Sage 10.4 Release Tour
Sage 10.4 was released on July 19, 2024. This is the current stable release.
Here is an overview of some of the main changes in this version.
The FreeModule constructor was recently generalized so that it can create CombinatorialFreeModule objects. In particular,
sage: ZZ^3
Ambient free module of rank 3 over the principal ideal domain Integer Ring
sage: ZZ^['a','b','c']
Free module generated by {'a', 'b', 'c'} over Integer RingNow MatrixSpace and matrix have been extended in a similar way: When lists or enumerated sets of row indices and column indices are given using the new parameters row_keys and column_keys, it constructs CombinatorialFreeModules whose bases are indexed by these index sets, and then returns the homset (or an element of it). #37514 #37692
sage: M = matrix([[1,2,3], [4,5,6]],
....: column_keys=['a','b','c'], row_keys=['u','v']);In particular, this enables the construction:
sage: ZZ^(2, 3)
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
sage: ZZ^(['x','y'], ['a', 'b', 'c'])
Set of Morphisms
from Free module generated by {'a', 'b', 'c'} over Integer Ring
to Free module generated by {'x', 'y'} over Integer Ring
in Category of finite dimensional modules with basis over Integer RingAs a first application, the methods incidence_matrix, [weighted_]adjacency_matrix, and kirchhoff_matrix of Graph and DiGraph have been extended to support constructing a free module morphism instead of a matrix. #37692 #37955
sage: D12 = posets.DivisorLattice(12).hasse_diagram()
sage: phi_VE = D12.incidence_matrix(vertices=True, edges=True); phi_VE
Generic morphism:
From: Free module generated by
{(1, 2), (1, 3), (2, 4), (2, 6), (3, 6), (4, 12), (6, 12)}
over Integer Ring
To: Free module generated by {1, 2, 3, 4, 6, 12} over Integer Ring
sage: print(phi_VE._unicode_art_matrix())
(1, 2) (1, 3) (2, 4) (2, 6) (3, 6) (4, 12) (6, 12)
1⎛ -1 -1 0 0 0 0 0⎞
2⎜ 1 0 -1 -1 0 0 0⎟
3⎜ 0 1 0 0 -1 0 0⎟
4⎜ 0 0 1 0 0 -1 0⎟
6⎜ 0 0 0 1 1 0 -1⎟
12⎝ 0 0 0 0 0 1 1⎠This style of printing the morphism as a "border matrix" suggests the viewpoint as "matrices whose rows and columns are labeled with arbitrary objects rather than numerical indices". To support this, we equip the morphisms of CombinatorialFreeModules with various methods pulled back from matrices.
- Endomorphisms of
CombinatorialFreeModule(and all other finite-dimensional modules with basis) now have methods for the invariantscharpoly,det,fcp,minpoly,trace, delegating to the methods of the representing matrices. #37731
Jordan decomposition of a matrix and is_semisimple() test #37710
Tensor products of combinatorial free modules now have a functorial construction. #37451
Free modules of finite rank without distinguished basis (defined in sage.tensor) have also seen a few improvements:
-
FiniteRankFreeModule.isomorphism_with_fixed_basisnow gives an instance of the new classSetIsomorphism, and its inverse is defined. #37512 - The new method
FiniteRankFreeModuleMorphism.displayshows the matrix with rows and columns decorated with the names of the basis elements. #37825 -
FreeModuleAutomorphismandFiniteRankFreeModuleEndomorphism(a new subclass ofFiniteRankFreeModuleMorphism) now define more methods providing invariantsdet,charpoly,fcp,trace, etc. #37826, delegating to the methods of the representing matrices in some basis #37831
The SetSystem representation is now more informative. #37904
sage: M = matroids.CompleteGraphic(7)
sage: M.bases()
SetSystem of 16807 sets over 21 elements
The methods independent_sets and independent_r_sets got combined into one method with an optional argument. Similarly, dependent_r_sets was renamed to dependent_sets (here the argument remains mandatory). #38057
sage: M = matroids.catalog.Fano()
sage: M.independent_sets()
SetSystem of 57 sets over 7 elements
sage: M.independent_sets(3)
SetSystem of 28 sets over 7 elements
sage: M.dependent_sets(3)
SetSystem of 7 sets over 7 elements
Matroids got relabel method. #37775
We improved the performance of GraphicMatroid (#37839), CircuitsMatroid (#37930), FlatsMatroid (#38027), and DualMatroid (#38013).
LinearMatroid.representation now supports constructing a free module morphism instead of a matrix, and the Matroid constructor accepts such morphisms as input. #37692 #37940
sage: M = matroids.catalog.Fano()
sage: A = M.representation(order=True); A
Generic morphism:
From: Free module generated by {'a', 'b', 'c', 'd', 'e', 'f', 'g'} over Finite Field of size 2
To: Free module generated by {0, 1, 2} over Finite Field of size 2
sage: Matroid(A)
Binary matroid of rank 3 on 7 elements, type (3, 0)Method measuring maximal angles between convex cones was added. #37854
A projective curve has now its Jacobian, whose rational points form a group isomorphic to the Picard group of degree 0 of the curve. It works via divisors of the function field and has no scheme structure (of course). #35467
sage: A2.<x,y> = AffineSpace(QQ, 2)
sage: f = y^3 + x^4 - 5*x^2*y + 2*x*y - x^2 - 5*y - 4*x + 1
sage: C = Curve(f, A2)
sage: X = C.projective_closure()
sage: X.genus()
3
sage: X.rational_points(bound=5)
[(0 : 0 : 1), (1/3 : 1/3 : 1)]
sage: Q = X(0,0,1).place()
sage: P = X(1,1,3).place()
sage: D = P - Q
sage: D.degree()
0
sage: J = X.jacobian(model='hess', base_div=3*Q)
sage: G = J.group()
sage: p = G.point(D) # a rational point of the Jacobian represented by D
sage: 2*p + 3*p == 5*p
TrueElliptic and hyperelliptic curves have had their own Jacobians. The "new" Jacobian is accessible from points of the "native" Jacobian:
sage: k.<a> = GF((5,2))
sage: E = EllipticCurve(k,[1,0]); E
Elliptic Curve defined by y^2 = x^3 + x over Finite Field in a of size 5^2
sage: E.order()
32
sage: P = E([a, 2*a + 4]) # elliptic curve is its own Jacobian
sage: P
(a : 2*a + 4 : 1)
sage: P.order()
8
sage: p = P.point_of_jacobian_of_curve()
sage: p
[Place (x + 4*a, y + 3*a + 1)]
sage: p.order()
8
sage: Q = 3*P
sage: q = Q.point_of_jacobian_of_curve()
sage: q == 3*p
True
sage: G = p.parent()
sage: G.order()
32
sage: G
Group of rational points of Jacobian over Finite Field in a of size 5^2 (Hess model)Rings of Drinfeld modular forms of any ranks for the full modular group
sage: q = 5
sage: A = GF(q)['T']
sage: K.<T> = Frac(A)
sage: M = DrinfeldModularForms(K, rank=3); M
Ring of Drinfeld modular forms of rank 2 over
Fraction Field of Univariate Polynomial Ring in T over Finite Field of size 5
sage: M.gens() # the generators are the coefficient forms
[g1, g2, g3]
sage: M.basis(20*(q - 1)) # basis generating the subspace of any given weight
[g1^2*g2^3, g1^8*g2^2, g1^14*g2, g1^20]
sage: (1/T)*M.0 + 3*(M.2*M.1)/T
-2/T*g2*g3 + 1/T*g1The Reference Manual in HTML format now provides links for each class, function, and method back to the source code on GitHub. This makes it convenient to make small edits to the docstring directly on GitHub, or just to inspect the source code. #37589 #38121
The documentation in HTML format now offers a dropdown menu for selecting a different version of the documentation. We strive to maintain documentations for stable releases up to last 2 years. #38285
Example code is now available also in pure Python form, along with Sage code (and live Sage code if live doc is available), in tabs for each EXAMPLES block. #37083
The package lists in the Reference Manual have been reorganized by categories. #37315
| Standard packages | Optional Packages | Experimental Packages |
|---|---|---|
| Mathematics | Mathematics | Mathematics |
| Front-end, graphics, document preparation | Front-end, graphics, document preparation | |
| Other dependencies | Other dependencies | Other dependencies |
The dependency graph and SBOM provided by GitHub for SageMath now includes all Python packages that Sage uses. #36999
"Καλώς ήρθατε στο Sage" a Greek version of "A Tour of Sage" was added to our documentation. #37198
If the Sage documentation has been built locally, sage -n jupyterlab now launches a documentation server that makes the documentation available in the Help menu in JupyterLab. Otherwise the online official documentation http://doc.sagemath.org is used as before. #37878
Please read our updated Sage Developer Guide. #30201 #37399 #37401 #37444 #37485 #37487 #37508 #38117
The Lint workflow, automatically run on every pull request, now additionally runs the Python linter Ruff. Any codestyle warnings are annotated in the "Files changed" tab. The minimal configuration used by the CI can be also used locally with ./sage -tox -e ruff-minimal and also runs as part of the default tests in ./sage -tox. A full configuration can be run using ./sage -tox -e ruff. #37453
The Build & Test workflow, automatically run on every pull request, now gives a much faster feedback to developers. Both the static check with Pyright and the doctests of the files changed in the PR (sage -t --new) now run in separate jobs, and the green checkmark or the red X are now shown within 10–20 minutes. #36498 #37926 #37988 #38046 #38144
The annotations of doctest failures in the "Files changed" tab become available when the run of the whole testsuite (sage -t --long) has been completed. To reduce the wait, sage -t --long has been split into multiple parallel jobs. Crashes during doctests, for example segmentation faults, are now annotated in the source code as well. #37738 #38090
The banner of the documentation preview now displays links back to the PR and to the diff of the generated documentation. #38127 #38129 #38213 #38332 #38353 #38378
The "CI Fix" mechanism has been switched from the "p: blocker" label to the new "p: CI Fix" label. #37950
The size of our pull requests is now classified by a new type of labels with the v: prefix. #37262 #38114
Sage now provides a standardized way for developers to enrich the Sage documentation by linking to the online documentation of many external packages. #37598 #37575
The section on hyperlinks in the Sage Developer Guide explains the two mechanisms:
-
For various packages that, like Sage, use Sphinx as the documentation system, we can refer to the modules, classes, methods, functions just like we do within the Sage library. This is now preconfigured for CVXOPT, CVXpy, cypari2, cysignals, FLINT, gmpy2, ipywidgets, Matplotlib, mpmath, NetworkX, NumPy, pplpy, rpy2 , SciPy, and SymPy, and it is easy to add support for more.
-
For the packages ECL, GAP, Giac, Maxima, Meson, Pari, polymake, PPL, QEPCAD, SCIP, Singular, SoPlex, we have defined Sphinx roles to facilitate creating documentation links; the Developer Guide gives clear examples for each package.
Linking to Sage repository files has been standardized using the new Sphinx role :sage_root:. #37546
Our GH Actions running on every release now build platform-independent wheels for the distribution packages sagemath-environment, sage-setup, sage-sws2rst. We provide platform wheels for more modularized distributions: To sagemath-objects and sagemath-categories, we add sagemath-bliss, sagemath-coxeter3, sagemath-mcqd, and sagemath-tdlib. Also, macOS arm64 wheels are now additionally built. #36525 #37099 #37503 #38200
Many source files now carry # sage_setup: distribution directives. These directives at the top of the source files inform developers about the assignment of modules to the existing pip-installable distributions. #38088
More information about the modularization project: Meta-ticket #29705
It is now possible to refer to Python packages via their PURL (see draft PEP 725) instead of their SPKG name.
For now a string of the form pkg:pypi/DISTRO-NAME is simply a nickname for the (unique) SPKG that has DISTRO-NAME in their version_requirements.txt or requirements.txt file. The scheme can also be omitted: pypi/DISTRO-NAME also works. We also map pkg:generic/PACKAGE-NAME to PACKAGE_NAME. #37500
sage --package create --pypi now also fills dependencies from the PyPI metadata of wheel packages. When some of the Python dependencies obtained in this way do not have SPKGs yet, they are also automatically created. #37500
The LinBox suite has been upgraded to givaro 4.2.0, fflas-ffpack 2.5.0, linbox 1.7.0. #37938 #38020 #38025 #38136
Singular has been upgraded to version 4.4.0. #37492 #37570
NTL has been upgraded from 11.4.3 to 11.5.1. #37251
SciPy has been upgraded to 1.12 (release notes). #37266
FLINT has been upgraded to 3.1.3. The new optional package python_flint provides alternative bindings to the FLINT library. We have added it as preparation for a later upgrade of SymPy. #37203 #37224
SymPy has been upgraded to 1.12.1, a small maintenance update (release notes). #38141
gnumake_tokenpool #37498
gc 8.2.6, libatomic_ops 7.8.2 #37249 #37931
ECL 24.5.10 #38009
openssl 3.2.2 #38157
Various Python package upgrades #37637 #38101 #38226
Sage continues to support system Python installations of versions 3.9.x to 3.12.x; support for Python 3.12 is now considered stable. The version of Python that is installed when no suitable system Python is available has been updated to 3.12.4 (release notes). #37834 #37914
The Sage distribution now builds wheels of Python packages using build, version 1.2.1, which has been made a standard package. Other Python build and packaging tools upgraded include: pip 24, setuptools 69.5.1, hatchling 1.22.5, platformdirs 4.2.0, packaging 24.0, setuptools_scm 8.1.0, trove_classifiers 2024.4.10, wheel 0.43.0. #35618 #37277 #37300 #38226
Cython has been upgraded to 3.0.10. #37584
cypari2 2.1.5, memory_allocator 0.1.4 #37665
The SCIP Optimization Suite has been updated to version 9. This includes updates of scip to 9.0.1, scip_sdp to 4.4, soplex to 7.0.1, papilo to 2.2.1, PySCIPOpt to 5, and of the dependency onetbb to 2021.12.0. #37392 #37494 #38147
The packages igraph and python_igraph have been upgraded to versions 0.10.12, 0.11.5 (release notes). #37819
The packages normaliz and pynormaliz have been upgraded to 3.10.3, 2.20. #38140 #38260
polymake has been upgraded to 4.12 (release notes). #38140
The polynomial system solver msolve has been upgraded from 0.5.0 to 0.6.5. #37673
The package fricas has been upgraded to 1.3.10 and now uses SBCL (if a suitable version is installed as a system package) instead of ECL as the Common Lisp implementation. #37041
The package tdlib (treedec) has been upgraded to 0.9.3. #38163
The packages sage_numerical_backends_coin, sage_numerical_backends_cplex, and sage_numerical_backends_gurobi have been upgraded to 10.4. This upgrade makes these packages compatible with Cython 3. #38319
pycryptosat has been reduced to a "pip" package. #37669
Sage now uses cryptographically secure SHA-256 hashes for authenticating downloaded upstream tarballs. #37726
For a list of all packages and their versions, see
Classes sage.groups.old.Group #37449, sage.rings.ring.CommutativeAlgebra #37464
Numerous is_... functions have been deprecated in favor of using either isinstance or testing membership in a category:
-
is_Cone,is_Polyhedron,is_LatticePolytope#37057 -
is_Hecke...#37895 -
is_FreeAlgebra,is_QuaternionAlgebra,is_SymmetricFunctionAlgebra#37896 -
is_Monoid,is_FreeMonoid,is_FreeAbelianMonoid#37897 -
is_AbelianGroup,is_DualAbelianGroup,is_MatrixGroup#37898 -
is_Category,is_Endset,is_Homset,is_Parent,is_RingHomset,is_SimplicialComplexHomset#37922 -
is_FGP_Module,is_FilteredVectorSpace,is_FreeQuadraticModule,is_FreeModule,is_FreeModuleHomspace,is_MatrixSpace,is_Module,is_VectorSpace,is_VectorSpaceHomspace#37924, -
is_AffineScheme,is_AffineSpace,is_AlgebraicScheme,is_AmbientSpaceis_Berkovich,is_Berkovich_Cp,is_CPRFanoToricVariety,is_DivisorGroup,is_EllipticCurve,is_HyperellipticCurve,is_ProductProjectiveSpaces,is_ProjectiveSpace,is_QuarticCurve,is_Scheme,is_SchemeHomset,is_ToricVariety#38022 -
is_Automaton,is_FiniteStateMachine,is_FSMProcessIterator,is_FSMState,is_FSMTransition,is_Transducer#38032 -
is_ArithmeticSubgroup,is_CongruenceSubgroup,is_DirichletGroup,is_Gamma,is_Gamma0,is_Gamma1,is_GammaH,is_ModularAbelianVariety,is_ModularFormsSpace,is_ModularSymbolsSpace,is_SL2Z#38035 -
is_AdditiveGroupElement,is_AlgebraElement,is_CommutativeAlgebraElement,is_CommutativeRingElement,is_DedekindDomainElement,is_Element,is_EuclideanDomainElement,is_FieldElement,is_InfinityElement,is_IntegralDomainElement,is_Matrix,is_ModuleElement,is_MonoidElement,is_MultiplicativeGroupElement,is_PrincipalIdealDomainElement,is_RingElement,is_Vector#38077 -
is_AbelianGroupMorphism,is_ChainComplexMorphism,is_Map,is_Morphism,is_PermutationGroupMorphism,is_SimplicialComplexMorphism#38103 -
is_AbsoluteNumberField,is_NumberFieldFractionalIdeal,is_NumberFieldFractionalIdeal_rel,is_NumberFieldIdeal,is_NumberFieldOrder,is_RelativeNumberField#38124 -
is_MutablePoset#38125 -
is_Fan,is_NefPartition,is_PointCollection,is_ToricLattice,is_ToricLatticeElement,is_ToricLatticeQuotient#38126 -
is_AlgebraicNumber,is_AlgebraicReal,is_ComplexDoubleElement,is_ComplexIntervalFieldElement,is_ComplexNumber,is_FractionField,is_FractionFieldElement,is_Integer,is_IntegerMod,is_IntegerRing,is_Rational,is_RationalField,is_RealDoubleElement,is_RealIntervalField,is_RealIntervalFieldElement,is_RealNumber#38128 -
is_AbelianGroupElement,is_ChainComplexHomspace,is_DirichletCharacter,is_DiscreteProbabilitySpace,is_DiscreteRandomVariable,is_DualAbelianGroupElement,is_FreeAbelianMonoidElement,is_FreeAlgebraQuotientElement,is_FreeModuleElement,is_FreeMonoidElement,is_Functor,is_Graphics,is_LinearConstraint,is_LinearFunction,is_LinearTensor,is_LinearTensorConstraint,is_ManinSymbol,is_ModularFormElement,is_ModularSymbolsElement,is_PermutationGroupElement,is_ProbabilitySpace,is_RandomVariable#38184
Previously deprecated functionality has been removed. #37312 #37722 #37855 #37856 #37867 #37868 #37869 #37870 #38095 #38099
Please read our updated Sage Installation Guide. #37184 #37309 #37411
The source code is available in the Sage GitHub repository.
Sage builds successfully on the following platforms:
-
Linux 64-bit (x86_64)
- ubuntu-{xenial-toolchain-gcc_9, bionic-gcc_8, focal, jammy, lunar, mantic, noble}
- debian-{bullseye, bookworm, trixie, sid}
- linuxmint-{20.1, 20.2, 21, 21.1, 21.2, 21.3}
- fedora-{30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
- centos-stream-9-python3.9
- almalinux-{8, 9}
- archlinux
- gentoo
- opensuse-{15.5-gcc_11-python3.11, tumbleweed}
-
Linux 32-bit (i386/i686)
- debian-bullseye
-
macOS (Intel) (x86_64) - with Homebrew or without
- macOS 12.x (Monterey)
- macOS 13.x (Ventura)
- macOS 14.x (Sonoma)
-
macOS (Apple Silicon, M1/M2/M3) - with Homebrew or without
- Make sure that
/usr/localdoes 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/M3 is installed in/opt/homebrew, not/usr/local. - Be sure to follow the README and the instructions that the
./configurecommand issues regarding the installation of system packages from Homebrew or conda.
- Make sure that
You can also build Sage on top of conda-forge on Linux and macOS.
./configure --disable-editable now implies --enable-wheels; Sage no longer supports the outdated, distutils-style direct installation of the Sage library in site-packages. #37973 #38304
The optional parts of the Sage library that use the optional packages bliss, coxeter3, mcqd, meataxe, sirocco, tdlib are no longer built automatically. Please use ./configure --enable-sagemath_bliss etc. before building, or use ./sage -i sagemath_bliss or make sagemath_bliss. #37857
Support of ubuntu-trusty, debian-buster, and centos-stream-8 has been dropped, as the platforms have reached their end of life. #37351 #38008 #38179
Support for fedora-40 has been added, as GCC 14.x is now accepted from the system. The gcc/gfortran packages have been upgraded from 12.3.0 to 13.2.0. #37537 #37646 #38008
Sage 10.x does not support Cygwin; use Windows Subsystem for Linux instead. The support code for Cygwin was removed in the Sage 10.3 development cycle. Users on Windows 10 and 11 should 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 Dev Containers or WSL remote.
Thanks to the work of downstream packagers, Sage 10.4 is already available in Arch Linux and Void Linux. See https://repology.org/project/sagemath/versions
On ubuntu-mantic, the Maxima package may fail to build when system ECL is in use. Workaround: Use ./configure --without-system-ecl #36672
OpenJPEG 2.5.1 is broken and leads to a build failure in Pillow. Upgrade OpenJPEG to 2.5.2 or use #37505 as a workaround.
No latex display in the Jupyter notebook when offline. Workaround: Use ./sage -pip uninstall jupyterlab-mathjax2. #36914
See README.md in the source distribution for installation instructions.
Visit sage-support for installation help.