Sage 3.4.1 Release Tour

Sage 3.4.1 was released on FIXME. For the official, comprehensive release note, please refer to 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.

Algebra

• FIXME: summarize ticket #5535.
• FIXME: summarize ticket #5658.

• 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

• FIXME: summarize #5629

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 ticket 5093.

• FIXME: summarize #5622

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.

  2. 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) -- Corrects the Robinson-Schensted algorithm on trivial permutations. 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]

  It also 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:

  • - 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 arbitrary large number and even infinity;

    - there were two redundant way 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 to:

  • - C.cardinality() which is more explicit and consistent with many other Sage libraries;

    - iter(C) / for x in C: via C.__iter__ with is clearly more Pythonic.

  • The functions  iterator and count are deprecated (with a warning) but still working for the moment (please fix your code). 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.

• FIXME: summarize #4549

Commutative Algebra

• New function weil_restriction() on multivariate ideals (Martin Albrecht) -- The new function weil_restriction() computes the 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

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

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

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

Miscellaneous

• FIXME: summarize #5638

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

Numerical

Packages

• FIXME: summarize #4987
• FIXME: summarize #4881
• FIXME: summarize #4880
• FIXME: summarize #4876
• FIXME: summarize #5672
• FIXME: summarize #5240

Quadratic Forms

Symbolics

User Interface

Website / Wiki