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| = Sage 3.4.1 Release Tour = Sage 3.4.1 was released on FIXME. For the official, comprehensive release note, please refer to [[http://www.sagemath.org/src/announce/sage-3.4.1.txt|sage-3.4.1.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: * Merging improvements during the Sage Days 13 coding sprint. * Other bug fixes post Sage 3.4. |
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| == Algebra == * Optimized {{{is_primitive()}}} method (Ryan Hinton) -- The method {{{is_primitive()}}} in {{{sage/rings/polynomial/polynomial_element.pyx}}} is used for determining whether or not a polynomial is primitive over a finite field. Prime divisors are calculated during the test for polynomial primitivity. Where n is large, calculating those prime divisors can dominate the running time of the test. The {{{is_primitive()}}} method now has the optional argument {{{n_prime_divs}}} for providing precomputed prime divisors. This optional argument can result in a performance improvement of up to 4x. On the machine sage.math, one has the following timing statistics: {{{ sage: R.<x> = PolynomialRing(GF(2), 'x') sage: nn = 128 sage: max_order = 2^nn - 1 sage: pdivs = max_order.prime_divisors() sage: poly = R.random_element(nn) sage: while not (poly.degree()==nn and poly.is_primitive(max_order, pdivs)): ....: poly = R.random_element(nn) ....: sage: %timeit poly.is_primitive() # without n_prime_divs optional argument 10 loops, best of 3: 285 ms per loop sage: %timeit poly.is_primitive(max_order, pdivs) # with n_prime_divs optional argument 10 loops, best of 3: 279 ms per loop sage: sage: nn = 256 sage: max_order = 2^nn - 1 sage: pdivs = max_order.prime_divisors() sage: poly = R.random_element(nn) sage: while not (poly.degree()==nn and poly.is_primitive(max_order, pdivs)): ....: poly = R.random_element(nn) ....: sage: %timeit poly.is_primitive() # without n_prime_divs optional argument 10 loops, best of 3: 3.22 s per loop sage: %timeit poly.is_primitive(max_order, pdivs) # with n_prime_divs optional argument 10 loops, best of 3: 700 ms per loop }}} * Speed-up the method {{{order_from_multiple()}}} (John Cremona) -- For groups of prime order n, every non-identity element has order n. The previous implementation of the method {{{order_from_multiple()}}} computes g^n twice when g is not the identity and n is prime. Such double computation is now avoided. Now for each prime p dividing the given multiple of the order, we avoid the last multiplication/powering by p, hence saving some computation time whenever the p-exponent of the order is maximal. The new implementation of {{{order_from_multiple()}}} results in a performance improvement of up to 25%. Here are some timing statistics obtained using the machine sage.math: {{{ # BEFORE sage: F = GF(2^1279, 'a') sage: n = F.cardinality() - 1 # Mersenne prime sage: order_from_multiple(F.random_element(), n, [n], operation='*') == n True sage: %timeit order_from_multiple(F.random_element(), n, [n], operation='*') == n 10 loops, best of 3: 63.7 ms per loop # AFTER sage: F = GF(2^1279, 'a') sage: n = F.cardinality() - 1 # Mersenne prime sage: %timeit order_from_multiple(F.random_element(), n, [n], operation='*') == n 10 loops, best of 3: 47.2 ms per loop }}} * Speed-up in irreducibility test (Ryan Hinton) -- For polynomials over the finite field {{{GF(2)}}}, the test for irreducibility is now up to 40,000 times faster than previously. On a 64-bit Debian/squeeze machine with Core 2 Duo running at 2.33 GHz, one has the following timing improvements: {{{ # BEFORE sage: P.<x> = GF(2)[] sage: f = P.random_element(1000) sage: %timeit f.is_irreducible() 10 loops, best of 3: 948 ms per loop sage: sage: f = P.random_element(10000) sage: %time f.is_irreducible() # gave up because it took minutes! # AFTER sage: P.<x> = GF(2)[] sage: f = P.random_element(1000) sage: %timeit f.is_irreducible() 10000 loops, best of 3: 22.7 µs per loop sage: sage: f = P.random_element(10000) sage: %timeit f.is_irreducible() 1000 loops, best of 3: 394 µs per loop sage: sage: f = P.random_element(100000) sage: %timeit f.is_irreducible() 100 loops, best of 3: 10.4 ms per loop }}} Furthermore, on Debian 5.0 Lenny with kernel 2.6.24-1-686, an Intel(R) Celeron(R) CPU running at 2.00GHz with 1.0GB of RAM, one has the following timing statistics: {{{ # BEFORE sage: P.<x> = GF(2)[] sage: f = P.random_element(1000) sage: %timeit f.is_irreducible() 10 loops, best of 3: 1.14 s per loop sage: sage: f = P.random_element(10000) sage: %time f.is_irreducible() CPU times: user 4972.13 s, sys: 2.83 s, total: 4974.95 s Wall time: 5043.02 s False # AFTER sage: P.<x> = GF(2)[] sage: f = P.random_element(1000) sage: %timeit f.is_irreducible() 10000 loops, best of 3: 40.7 µs per loop sage: sage: f = P.random_element(10000) sage: %timeit f.is_irreducible() 1000 loops, best of 3: 930 µs per loop sage: sage: sage: f = P.random_element(100000) sage: %timeit f.is_irreducible() 10 loops, best of 3: 27.6 ms per loop }}} == Algebraic Geometry == * Refactor {{{dimension()}}} method for schemes (Alex Ghitza) -- Implement methods {{{dimension_absolute()}}} and {{{dimension_relative()}}}, where {{{dimension()}}} is an alias for {{{dimension_absolute()}}}. Here are some examples of using {{{dimension_absolute()}}} and {{{dimension()}}}: {{{ sage: A2Q = AffineSpace(2, QQ) sage: A2Q.dimension_absolute() 2 sage: A2Q.dimension() 2 }}} And here's an example demonstrating the use of {{{dimension_relative()}}}: {{{ sage: S = Spec(ZZ) sage: S.dimension_relative() 0 }}} * Plotting affine and projective curves (Alex Ghitza) -- Improving the plotting usability so it is now easier to plot affine and projective curves. For example, we can plot a [[attachment:5-nodal curve]] of degree 11: {{{ sage: R.<x, y> = ZZ[] sage: C = Curve(32*x^2 - 2097152*y^11 + 1441792*y^9 - 360448*y^7 + 39424*y^5 - 1760*y^3 + 22*y - 1) sage: C.plot((x, -1, 1), (y, -1, 1), plot_points=400) }}} Now we plot an [[attachment:elliptic curve]]: {{{ sage: E = EllipticCurve('101a') sage: C = Curve(E) sage: C.plot() }}} == Basic Arithmetic == * Speed-up in dividing a polynomial by an integer (Burcin Erocal) -- Dividing a polynomial by an integer is now up to 6x faster than previously. On Debian 5.0 Lenny with kernel 2.6.24-1-686, an Intel(R) Celeron(R) CPU running at 2.00GHz with 1.0GB of RAM, one has the following timing statistics: {{{ # BEFORE sage: R.<x> = ZZ["x"] sage: f = 389 * R.random_element(1000) sage: timeit("f//389") 625 loops, best of 3: 312 µs per loop # AFTER sage: R.<x> = ZZ["x"] sage: f = 389 * R.random_element(1000) sage: timeit("f//389") 625 loops, best of 3: 48.3 µs per loop }}} * New {{{fast_float}}} supports more datatypes with improved performance (Carl Witty) -- A rewrite of {{{fast_float}}} to support multiple types. Here, we get accelerated evaluation over {{{RealField(k)}}} as well as {{{RDF}}}, real double field. As compared with the previous {{{fast_float}}}, improved performance can range from 2% faster to more than 2x as fast. An extended list of benchmark details is available at [[http://trac.sagemath.org/sage_trac/ticket/5093|ticket 5093]]. * Complex double fast callable interpreter (Robert Bradshaw) -- Support for complex double floating point (CDF). The new interpreter is implemented in the class {{{CDFInterpreter}}} of {{{sage/ext/gen_interpreters.py}}}. * Speed-up the function {{{solve_mod()}}} (Wilfried Huss) -- Performance improvement for the function {{{solve_mod()}}} is now up to 5x when solving an equation or a list of equations modulo a given integer modulus. On the machine sage.math, we have the following timing statistics: {{{ # BEFORE sage: x, y = var('x,y') sage: time solve_mod([x^2 + 2 == x, x^2 + y == y^2], 14) CPU times: user 0.01 s, sys: 0.02 s, total: 0.03 s Wall time: 0.18 s [(4, 2), (4, 6), (4, 9), (4, 13)] sage: sage: x,y,z = var('x,y,z') sage: time solve_mod([x^5 + y^5 == z^5], 3) CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.10 s [(0, 0, 0), (0, 1, 1), (0, 2, 2), (1, 0, 1), (1, 1, 2), (1, 2, 0), (2, 0, 2), (2, 1, 0), (2, 2, 1)] # AFTER sage: x, y = var('x,y') sage: time solve_mod([x^2 + 2 == x, x^2 + y == y^2], 14) CPU times: user 0.03 s, sys: 0.01 s, total: 0.04 s Wall time: 0.16 s [(4, 2), (4, 6), (4, 9), (4, 13) sage: sage: x,y,z = var('x,y,z') sage: time solve_mod([x^5 + y^5 == z^5], 3) CPU times: user 0.01 s, sys: 0.01 s, total: 0.02 s Wall time: 0.02 s [(0, 0, 0), (0, 1, 1), (0, 2, 2), (1, 0, 1), (1, 1, 2), (1, 2, 0), (2, 0, 2), (2, 1, 0), (2, 2, 1)] }}} * Optimized binomial function when an input is real or complex floating point (Dan Drake, William Stein) -- The function {{{binomial()}}} for returning the binomial coefficients is now much faster. In some cases, speed efficiency can be up to 4000x. Here are some timing statistics obtained using the machine sage.math: {{{ # BEFORE sage: x, y = 1140000.78, 420000 sage: %timeit binomial(x, y) 10 loops, best of 3: 1.19 s per loop sage: sage: x, y = RR(pi^5), 10 sage: %timeit binomial(x, y) 10000 loops, best of 3: 28.2 µs per loop sage: sage: x, y = RR(pi^15), 500 sage: %timeit binomial(x, y) 1000 loops, best of 3: 799 µs per loop sage: sage: x, y = RealField(500)(1729000*sqrt(2)), 17000 sage: %timeit binomial(x, y) 10 loops, best of 3: 34.4 ms per loop # AFTER sage: x, y = 1140000.78, 420000 sage: %timeit binomial(x, y) 1000 loops, best of 3: 297 µs per loop sage: sage: x, y = RR(pi^5), 10 sage: %timeit binomial(x, y) 10000 loops, best of 3: 189 µs per loop sage: sage: x, y = RR(pi^15), 500 sage: %timeit binomial(x, y) 1000 loops, best of 3: 335 µs per loop sage: sage: x, y = RealField(500)(1729000*sqrt(2)), 17000 sage: %timeit binomial(x, y) 1000 loops, best of 3: 692 µs per loop }}} * Enhanced {{{nth_root()}}} in {{{ZZ}}} and {{{QQ}}} and related utilities (John Cremona) -- Some consistency in the method {{{nth_root()}}} of {{{ZZ}}} and {{{QQ}}}. There are also some new utility methods for the rational numbers: 1. {{{prime_to_S_part(self, S=[])}}} -- Returns {{{self}}} with all powers of all primes in S removed. 1. {{{is_nth_power(self, int n)}}} -- Returns {{{True}}} if {{{self}}} is an n-th power; else {{{False}}}. 1. {{{is_S_integral(self, S=[])}}} -- Determine if the rational number is S-integral. 1. {{{is_S_unit(self, S=None)}}} -- Determine if the rational number is an S-unit. == Build == == Calculus == * Deprecate the calling of symbolic functions with unnamed arguments (Carl Witty, Michael Abshoff) -- Previous releases of Sage supported symbolic functions with "no arguments". This style of constructing symbolic functions is now deprecated. For example, previously Sage allowed for defining a symbolic function in the following way {{{ f2 = 5 - x^2 # bad; this is deprecated }}} But users are encouraged to explicitly declare the variables used in a symolic function. For instance, the following is encouraged: {{{ sage: x,y = var("x, y") # explicitly declare your variables sage: f(x, y) = x^2 + y^2 # this syntax is encouraged }}} == Coercion == == Combinatorics == * Enhancements to the {{{Subsets}}} and {{{Subwords}}} modules (Florent Hivert) -- Numerous enhancements to the modules {{{Subsets}}} and {{{Subwords}}} include: 1. An implementation of subsets for finite multisets, i.e. sets with repetitions. 1. Adding the method {{{__contains__}}} for {{{Subsets}}} and {{{Subwords}}}. Here's an example for working with multisets: {{{ sage: S = Subsets([1, 2, 2], submultiset=True); S SubMultiset of [1, 2, 2] sage: S.list() [[], [1], [2], [1, 2], [2, 2], [1, 2, 2]] sage: Set([1,2]) in S # this uses __contains__ in Subsets True sage: Set([]) in S True sage: Set([3]) in S False }}} And here's an example of using {{{__contains__}}} with {{{Subwords}}}: {{{ sage: [] in Subwords([1,2,3,4,3,4,4]) True sage: [2,3,3,4] in Subwords([1,2,3,4,3,4,4]) True sage: [2,3,3,1] in Subwords([1,2,3,4,3,4,4]) False }}} * Fix and enhancements to permutations (Sebastien Labbe) -- This corrects the Robinson-Schensted algorithm on trivial permutations. It implements the inverse Robinson-Schensted algorithm: {{{ sage: Permutation((Tableau([[1,2,4],[3]]), Tableau([[1,3,4],[2]]))) [3, 1, 2, 4] sage: Permutation(([[1,2,4],[3]], [[1,3,4],[2]])) [3, 1, 2, 4] }}} And it works for arbitrary words (with semi-standard tableaux): {{{ sage: Permutation(([[1,2,2],[3]], [[1,3,4],[2]])) [3, 1, 2, 2] }}} * First pass of cleanup of the interface of combinatorial classes (Florent Hivert) -- Before the patch, the interface of combinatorial classes had two problems: 1. There were two redundant ways to get the number of elements {{{len(C)}}} and {{{C.count()}}}. Moreover {{{len}}} must return a plain {{{int}}} where we want an arbitrary large number and even {{{infinity}}}; 1. There were two redundant ways to get an iterator for the elements {{{C.iterator()}}} and {{{iter(C)}}} (allowing for {{{for c in C: ...}}}) via {{{C.__iter__}}}. The patch standardize those issues to: 1. {{{C.cardinality()}}} which is more explicit and consistent with many other Sage libraries; 1. {{{iter(C)}}} / {{{for x in C:}}} via {{{C.__iter__}}} which is clearly more Pythonic. The functions {{{iterator()}}} and {{{count()}}} are deprecated (with a warning), but will be removed in a later release. On the other hand, there was no way to keep backward compatibility for {{{len}}}. Indeed, many of function such as {{{list / filter / map}}} try silently to call {{{len}}}, which would have caused miriads of warnings to be issued in seemingly unrelated places. So it was decided to simply remove it and issue an error, suggesting to call {{{cardinality}}} instead. * New class {{{IntegerListLex}}} for generating integer lists (Nicolas M. Thiery, Florent Hivert) -- The new class provides a Constant Amortized Time iterator through the combinatorial classes of integer lists. For example, we create the combinatorial class of lists of length 3 and sum 2 as follows: {{{ sage: C = IntegerListsLex(2, length=3); C Integer lists of sum 2 satisfying certain constraints sage: C.count() 6 sage: [p for p in C] [[2, 0, 0], [1, 1, 0], [1, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]] }}} Here's the list of all compositions of 4: {{{ sage: list(IntegerListsLex(4, min_part = 1)) [[4], [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1]] }}} * Cleanup of crystal code (Anne Schilling, Nicolas M. Thiery) -- Cartan type is now implemented as the method {{{cartan_type}}}, rather than an attribute as was previously the case. * Deprecate the function {{{RestrictedPartitions()}}} (Dan Drake) -- The function {{{RestrictedPartitions()}}} in {{{sage/combinat/partition.py}}} is now deprecated and will be removed in a future release. Users are advised to instead consider the function {{{Partitions()}}} with the {{{parts_in}}} keyword, which is functionally equivalent to {{{RestrictedPartitions()}}} but is more memory and time efficient. The timing improvement in {{{Partitions()}}} is up to 5x faster than {{{RestrictedPartitions()}}}. The following memory and timing statistics are produced using the machine sage.math: {{{ # BEFORE sage: get_memory_usage() 721.26171875 sage: ps = RestrictedPartitions(100, ([1,6..100] + [4,9..100])) sage: %time sum(1 for p in ps) CPU times: user 27.26 s, sys: 1.06 s, total: 28.32 s Wall time: 28.99 s 74040 sage: get_memory_usage() 1807.03515625 sage: get_memory_usage() 721.265625 sage: ps = RestrictedPartitions(3000, [10,50,100,500,1000]) sage: %time sum(1 for p in ps) CPU times: user 5.60 s, sys: 0.21 s, total: 5.81 s Wall time: 5.95 s 3506 sage: get_memory_usage() 962.54296875 # AFTER sage: get_memory_usage() 719.3984375 sage: ps = Partitions(100, parts_in=([1,6..100] + [4,9..100])) sage: %time sum(1 for p in ps) CPU times: user 5.09 s, sys: 0.01 s, total: 5.10 s Wall time: 5.10 s 74040 sage: get_memory_usage() 719.3984375 sage: get_memory_usage() 719.3984375 sage: ps = Partitions(3000, parts_in=[10,50,100,500,1000]) sage: %time sum(1 for p in ps) CPU times: user 1.12 s, sys: 0.01 s, total: 1.13 s Wall time: 1.13 s 3506 sage: get_memory_usage() 719.3984375 }}} * Speed-up the {{{weyl_characters.py}}} module (Mike Hansen, Daniel Bump, Michael Abshoff) -- The timing efficiency is between 4x to 10x, depending on the operations involved. Here are some timing statistics produced using the machine sage.math: {{{ # BEFORE sage: R = WeylCharacterRing(['B',3], prefix = "R") sage: %time r = R(1,1,0) CPU times: user 0.14 s, sys: 0.00 s, total: 0.14 s Wall time: 0.14 s sage: sage: R = WeylCharacterRing(['B',3], prefix = "R") sage: %time [R(w) for w in R.lattice().fundamental_weights()] CPU times: user 0.25 s, sys: 0.00 s, total: 0.25 s Wall time: 0.25 s [R(1,0,0), R(1,1,0), R(1/2,1/2,1/2)] sage: sage: A2 = WeylCharacterRing(['A',2]) sage: %time [A2(0,0,0)+A2(2,1,0), A2(2,1,0)+A2(0,0,0), - A2(0,0,0)+2*A2(0,0,0), -2*A2(0,0,0)+A2(0,0,0), -A2(2,1,0)+2*A2(2,1,0)-A2(2,1,0)] CPU times: user 0.18 s, sys: 0.00 s, total: 0.18 s Wall time: 0.19 s [A2(0,0,0) + A2(2,1,0), A2(0,0,0) + A2(2,1,0), A2(0,0,0), -A2(0,0,0), 0] sage: sage: A2 = WeylCharacterRing(['A',2]) sage: %timeit [-x for x in [A2(0,0,0), 2*A2(0,0,0), -A2(0,0,0), -2*A2(0,0,0)]] 10 loops, best of 3: 20 ms per loop sage: sage: A2 = WeylCharacterRing(['A',2]) sage: chi = A2(0,0,0)+2*A2(1,0,0)+3*A2(2,0,0) sage: mu = 3*A2(0,0,0)+2*A2(1,0,0)+A2(2,0,0) sage: %timeit chi - mu 100 loops, best of 3: 8.16 ms per loop sage: sage: A2 = WeylCharacterRing(['A',2]) sage: chi = A2(1,0,0) sage: %time [chi^k for k in range(6)] CPU times: user 1.05 s, sys: 0.02 s, total: 1.07 s Wall time: 1.07 s [A2(0,0,0), A2(1,0,0), A2(1,1,0) + A2(2,0,0), A2(1,1,1) + 2*A2(2,1,0) + A2(3,0,0), 3*A2(2,1,1) + 2*A2(2,2,0) + 3*A2(3,1,0) + A2(4,0,0), 5*A2(2,2,1) + 6*A2(3,1,1) + 5*A2(3,2,0) + 4*A2(4,1,0) + A2(5,0,0)] # AFTER sage: R = WeylCharacterRing(['B',3], prefix = "R") sage: %time r = R(1,1,0) CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s Wall time: 0.03 s sage: sage: R = WeylCharacterRing(['B',3], prefix = "R") sage: %time [R(w) for w in R.lattice().fundamental_weights()] CPU times: user 0.05 s, sys: 0.00 s, total: 0.05 s Wall time: 0.05 s [R(1,0,0), R(1,1,0), R(1/2,1/2,1/2)] sage: sage: A2 = WeylCharacterRing(['A',2]) sage: %time [A2(0,0,0)+A2(2,1,0), A2(2,1,0)+A2(0,0,0), - A2(0,0,0)+2*A2(0,0,0), -2*A2(0,0,0)+A2(0,0,0), -A2(2,1,0)+2*A2(2,1,0)-A2(2,1,0)] CPU times: user 0.04 s, sys: 0.00 s, total: 0.04 s Wall time: 0.04 s [A2(0,0,0) + A2(2,1,0), A2(0,0,0) + A2(2,1,0), A2(0,0,0), -A2(0,0,0), 0] sage: sage: A2 = WeylCharacterRing(['A',2]) sage: %timeit [-x for x in [A2(0,0,0), 2*A2(0,0,0), -A2(0,0,0), -2*A2(0,0,0)]] 100 loops, best of 3: 3.33 ms per loop sage: sage: A2 = WeylCharacterRing(['A',2]) sage: chi = A2(0,0,0)+2*A2(1,0,0)+3*A2(2,0,0) sage: mu = 3*A2(0,0,0)+2*A2(1,0,0)+A2(2,0,0) sage: %timeit chi - mu 1000 loops, best of 3: 771 µs per loop sage: sage: A2 = WeylCharacterRing(['A',2]) sage: chi = A2(1,0,0) sage: %time [chi^k for k in range(6)] CPU times: user 0.20 s, sys: 0.00 s, total: 0.20 s Wall time: 0.20 s [A2(0,0,0), A2(1,0,0), A2(1,1,0) + A2(2,0,0), A2(1,1,1) + 2*A2(2,1,0) + A2(3,0,0), 3*A2(2,1,1) + 2*A2(2,2,0) + 3*A2(3,1,0) + A2(4,0,0), 5*A2(2,2,1) + 6*A2(3,1,1) + 5*A2(3,2,0) + 4*A2(4,1,0) + A2(5,0,0)] }}} == Commutative Algebra == * New function {{{weil_restriction()}}} on multivariate ideals (Martin Albrecht) -- The new function {{{weil_restriction()}}} computes the [[http://en.wikipedia.org/wiki/Weil_restriction|Weil restriction]] of a multivariate ideal over some extension field. A Weil restriction is also known as a restriction of scalars. Here's an example on computing a Weil restriction: {{{ sage: k.<a> = GF(2^2) sage: P.<x,y> = PolynomialRing(k, 2) sage: I = Ideal([x*y + 1, a*x + 1]) sage: I.variety() [{y: a, x: a + 1}] sage: J = I.weil_restriction() sage: J Ideal (x1*y0 + x0*y1 + x1*y1, x0*y0 + x1*y1 + 1, x0 + x1, x1 + 1) of Multivariate Polynomial Ring in x0, x1, y0, y1 over Finite Field of size 2 }}} * FIXME: summarize #5146 * FIXME: summarize #5353 * FIXME: summarize #3812 == Distribution == == Doctest == * FIXME: summarize #5318 == Documentation == == Geometry == * Improved enumeration of vertices and 0-dimensional faces of LatticePolytope's. There was an inconsistency between indicies of vertices, i.e. columns of the .vertices() matrix, and indicies of 0-dimensional faces, i.e. objects returned by .faces(dim=0). E.g. the 5-th 0-dimensional face could be generated by the 7-th vertex etc. Now the i-th 0-dimensional face is generated by the i-th vertex. (The reason for the old behaviour was the output of the underlying software package PALP, now there is extra sorting.) == Graph Theory == * FIXME: summarize #5623 == Graphics == * FIXME: summarize #5606 * FIXME: summarize #5450 == Group Theory == * Speed-up in comparing elements of a permutation group (Robert Bradshaw, John H. Palmieri, Rob Beezer) -- For elements of a permutation group, comparison between those elements is now up to 13x faster. On Mac OS X 10.4 with Intel Core 2 duo running at 2.33 GHz, one has the following improvement in timing statistics: {{{ # BEFORE sage: a = SymmetricGroup(20).random_element() sage: b = SymmetricGroup(10).random_element() sage: timeit("a == b") 625 loops, best of 3: 3.19 µs per loop # AFTER sage: a = SymmetricGroup(20).random_element() sage: b = SymmetricGroup(10).random_element() sage: time v = [a == b for _ in xrange(2000)] CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: timeit("a == b") 625 loops, best of 3: 240 ns per loop }}} * FIXME: summarize #5264 == Interfaces == == Linear Algebra == * Deprecate the function {{{invert()}}} (John H. Palmieri) -- The function {{{invert()}}} for calculating the inverse of a dense matrix with rational entries is now deprecated. Instead, users are now advised to use the function {{{inverse()}}}. Here's an example of using the function {{{inverse()}}}: {{{ sage: a = matrix(QQ, 2, [1, 5, 17, 3]) sage: a.inverse() [-3/82 5/82] [17/82 -1/82] }}} * Speed-up in calculating determinants of matrices (John H. Palmieri, William Stein) -- For matrices over {{{Z/nZ}}} with {{{n}}} composite, calculating their determinants is now up to 1500x faster. On Debian 5.0 Lenny with kernel 2.6.24-1-686, an Intel(R) Celeron(R) 2.00GHz CPU with 1.0GB of RAM, one has the following timing statistics: {{{ # BEFORE sage: time random_matrix(Integers(26), 10).determinant() CPU times: user 15.52 s, sys: 0.02 s, total: 15.54 s Wall time: 15.54 s 13 sage: time random_matrix(Integers(256), 10).determinant() CPU times: user 15.38 s, sys: 0.00 s, total: 15.38 s Wall time: 15.38 s 144 # AFTER sage: time random_matrix(Integers(26), 10).determinant() CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 s 23 sage: time random_matrix(Integers(256), 10).determinant() CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s }}} * FIXME: summarize #5715 == Miscellaneous == * FIXME: summarize #5638 * FIXME: summarize #5386 == Modular Forms == * FIXME: summarize #5520 * FIXME: summarize #5648 * FIXME: summarize #5180 == Notebook == FIXME: A number of tickets related to UTF-8 text got merged and should definitely be mentioned! #4547, #5211; #2896 and #1477 got fixed by those tickets. There's also #5564, which may not get merged for 3.4.1 but should get in soon; it pulls together a whole bunch of UTF-8 fixes and improvements. * FIXME: summarize #5681 == Number Theory == * FIXME: summarize #5518 * FIXME: summarize #5508 * FIXME: summarize #793 * FIXME: summarize #4667 * FIXME: summarize #5159 * FIXME: summarize #4990 * FIXME: summarize #3081 * FIXME: summarize #4724 * FIXME: summarize #5673 == Numerical == == Packages == * FIXME: summarize #4987 * FIXME: summarize #4881 * FIXME: summarize #4880 * FIXME: summarize #4876 * FIXME: summarize #5672 * FIXME: summarize #5240 * FIXME: summarize #5738 * FIXME: summarize #5696 * FIXME: summarize #4987 * FIXME: summarize #5697 * FIXME: summarize #5823 == Quadratic Forms == == Symbolics == * FIXME: summarize #5737 == User Interface == == Website / Wiki == |
moved to https://github.com/sagemath/sage/releases |
