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| = Sage 3.0.2 Release Tour = Sage 3.0.2 was released on May 24th, 2008. For the official, comprehensive release notes, see the HISTORY.txt file that comes with the release. For the latest changes see [http://sagemath.org/announce/sage-3.0.2.txt sage-3.0.2.txt]. == Self-orthogonal Binary Codes (Robert Miller) == == Notebook Improvements (William Stein, Tom Boothby) == == Portability of Sage to 64 bit OSX and Cygwin (Michael Abshoff, William Stein) == == Posets and Semi-Lattices (Peter Jipsen and Franco Saliola) == Sage now includes basic support for finite posets and semi-lattices. There are several ways to define a finite poset. 1. A tuple of elements and cover relations: {{{#!python sage: Poset(([1,2,3,4,5,6,7],[[1,2],[3,4],[4,5],[2,5]])) Finite poset containing 7 elements }}} 2. Alternatively, using the ''cover_relations=False'' keyword, the relations need not be cover relations (and they will be computed). {{{#!python sage: elms = [1,2,3,4] sage: rels = [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]] sage: P = Poset( (elms,rels) ,cover_relations=False); P Finite poset containing 4 elements sage: P.cover_relations() [[1, 2], [2, 3], [3, 4]] }}} 3. A list or dictionary of upper covers: {{{#!python sage: Poset({'a':['b','c'], 'b':['d'], 'c':['d'], 'd':[]}) Finite poset containing 4 elements sage: Poset([[1,2],[4],[3],[4],[]]) Finite poset containing 5 elements }}} 4. An acyclic directory graph: {{{#!python sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) sage: Poset(dag) Finite poset containing 6 elements }}} Once a poset has been created, several methods are available: {{{#!python sage: dag = DiGraph({0:[2,3], 1:[3,4], 2:[5], 3:[5], 4:[5]}) sage: P = Poset(dag) sage: P.has_bottom() False sage: P.has_top() True sage: P.top() 5 sage: P.linear_extension() [1, 4, 0, 2, 3, 5] sage: P.is_meet_semilattice() False sage: P.is_join_semilattice() True sage: P.mobius_function_matrix() [ 1 -1 0 0 -1 1] [ 0 1 0 0 0 -1] [ 0 0 1 -1 -1 1] [ 0 0 0 1 0 -1] [ 0 0 0 0 1 -1] [ 0 0 0 0 0 1] sage: type(P(5)) <class 'sage.combinat.posets.elements.PosetElement'> sage: P(5) < P(1) False sage: P(1) < P(5) True sage: x = P(4) sage: [v for v in P if v <= x] [1, 4] sage: P.show() }}} == Frobby for monomial ideals (Bjarke Hammersholt Roune) == Frobby is software for computations with monomial ideals, and is included in Sage 3.0.2 as an optional spkg. The current functionality of the Sage interface to Frobby is irreducible decomposition of monomial ideals, while work is on-going to expose more of the capabilities of Frobby, such as Hilbert-Poincare series, primary decomposition and Alexander dual. Frobby is orders of magnitude faster than other programs for many of its computations, primarily owing to an optimized implementation of the Slice Algorithm. See http://www.broune.com/frobby/ for more on Frobby. |
