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| = Sage 4.0 Release Tour = Sage 4.0 was released on FIXME. For the official, comprehensive release note, please refer to [[http://www.sagemath.org/src/announce/sage-4.0.txt|sage-4.0.txt]]. A nicely formatted version of this release tour can be found at FIXME. The following points are some of the foci of this release: * == Algebra == * Deprecate the {{{order()}}} method on elements of rings (John Palmieri) -- The method {{{order()}}} of the class {{{sage.structure.element.RingElement}}} is now deprecated and will be removed in a future release. For additive or multiplicative order, use the {{{additive_order}}} or {{{multiplicative_order}}} method respectively. * FIXME: summarize #6052 == Algebraic Geometry == * Various invariants for genus 2 hyperelliptic curves (Nick Alexander) -- The following invariants for genus 2 hyperelliptic curves are implemented in the module {{{sage/schemes/hyperelliptic_curves/hyperelliptic_g2_generic.py}}}: * the Clebsch invariants * the Igusa-Clebsch invariants * the absolute Igusa invariants == Basic Arithmetic == * FIXME: summarize #6036 * FIXME: summarize #6080 == Build == == Calculus == == Coercion == * FIXME: summarize #5582 == Combinatorics == * ASCII art output for Dynkin diagrams (Dan Bump) -- Support for ASCII art representation of [[http://en.wikipedia.org/wiki/Dynkin_diagram|Dynkin diagrams]] of a finite Cartan type. Here are some examples: {{{ sage: DynkinDiagram("E6") O 2 | | O---O---O---O---O 1 3 4 5 6 E6 sage: DynkinDiagram(['E',6,1]) O 0 | | O 2 | | O---O---O---O---O 1 3 4 5 6 E6~ }}} * FIXME: summarize #5879 == Commutative Algebra == * Improved performance for {{{SR}}} (Martin Albrecht) -- The speed-up gain for {{{SR}}} is up to 6x. The following timing statistics were obtained using the machine sage.math: {{{ # BEFORE sage: sr = mq.SR(4, 4, 4, 8, gf2=True, polybori=True, allow_zero_inversions=True) sage: %time F,s = sr.polynomial_system() CPU times: user 21.65 s, sys: 0.03 s, total: 21.68 s Wall time: 21.83 s # AFTER sage: sr = mq.SR(4, 4, 4, 8, gf2=True, polybori=True, allow_zero_inversions=True) sage: %time F,s = sr.polynomial_system() CPU times: user 3.61 s, sys: 0.06 s, total: 3.67 s Wall time: 3.67 s }}} * Symmetric Groebner bases and infinitely generated polynomial rings (Simon King, Mike Hansen) -- The new modules {{{sage/rings/polynomial/infinite_polynomial_element.py}}} and {{{sage/rings/polynomial/infinite_polynomial_ring.py}}} support computation in polynomial rings with a countably infinite number of variables. Here are some examples for working with these new modules: {{{ sage: from sage.rings.polynomial.infinite_polynomial_element import InfinitePolynomial sage: X.<x> = InfinitePolynomialRing(QQ) sage: a = InfinitePolynomial(X, "(x1 + x2)^2"); a x2^2 + 2*x2*x1 + x1^2 sage: p = a.polynomial() sage: b = InfinitePolynomial(X, a.polynomial()) sage: a == b True sage: InfinitePolynomial(X, int(1)) 1 sage: InfinitePolynomial(X, 1) 1 sage: Y.<x,y> = InfinitePolynomialRing(GF(2), implementation="sparse") sage: InfinitePolynomial(Y, a) x2^2 + x1^2 sage: X.<x,y> = InfinitePolynomialRing(QQ, implementation="sparse") sage: A.<a,b> = InfinitePolynomialRing(QQ, order="deglex") sage: f = x[5] + 2; f x5 + 2 sage: g = 3*y[1]; g 3*y1 sage: g._p.parent() Univariate Polynomial Ring in y1 over Rational Field sage: f2 = a[5] + 2; f2 a5 + 2 sage: g2 = 3*b[1]; g2 3*b1 sage: A.polynomial_ring() Multivariate Polynomial Ring in b5, b4, b3, b2, b1, b0, a5, a4, a3, a2, a1, a0 over Rational Field sage: f + g 3*y1 + x5 + 2 sage: p = x[10]^2 * (f + g); p 3*y1*x10^2 + x10^2*x5 + 2*x10^2 }}} Furthermore, the new module {{{sage/rings/polynomial/symmetric_ideal.py}}} supports ideals of polynomial rings in a countably infinite number of variables that are invariant under variable permuation. Symmetric reduction of infinite polynomials is provided by the new module {{{sage/rings/polynomial/symmetric_reduction.pyx}}}. == Distribution == == Doctest == == Documentation == == Geometry == * FIXME: summarize #6077 * FIXME: summarize #5581 == Graph Theory == * Graph colouring (Robert Miller) -- New method {{{coloring()}}} of the class {{{sage.graphs.graph.Graph}}} for obtaining the first (optimal) coloring found on a graph. Here are some examples on using this new method: {{{ sage: G = Graph("Fooba") sage: P = G.coloring() sage: G.plot(partition=P) sage: H = G.coloring(hex_colors=True) sage: G.plot(vertex_colors=H) }}} {{attachment:graph-colour-1.png}} {{attachment:graph-colour-2.png}} * FIXME: summarize #6066 * FIXME: summarize #3932 * FIXME: summarize #5940 * FIXME: summarize #6086 == Graphics == * FIXME: summarize #5249 * FIXME: summarize #4875 == Group Theory == * Improved efficiency of {{{is_subgroup}}} (Simon King) -- Testing whether a group is a subgroup of another group is now up to 2x faster than previously. The following timing statistics were obtained using the machine sage.math: {{{ # BEFORE sage: G = SymmetricGroup(7) sage: H = SymmetricGroup(6) sage: %time H.is_subgroup(G) CPU times: user 4.12 s, sys: 0.53 s, total: 4.65 s Wall time: 5.51 s True sage: %timeit H.is_subgroup(G) 10000 loops, best of 3: 118 µs per loop # AFTER sage: G = SymmetricGroup(7) sage: H = SymmetricGroup(6) sage: %time H.is_subgroup(G) CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s True sage: %timeit H.is_subgroup(G) 10000 loops, best of 3: 56.3 µs per loop }}} == Interfaces == * Viewing Sage objects with a PDF viewer (Nicolas Thiery) -- Implements the option {{{viewer="pdf"}}} for the command {{{view()}}} so that one can invoke this command in the form {{{view(object, viewer="pdf")}}} in order to view {{{object}}} using a PDF viewer. Typical uses of this new optional argument include: * You prefer to use a PDF viewer rather than a DVI viewer. * You want to view LaTeX snippets which are not displayed well in DVI viewers (e.g. graphics produced using tikzpicture). * Change name of Pari's {{{sum}}} function when imported (Craig Citro) -- When Pari's {{{sum}}} function is imported, it is renamed to {{{pari_sum}}} in order to avoid conflict Python's {{{sum}}} function. == Linear Algebra == * Improved performance for the generic {{{linear_combination_of_rows}}} and {{{linear_combination_of_columns}}} functions for matrices (William Stein) -- The speed-up for the generic functions {{{linear_combination_of_rows}}} and {{{linear_combination_of_columns}}} is up to 4x. The following timing statistics were obtained using the machine sage.math: {{{ # BEFORE sage: A = random_matrix(QQ, 50) sage: v = [1..50] sage: %timeit A.linear_combination_of_rows(v); 1000 loops, best of 3: 1.99 ms per loop sage: %timeit A.linear_combination_of_columns(v); 1000 loops, best of 3: 1.97 ms per loop # AFTER sage: A = random_matrix(QQ, 50) sage: v = [1..50] sage: %timeit A.linear_combination_of_rows(v); 1000 loops, best of 3: 436 µs per loop sage: %timeit A.linear_combination_of_columns(v); 1000 loops, best of 3: 457 µs per loop }}} * Massively improved performance for {{{4 x 4}}} determinants (Tom Boothby) -- The efficiency of computing the determinants of {{{4 x 4}}} matrices can range from 16x up to 58,083x faster than previously, depending on the base ring. The following timing statistics were obtained using the machine sage.math: {{{ # BEFORE sage: S = MatrixSpace(ZZ, 4) sage: M = S.random_element(1, 10^8) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 53 µs per loop sage: M = S.random_element(1, 10^10) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 54.1 µs per loop sage: sage: M = S.random_element(1, 10^200) sage: timeit("M.det(); M._clear_cache()") 5 loops, best of 3: 121 ms per loop sage: M = S.random_element(1, 10^300) sage: timeit("M.det(); M._clear_cache()") 5 loops, best of 3: 338 ms per loop sage: M = S.random_element(1, 10^1000) sage: timeit("M.det(); M._clear_cache()") 5 loops, best of 3: 9.7 s per loop # AFTER sage: S = MatrixSpace(ZZ, 4) sage: M = S.random_element(1, 10^8) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 3.17 µs per loop sage: M = S.random_element(1, 10^10) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 3.44 µs per loop sage: sage: M = S.random_element(1, 10^200) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 15.3 µs per loop sage: M = S.random_element(1, 10^300) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 27 µs per loop sage: M = S.random_element(1, 10^1000) sage: timeit("M.det(); M._clear_cache()") 625 loops, best of 3: 167 µs per loop }}} * Refactor matrix kernels (Rob Beezer) -- The core section of kernel computation for each (specialized) class is now moved into the method {{{right_kernel()}}}. Mostly these would replace {{{kernel()}}} methods that are computing left kernels. A call to {{{kernel()}}} or {{{left_kernel()}}} should arrive at the top of the hierarchy where it would take a transpose and call the (specialized) {{{right_kernel()}}}. So there wouldn't be a change in behavior in routines currently calling {{{kernel()}}} or {{{left_kernel()}}}, and Sage's preference for the left is retained by having the vanilla {{{kernel()}}} give back a left kernel. The speed-up for the computation of left kernels is up to 5% faster, and the computation of right kernels is up to 31% by eliminating paired transposes. The followingn timing statistics were obtained using sage.math: {{{ # BEFORE sage: n = 2000 sage: entries = [[1/(i+j+1) for i in srange(n)] for j in srange(n)] sage: mat = matrix(QQ, entries) sage: %time mat.left_kernel(); CPU times: user 21.92 s, sys: 3.22 s, total: 25.14 s Wall time: 25.26 s sage: %time mat.right_kernel(); CPU times: user 23.62 s, sys: 3.32 s, total: 26.94 s Wall time: 26.94 s # AFTER sage: n = 2000 sage: entries = [[1/(i+j+1) for i in srange(n)] for j in srange(n)] sage: mat = matrix(QQ, entries) sage: %time mat.left_kernel(); CPU times: user 20.87 s, sys: 2.94 s, total: 23.81 s Wall time: 23.89 s sage: %time mat.right_kernel(); CPU times: user 18.43 s, sys: 0.00 s, total: 18.43 s Wall time: 18.43 s }}} * FIXME: summarize #5554 == Miscellaneous == * Allow use of {{{pdflatex}}} instead of {{{latex}}} (John Palmieri) -- One can now use {{{pdflatex}}} instead of {{{latex}}} in two different ways: * Use a {{{%pdflatex}}} cell in a notebook; or * Call {{{latex.pdflatex(True)}}} after which any use of {{{latex}}} (in a {{{%latex}}} cell or using the {{{view}}} command) will use {{{pdflatex}}}. One visually appealing aspect of this is that if you have the most recent version of [[http://pgf.sourceforge.net|pgf]] installed, as well as the {{{tkz-graph}}} package, you can produce images like the following: {{attachment:pgf-graph.png}} * FIXME: summarize #5783 * FIXME: summarize #5796 * FIXME: summarize #5120 == Modular Forms == * Action of Hecke operators on {{{Gamma_1(N)}}} modular forms (David Loeffler) -- Here's an example: {{{ sage: ModularForms(Gamma1(11), 2).hecke_matrix(2) [ -2 0 0 0 0 0 0 0 0 0] [ 0 -381 0 -360 0 120 -4680 -6528 -1584 7752] [ 0 -190 0 -180 0 60 -2333 -3262 -789 3887] [ 0 -634/11 1 -576/11 0 170/11 -7642/11 -10766/11 -231 12555/11] [ 0 98/11 0 78/11 0 -26/11 1157/11 1707/11 30 -1959/11] [ 0 290/11 0 271/11 0 -50/11 3490/11 5019/11 99 -5694/11] [ 0 230/11 0 210/11 0 -70/11 2807/11 3940/11 84 -4632/11] [ 0 122/11 0 120/11 1 -40/11 1505/11 2088/11 48 -2463/11] [ 0 42/11 0 46/11 0 -30/11 554/11 708/11 21 -970/11] [ 0 10/11 0 12/11 0 7/11 123/11 145/11 7 -177/11] }}} * FIXME: summarize #6019 * FIXME: summarize #5924 == Notebook == == Number Theory == * FIXME: summarize #5250 * FIXME: summarize #6013 * FIXME: summarize #6008 * FIXME: summarize #6004 * FIXME: summarize #6059 * FIXME: summarize #6064 == Numerical == == Packages == * FIXME: summarize #4223 * FIXME: summarize #6031 * FIXME: summarize #5934 * FIXME: summarize #1338 * FIXME: summarize #6032 * FIXME: summarize #6024 == P-adics == * FIXME: summarize #5105 * FIXME: summarize #5236 == Quadratic Forms == * FIXME: summarize #6037 == Symbolics == * FIXME: summarize #5777 * FIXME: summarize #5930 == Topology == * Random simplicial complexes (John Palmieri) -- New method {{{RandomComplex()}}} in the module {{{sage/homology/examples.py}}} for producing a random {{{d}}}-dimensional simplicial complex on {{{n}}} vertices. Here's an example: {{{ sage: simplicial_complexes.RandomComplex(6,12) Simplicial complex with vertex set (0, 1, 2, 3, 4, 5, 6, 7) and facets {(0, 1, 2, 3, 4, 5, 6, 7)} }}} == User Interface == == Website / Wiki == |
