and choose the particular branch to see what went wrong.

The idea is that these three status badges complement the existing patchbots (and maybe even replace them in the future). In particular, they are supposed to always be green.

Sage patchbot on GitHub Actions

The Sage patchbot can now be run on GitHub Actions, on top of any of the Linux platforms for which we have prebuilt Docker images.#33253

Availability of Sage 9.6 and installation help

The first development release of the 9.6 series, 9.6.beta0, was tagged on 2022-02-06. The current development release is 9.6.beta4, tagged on 2022-03-08.

The SageMath installation guide now provides a decision tree that guides users and developers to a type of installation suitable for their system and their needs.

The Sage source code is available in the sage git repository.

SageMath 9.6 supports all platforms that were supported by Sage 9.5 and adds support for building on distributions that use the (unreleased) GCC 12 series (fedora-36). #33187

• See sage-devel for development discussions and sage-release for announcements of beta versions and release candidates.

More details

• Open Meta-Tickets

• Trac tickets with milestone 9.6

• Diff from 9.5