Sage 9.4 Release Tour

current development cycle (2021)

Goals and tickets

• Add support for Python 3.10
• Add support for gcc 11
• Add support for macOS Big Sur that does not depend on homebrew's gcc@10
• packages upgrades

  • - https://repology.org/projects/?inrepo=sagemath_develop - many upgrades enabled by dropping support for Python 3.6

• Drop support for optional packages with system gcc 4.x

• Open Meta-Tickets

• Trac tickets with milestone 9.4

Symbolics

Extended interface with SymPy

The SymPy package has been updated to version 1.8.

SageMath has a bidirectional interface with SymPy. Symbolic expressions in Sage provide a _sympy_ method, which converts to SymPy; also, Sage attaches _sage_ methods to various SymPy classes, which provide the opposite conversion.

In Sage 9.4, several conversions have been added. Now there is a bidirectional interface as well for matrices and vectors. #31942

sage: M = matrix([[sin(x), cos(x)], [-cos(x), sin(x)]]); M
[ sin(x)  cos(x)]
[-cos(x)  sin(x)]
sage: sM = M._sympy_(); sM
Matrix([
[ sin(x), cos(x)],
[-cos(x), sin(x)]])
sage: sM.subs(x, pi/4)           # computation in SymPy
Matrix([
[ sqrt(2)/2, sqrt(2)/2],
[-sqrt(2)/2, sqrt(2)/2]])

Work is underway to make SymPy's symbolic linear algebra methods available in Sage via this route.

Sage has added a formal set membership function element_of for use in symbolic expressions; it converts to a SymPy's Contains expression. #24171

Moreover, all sets and algebraic structures (Parents) of SageMath are now accessible to SymPy by way of a wrapper class, which implements the SymPy Set API. #31938

sage: F = Family([2, 3, 5, 7]); F
Family (2, 3, 5, 7)
sage: sF = F._sympy_(); sF
SageSet(Family (2, 3, 5, 7))          # this is how the wrapper prints
sage: sF._sage_() is F
True                                  # bidirectional
sage: bool(sF)
True
sage: len(sF)
4
sage: sF.is_finite_set                # SymPy property
True

Finite or infinite, we can wrap it:

sage: W = WeylGroup(["A",1,1])
sage: sW = W._sympy_(); sW
SageSet(Weyl Group of type ['A', 1, 1] (as a matrix group acting on the root space))
sage: sW.is_finite_set
False
sage: sW.is_iterable
True
sage: sB3 = WeylGroup(["B", 3])._sympy_(); sB3
SageSet(Weyl Group of type ['B', 3] (as a matrix group acting on the ambient space))
sage: len(sB3)
48

Some parents or constructions have a more specific conversion to SymPy #31931.

sage: ZZ3 = cartesian_product([ZZ, ZZ, ZZ])
sage: sZZ3 = ZZ3._sympy_(); sZZ3
ProductSet(Integers, Integers, Integers)
sage: (1, 2, 3) in sZZ3

sage: NN = NonNegativeIntegers()
sage: NN._sympy_()
Naturals0

sage: (RealSet(1, 2).union(RealSet.closed(3, 4)))._sympy_()
Union(Interval.open(1, 2), Interval(3, 4))

See Meta-ticket #31926: Connect Sage sets to SymPy sets

Convex geometry

ABC for convex sets

Sage 9.4 has added an abstract base class ConvexSet_base (as well as abstract subclasses ConvexSet_closed, ConvexSet_compact, ConvexSet_relatively_open, ConvexSet_open) for convex subsets of finite-dimensional vector spaces. The abstract methods and default implementations of methods provide a unifying API to the existing classes Polyhedron_base, ConvexRationalPolyhedralCone, LatticePolytope, and PolyhedronFace. #31919, #31959, #31990

As part of the API, there are new methods for point-set topology such as is_open, relative_interior, and closure. For example, taking the relative_interior of a polyhedron constructs an instance of RelativeInterior, a simple object that provides a __contains__ method and all other methods of the ConvexSet_base API. #31916

sage: P = Polyhedron(vertices=[(1,0), (-1,0)])
sage: ri_P = P.relative_interior(); ri_P
Relative interior of
 a 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
sage: (0, 0) in ri_P
True
sage: (1, 0) in ri_P
False

Configuration changes

• Drop support for system Python 3.6 (deprecated in Sage 9.3). #30551

  • It is still possible to build the Sage distribution on systems with old Python versions, but Sage will build its own copy of Python 3.9.x in this case.

Availability of Sage 9.4 and installation help

The first beta of the 9.4 series, 9.4.beta0, was tagged on 2021-05-26.

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