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Sage 9.8 Release Tour

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Sebastian Oehms edited this page May 26, 2023 · 16 revisions

Sage 9.8 was released on February 11, 2023.

A total of 80 people were involved as authors or reviewers of code contributions to Sage 9.8.

Here is an overview of some of the main changes in this version.

Linear algebra

Submodules of tensor modules with prescribed symmetries

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.

Free module isomorphisms corresponding to fixed standard bases of tensor modules

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]

Commutative algebra

Solving polynomial systems using msolve

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_basis method of polynomial ideals now supports using msolve to compute Gröbner bases over prime fields (with some cardinality constraints).
  • The variety method supports computing real or complex solutions of zero-dimensional polynomial systems over the rational numbers using msolve.

(Some of these features use probabilistic algorithms.)

Lazy power series ring

The lazy power series ring has now been replaced by what was previously known as the lazy Taylor series ring. #32367 This now supports multiple variables with many other features that are also available for lazy Laurent series.

sage: R.<a,b,c,d> = LazyPowerSeriesRing(QQ)
sage: (1 - c + d) / (1 + a*b)
1 + (-c+d) + (-a*b) + (a*b*c-a*b*d) + a^2*b^2 + (-a^2*b^2*c+a^2*b^2*d) + (-a^3*b^3) + O(a,b,c,d)^7
sage: exp(a + b/(1 - c))
1 + (a+b) + (1/2*a^2+a*b+1/2*b^2+b*c) + (1/6*a^3+1/2*a^2*b+1/2*a*b^2+1/6*b^3+a*b*c+b^2*c+b*c^2) + ... + O(a,b,c,d)^7
sage: U = R.undefined()
sage: U.define(a + b * U + c*U^2)
sage: U
a + a*b + (a*b^2+a^2*c) + (a*b^3+3*a^2*b*c) + (a*b^4+6*a^2*b^2*c+2*a^3*c^2) + (a*b^5+10*a^2*b^3*c+10*a^3*b*c^2) + O(a,b,c,d)^7
sage: U(d,d,d,d)
d + d^2 + 2*d^3 + 4*d^4 + 9*d^5 + 21*d^6 + O(a,b,c,d)^7
sage: [c.lc() for c in U(d,d,d,d)[:15]]  # The Motzkin numbers
[1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835]

The ability to compute a (infinite) q-Pochhammer $(z; q)_{\infty}$ has been added: #34381

sage: q = ZZ['q'].fraction_field().gen()
sage: P.<x,y> = LazyPowerSeriesRing(q.parent())
sage: x.q_pochhammer(q)
1 + ((-1/(-q+1))*x) + ((q/(q^3-q^2-q+1))*x^2) + ((-q^3/(-q^6+q^5+q^4-q^2-q+1))*x^3) + ... + O(x,y)^7
sage: (x+y).q_pochhammer(q)
1 + ((-1/(-q+1))*x+(-1/(-q+1))*y) + ((q/(q^3-q^2-q+1))*x^2+(2*q/(q^3-q^2-q+1))*x*y+(q/(q^3-q^2-q+1))*y^2) + ... + O(x,y)^7

sage: L.<z> = LazyLaurentSeriesRing(q.parent())
sage: L.q_pochhammer(q)
1 + (-1/(-q + 1))*z + (q/(q^3 - q^2 - q + 1))*z^2 + (-q^3/(-q^6 + q^5 + q^4 - q^2 - q + 1))*z^3 + ... + O(z^7)
sage: L.q_pochhammer(q) / (z*q^3).q_pochhammer(q)
1 + (-q^2 - q - 1)*z + (q^3 + q^2 + q)*z^2 - q^3*z^3 + O(z^7)

Taking powers in the lazy series rings is now (much) faster. #34350

Free resolution

Free resolutions of modules over polynomial rings are directly accessible from the module. #34379

sage: S.<x,y,z,w> = PolynomialRing(QQ)
sage: I = S.ideal([y*w - z^2, -x*w + y*z, x*z - y^2])
sage: from sage.homology.free_resolution import FreeResolution
sage: FreeResolution(I)
S^1 <-- S^3 <-- S^2 <-- 0
sage: FreeResolution(I, graded=True)
S(0) <-- S(-2)⊕S(-2)⊕S(-2) <-- S(-3)⊕S(-3) <-- 0
sage: I.free_resolution()
S^1 <-- S^3 <-- S^2 <-- 0
sage: I.graded_free_resolution()
S(0) <-- S(-2)⊕S(-2)⊕S(-2) <-- S(-3)⊕S(-3) <-- 0

Miscellaneous

  • Tensor products of commutative algebras now know they are commutative. #34453

Algebra

  • Fixed a multiplication bug in the exterior algebra. #34707
  • We can construct the ring of q-commuting polynomials: #34412 
sage: q = ZZ['q'].fraction_field().gen()
sage: R.<x,y> = algebras.qCommutingPolynomials(q)
sage: x * y
x*y
sage: y * x
q*x*y
sage: f = (x + y)^10
sage: all(f[b] == q_binomial(10, b.list()[0]) for b in f.support())  # the q-binomial theorem
True

These can also be constructed with respect to any skew-symmetric matrix:

sage: B = matrix([[0,1,2],[-1,0,3],[-2,-3,0]])
sage: B
[ 0  1  2]
[-1  0  3]
[-2 -3  0]
sage: q = ZZ['q'].gen()
sage: R.<x,y,z> = algebras.qCommutingPolynomials(q, B)
sage: y * x
q*x*y
sage: z * x
q^2*x*z
sage: z * y
q^3*y*z
  • All tensor products of modules now must implement a tensor_factors() method. #34393
  • Minimal polynomials are now computed using NTL's MinPolyMod() in important special cases. #34906
  • All finite fields now implement .to_integer() and .from_integer() methods, generalizing the (now deprecated) .fetch_int() and .integer_representation() methods. #33941
  • BinaryQF and QuadraticForm objects can now be initialized from a polynomial. #34863
  • A generic ProductTree class is now available in sage.rings.generic. #34791

Combinatorics

More constructions of Hadamard matrices, general and skew, were added. #34807

Sage now is able to construct a Hadamard matrix for all orders 4n < 668. (668 is the first order for which the existence of a Hadamard matrix is open.)

A similar effort for skew Hadamard matrices is underway. #34848

Polyhedral geometry

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

Number theory

  • CRT_list() now uses a binary tree instead of folding the input from one side, which can be much faster. #34512

Elliptic curves

  • Frobenius isogenies (in particular, endomorphisms) are now available as EllipticCurveHom objects. #33915
  • Scalar multiplications are now available as EllipticCurveHom objects. #32826
  • Isomorphisms are now sorted in such a way that identity and negation morphisms come first. #34728
  • The extent of copying cached orders through isogenies has been extended. #34732

Knot theory

Manifolds

  • New features in the algebraic part, cf. examples involving FiniteRankFreeModule in the Linear algebra section
  • Tensor products of modules of tensor fields have been implemented via the new methods tensor_product and tensor_power (#34589); for example:
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: XM = M.vector_field_module(); XM
Free module X(M) of vector fields on the 2-dimensional differentiable manifold M
sage: OM = XM.dual(); OM
Free module Omega^1(M) of 1-forms on the 2-dimensional differentiable manifold M
sage: T = XM.tensor_product(OM); T
Free module T^(1,1)(M) of type-(1,1) tensors fields on the 2-dimensional differentiable manifold M
sage: a = T.an_element(); a
Tensor field of type (1,1) on the 2-dimensional differentiable manifold M
sage: a.display()
2 ∂/∂x⊗dx
sage: T is M.tensor_field_module((1, 1))
True
sage: XM.tensor_power(3)
Free module T^(3,0)(M) of type-(3,0) tensors fields on the 2-dimensional differentiable manifold M
sage: XM.tensor_power(3) is M.tensor_field_module((3,0))
True
sage: T2 = T.tensor_power(2); T2
Free module T^(2,2)(M) of type-(2,2) tensors fields on the 2-dimensional differentiable manifold M
sage: T2 is M.tensor_field_module((2, 2))
True
sage: T2.tensor_factors()
[Free module X(M) of vector fields on the 2-dimensional differentiable manifold M,
 Free module X(M) of vector fields on the 2-dimensional differentiable manifold M,
 Free module Omega^1(M) of 1-forms on the 2-dimensional differentiable manifold M,
 Free module Omega^1(M) of 1-forms on the 2-dimensional differentiable manifold M]
  • Internal code improvements have been performed, see the changelog for more details.

New packages and package upgrades

SCIP Optimization Suite 8.0

SCIP, one of the fastest non-commercial solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP), was relicensed from a non-free academic license to a permissive open source license (Apache 2.0) on the occasion of the 20th anniversary of the SCIP project in December 2022.

Sage now provides up-to-date packages from the SCIP Optimization Suite:

  • SoPlex 6.0.x, a high performance LP solver using the revised simplex method, with special support for computing high-precision solutions and for the exact solution of LPs with rational input data. #34742
  • SCIP 8.0.x, the mixed integer (linear and nonlinear) programming solver and constraint programming framework. #31329
  • PaPILO, providing parallel presolve routines for (mixed integer) linear programming problems, including support for exact rational arithmetic. #34726 In addition, Sage provides:
  • SCIP-SDP, an extension of SCIP for solving mixed integer semidefinite programs. A new optional package provides the SDP solver DSDP. #34749
  • https://github.com/scipopt/PySCIPOpt, a Cython interface to the SCIP library. #21003

A new MixedIntegerLinearProgram backend using PySCIPOpt provides access to the solver. Use the keyword argument solver="SCIP". This keyword argument can also be passed to various methods that use MixedIntegerLinearProgram internally.

sage: g = graphs.PetersenGraph()
sage: g.pathwidth(algorithm='MILP', solver='SCIP')
5

msolve: polynomial system solver

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

Kissat SAT Solver

The new optional package kissat provides an additional SAT solver. #34909, #34911

Python 3.11

Python has been upgraded to 3.11.1. The Python 3.11 series brings many improvements, including fine-grained error locations in tracebacks and major speed improvements over Python 3.10. Sage continues to support system Python 3.8.x, 3.9.x, 3.10.x, and now also supports system Python 3.11.x. #34271, #33842

Other package upgrades

PARI has been upgraded to version 2.15.2. #34537

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

SymPy has been updated to 1.11.1 (release notes for 1.11). #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

Sphinx has been upgraded from 4.4.x to 5.2.3. #34615

For a list of all packages and their versions, see

New tools for developers

Sage development has moved from Trac to GitHub

Sage development has moved to GitHub. After over 17 years (2005–2023) of development coordinated on our Trac server, our development workflow now uses issues/PRs in our main GitHub repository sagemath/sage. #30363

All 35,000 Trac tickets have been migrated using our custom script that created a migration archive suitable for importing to GitHub. This preserves the valuable discussions that are a part of the rich history of the project.

Our development guide is still in need of updating to reflect this change, but we have prepared a transition guide from Trac to GitHub.

The migration has been a long time in the making, and many developers have contributed to making it happen.

Faster portability testing with tox -e docker-...-incremental

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

Wheels for venvs: ./configure --enable-wheels

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. Running sage -b or make build is 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, use make wheels.

  • ./configure --enable-wheels: When running sage -b or make 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 legacy setup.py install command. For any source changes to take effect, use sage -b or make build. No wheel is available; to build a wheel once, use make wheels.

  • ./configure --disable-editable --enable-wheels: Sage builds a wheel for sagemath-standard and installs the wheel.

make -j list-broken-packages

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

Configuration changes

Support for GCC < 8 dropped; C++17 features now available

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.

Native support for Apple Silicon (M1/M2)

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

Availability of Sage 9.8 and installation help

Sources

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

Sage builds successfully on the following platforms:

  • Linux 64-bit (x86_64)
  • Linux 32-bit (i386/i686)
    • ubuntu-bionic-gcc_8
    • debian-buster
  • macOS (Intel) (x86_64) - with Homebrew or without
    • macOS 11.x (Big Sur)
    • macOS 12.x (Monterey)
    • macOS 13.x (Ventura)
  • macOS (Apple Silicon, M1/M2) - with Homebrew or without
    • Make sure that /usr/local does not contain an old copy of homebrew (or other software) for x86_64 that you may have copied from an old machine. Homebrew for the M1/M2 is installed in /opt/homebrew, not /usr/local.
    • Be sure to follow the README and the instructions that the ./configure command issues regarding the installation of system packages from Homebrew or conda.

You can also build Sage on top of conda-forge on Linux and macOS.

Known issues and workarounds:

  • If your system singular package is very new (>= 4.3.1p3), then sagelib will fail to build. Workaround: Use ./configure --without-system-singular. Alternatively, switch to the current development version. #34851
  • On 32-bit platforms, the combination of Python 3.11 with GCC 12 leads to errors in handling large integers. Workaround: Use Python 3.10.x or a different compiler version. Alternatively, switch to the current development version. #34997
  • If your system openblas package is very new (0.3.22), then scipy.linalg and Sage are defective. Workaround: Use ./configure --without-system-openblas. Alternatively, switch to the current development version. #35371

Sage 9.8 does not support Cygwin; use Windows Subsystem for Linux instead. Because of unresolved problems with standard packages GIAC (#34269), ECL (#34127), Maxima (#30796), and the rebasing facility (#34223), Sage 9.8 does not support Cygwin. Users on Windows 10 and 11 can migrate to using WSL as described in our installation guide. A convenient way to use such an installation of Sage is via VS Code's WSL remote. #34301, #30484

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