Sage 9.4 Release Tour
current development cycle (2021)
Contents
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 SageSet, 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, #32015
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)) sage: X = Set(QQ).difference(Set(ZZ)); X Set-theoretic difference of Set of elements of Rational Field and Set of elements of Integer Ring sage: X._sympy_() Complement(Rationals, Integers) sage: X = Set(ZZ).difference(Set(QQ)); X Set-theoretic difference of Set of elements of Integer Ring and Set of elements of Rational Field sage: X._sympy_() EmptySet
See Meta-ticket #31926: Connect Sage sets to SymPy sets
ConditionSet
Sage 9.4 introduces a class ConditionSet for subsets of a parent (or another set) consisting of elements that satisfy the logical "and" of finitely many predicates.
The name ConditionSet is borrowed from SymPy. In fact, if the given predicates (condition) are symbolic, a ConditionSet can be converted to a SymPy ConditionSet; the _sympy_ method falls back to creating a SageSet wrapper otherwise.
symbolic_expression(lambda x, y: ...)
Sage 9.4 has added a new way to create callable symbolic expressions. #32103
The global function symbolic_expression now accepts a callable such as those created by lambda expressions. The result is a callable symbolic expression, in which the formal arguments of the callable are the symbolic arguments.
Example:
symbolic_expression(lambda x,y: x^2+y^2) == (SR.var("x")^2 + SR.var("y")^2).function(SR.var("x"), SR.var("y"))This provides a convenient syntax in particular in connection to ConditionSet.
Instead of
sage: predicate(x, y, z) = sqrt(x^2 + y^2 + z^2) < 12 # preparser syntax, creates globals sage: ConditionSet(ZZ^3, predicate)
one is now able to write
sage: ConditionSet(ZZ^3, symbolic_expression(lambda x, y, z: ....: sqrt(x^2 + y^2 + z^2) < 12))
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 real 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
Polyhedral geometry
Manifolds
Defining submanifolds and manifold subsets by pullbacks from Sage sets
pullbacks #31688
Polyhedron.affine_hull_manifold #31659
Families and posets of manifold subsets
Configuration changes
Support for system gcc/g++/gfortran 11 added
Sage can now be built using GCC 11. #31786
This enables building Sage using the default compiler on Fedora 34, and on macOS with homebrew using the default compilers. (Previously, in Sage 9.3, specific older versions of the compilers had to be installed.)
Support for system Python 3.6 dropped
It was already 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.
Support for optional packages on systems with gcc 4.x dropped
Sage is phasing out its support for building from source using very old compilers from the gcc 4.x series.
As of Sage 9.4, on systems such as ubuntu-trusty (Ubuntu 14.04), debian-jessie (8), linuxmint-17, and centos-7 that only provide gcc from the outdated 4.x series, it is still supported to build Sage from source with the system compilers. However, building optional and experimental packages is no longer supported, and we have removed these configurations from our CI. #31526
Users in scientific computing environments using these platforms should urge their system administrators to upgrade to a newer distribution, or at least to a newer toolchain.
For developers: ./configure --prefix=SAGE_LOCAL --with-sage-venv=SAGE_VENV
Sage 9.4 makes it possible to configure the build to make a distinction between:
the installation tree for non-Python packages (SAGE_LOCAL, which defaults to SAGE_ROOT/local and can be set using the configure option --prefix), and
the installation tree (virtual environment) for Python packages (SAGE_VENV). By default, SAGE_VENV is just the same as SAGE_LOCAL, but it can be set to an arbitrary directory using the configure option --with-sage-venv.
Package installation records are kept within each tree, and thus separately. This allows developers to switch between different system Python versions without having to rebuild the whole set of non-Python packages. See #29013 for details.
Package upgrades
- many upgrades were enabled by dropping support for Python 3.6
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.