------- Forwarded message ------- From: "Andrey Novoseltsev" <[EMAIL PROTECTED]> To: [EMAIL PROTECTED], [EMAIL PROTECTED] Cc: "William Stein" <[EMAIL PROTECTED]> Subject: PALP is integrated into SAGE Date: Tue, 16 Jan 2007 22:52:13 -0800 Dear Maximilian Kreuzer and Harald Skarke, I am glad to let you know that PALP is included into standard distribution of SAGE (Software for Algebra and Geometry Experimentation), available at http://sage.math.washington.edu/sage/ This project was started by William Stein two years ago and currently it includes many powerful packages, including palp-1.1. This is a short quote from the above site: "SAGE is free open source math software that supports research and teaching in algebra, geometry, number theory, cryptography, and related areas. Both the SAGE development model and the technology in SAGE itself is distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. Our overall goal is to create a viable free open source alternative to Maple, Mathematica, Magma, and MATLAB." The advantages of using PALP via SAGE are interactive mode and uniform access to other packages (e.g. for doing linear algebra operations with vertices or points of polytopes). In the end of this letter you can find a session of work with the interface to PALP in SAGE, which I have written with William Stein's help. It would be really nice, if you could add on your PALP homepage the link to SAGE official site: http://sage.math.washington.edu/sage/ Thank you, Andrey Novoseltsev, Graduate Student Department of Mathematics University of Washington sage: from sage.geometry.lattice_polytope import * sage: o = octahedron(3) sage: o.is_reflexive() True sage: o.vertices() [ 1 0 0 -1 0 0] [ 0 1 0 0 -1 0] [ 0 0 1 0 0 -1] sage: o.points() [ 1 0 0 -1 0 0 0] [ 0 1 0 0 -1 0 0] [ 0 0 1 0 0 -1 0] sage: o.polar() A polytope polar to An octahedron: 3-dimensional, 8 vertices. sage: cube = o.polar() sage: cube.facets() [[0, 1, 2, 3], [0, 1, 4, 5], [0, 2, 4, 6], [1, 3, 5, 7], [2, 3, 6, 7], [4, 5, 6, 7]] sage: facet = cube.facets()[0] sage: facet.points() [0, 1, 2, 3, 11, 15, 18, 21, 25] sage: facet.interior_points() [18] sage: cube.points().matrix_from_columns(facet.interior_points()) [0] [0] [1] sage: cube.points().matrix_from_columns(facet.boundary_points()) [-1 1 -1 1 -1 0 0 1] [-1 -1 1 1 0 -1 1 0] [ 1 1 1 1 1 1 1 1] sage: facet.nboundary_points() 8 sage: o.nef_partitions() [ [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0], [1, 1, 1, 1, 0, 0] ] sage: print o.nef_x("-V -N") M:27 8 N:7 6 codim=2 #part=5 3 6 Vertices of P: 1 0 0 -1 0 0 0 1 0 0 -1 0 0 0 1 0 0 -1 H:[0] P:0 V:2 4 5 0sec 0cpu H:[0] P:2 V:3 4 5 0sec 0cpu H:[0] P:3 V:4 5 0sec 0cpu np=3 d:1 p:1 0sec 0cpu sage: print o.poly_x("g") M:7 6 N:27 8 Pic:17 Cor:0 sage: K3 = read_all_polytopes("K3vertices", "K3 %4d") sage: K3[24] K3 24: 3-dimensional, 6 vertices. sage: K3[24].vertices() [ 1 -1 0 -1 0 1] [ 0 0 1 -1 0 0] [ 0 0 0 0 1 -1] sage: all_points(K3) sage: r = filter_polytopes(lambda p: p.npoints() == 6, K3) sage: len(r) 7 sage: r [1, 2, 3, 4, 5, 6, 7] sage: all_faces(K3) sage: r = filter_polytopes(lambda p: p.nfacets() == 13, K3) sage: len(r) 8 sage: r [739, 740, 1112, 1113, 1526, 1528, 1942, 2354] sage: K3[1112].facets() [[0, 2, 6, 8], [0, 4, 6], [4, 6, 7], [6, 7, 8, 9], [0, 2, 10], [0, 1, 4, 10], [2, 3, 5, 10], [1, 3, 10], [2, 5, 8], [1, 4, 7], [1, 3, 7, 9], [5, 8, 9], [3, 5, 9]] sage: --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
