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.

• 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

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.

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

• FIXME: summarize #5200

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

Documentation

Geometry

Graph Theory

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

Modular Forms

Notebook

Number Theory

• FIXME: summarize #5518
• FIXME: summarize #5508

Numerical

Optional Packages

Packages

• FIXME: summarize #4987

Quadratic Forms

Symbolics

User Interface

Website / Wiki