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| = Sage 9.0 Release Tour = released Jan 1, 2020 <<TableOfContents>> == Python 3 transition == Just in time for the new decade, this is the first version of Sage running on Python 3 by default. See [[Python3-Switch]] for more details == Three.js is the new default 3D viewer == [[https://doc.sagemath.org/html/en/reference/plot3d/threejs.html|Three.js]] has become the default viewer for 3D plots, in replacement of Jmol. Note that Jmol is still available, via the option ''viewer='jmol' '' in the plot functions. == New plotting capabilities == * [[https://doc.sagemath.org/html/en/reference/plotting/sage/plot/plot.html#sage.plot.plot.multi_graphics|multi-graphics]] * [[https://doc.sagemath.org/html/en/reference/plotting/sage/plot/graphics.html#sage.plot.graphics.Graphics.inset|graphic insets]] == Polyhedral Geometry == Sage uses a new algorithm to obtain the f-vector for polyhedra. This is the only memory efficient implementation for the f-vector at the time of writing and it is as fast or faster as other implementations: {{{ sage: P = polytopes.permutahedron(7) sage: %time P.incidence_matrix() CPU times: user 679 ms, sys: 4.01 ms, total: 683 ms Wall time: 682 ms 5040 x 127 dense matrix over Integer Ring (use the '.str()' method to see the entries) sage: %time P.f_vector() CPU times: user 901 ms, sys: 16 ms, total: 917 ms Wall time: 916 ms (1, 5040, 15120, 16800, 8400, 1806, 126, 1) }}} There is ongoing work to improve this implementation. It is implemented in the combinatorial polyhedron of `P`, which is newly exposed: {{{ sage: P.combinatorial_polyhedron() A 6-dimensional combinatorial polyhedron with 126 facets }}} Sage has the classical construction of the 120-cell of Coxeter from 1969. This construction is much faster than to realize it as generalized permutahedron so that even without the optional package `normaliz` you won't waste much time: {{{ sage: %time P = polytopes.one_hundred_twenty_cell(backend='normaliz') CPU times: user 942 ms, sys: 81.8 ms, total: 1.02 s Wall time: 457 ms sage: %time P = polytopes.one_hundred_twenty_cell(backend='field') CPU times: user 15.9 s, sys: 87.2 ms, total: 16 s Wall time: 16 s sage: %time P = polytopes.one_hundred_twenty_cell(backend='normaliz', construction='as_permutahedron') CPU times: user 18.6 s, sys: 137 ms, total: 18.8 s Wall time: 18 s }}} Ehrhart polynomials are computable for lattice polytopes defined with base ring `QQ`: {{{ sage: P = polytopes.cube()*1/1 sage: P.base_ring() Rational Field sage: P.ehrhart_polynomial() 8*t^3 + 12*t^2 + 6*t + 1 }}} Note that this computation requires optional package `latte_int` or `normaliz`. There is a new method to obtain the boundary of complex simplicial polytopes: {{{ sage: oc = polytopes.octahedron() sage: oc.boundary_complex() Simplicial complex with vertex set (0, 1, 2, 3, 4, 5) and 8 facets }}} Hyperplane arrangements have a new method `center`: {{{ sage: H.<x,y> = HyperplaneArrangements(QQ) sage: A = H() sage: A.center() A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 1 vertex and 2 lines }}} There are also some bug fixes and other improvements. For more details see the [[https://trac.sagemath.org/wiki/SagePolyhedralGeometry#release_9.0|release notes for optimization and polyhedral geometry softwares interactions in Sage]]. == Manifolds == * [[https://sagemanifolds.obspm.fr/changelog.html|Changes in the manifold part]] == Availability of Sage 9.0 and installation help == * Release announcements: See https://groups.google.com/forum/#!forum/sage-release === Availability in distributions === (TBD) === Installation FAQ === See [[https://groups.google.com/forum/#!forum/sage-support|sage-suppport]], [[https://groups.google.com/forum/#!forum/sage-devel|sage-devel]]. == More details == * [[https://trac.sagemath.org/query?milestone=sage-9.0&groupdesc=1&group=status&max=1500&col=id&col=summary&col=author&col=reviewer&col=time&col=changetime&col=component&col=keywords&order=component|Trac tickets with milestone 9.0]] |
