Sage 3.1.2 Release Tour

Sage 3.1.2 was released on XXX, 2008. For the official, comprehensive release notes, see the HISTORY.txt file that comes with the release. For the latest changes see sage-3.1.2.txt.

Doctest Coverage Hits 60%

• Mike Hansen wrote doctests for almost all pexpect interfaces, which will ensure greater stability across the board.

Hidden Markov Models

• William Stein wrote Cython bindings for the GHMM C library for computing with Hidden Markov Models, which are a statistical tool that is important in machine learning, natural language processing, bioinformatics, and other areas. GHMM is also now included standard in Sage.

Notebook Bugs

• Many bugs introduced in 3.1.1 were fixed by Mike Hansen and Timothy Clemans.
• A new testing procedure was implemented, hopefully preventing regressions like in 3.1.1 in the future.

New Structures for Partition Refinement

Robert Miller

• Hypergraphs (i.e. incidence structures) -- this includes simplicial complexes and block designs
• Matrices -- the automorphism group of a matrix is the set of column permutations which leave the (unordered) set of rows unchanged

Improved Dense Linear Algebra over GF(2)

• M4RI (http://m4ri.sagemath.org) was updated to the newest upstream release which

  • provides much improved performance for multiplication (see [http://m4ri.sagemath.org/performance.html M4RI's "performance" page]),

  • provides improved performance for elimination,
  • contains several build and bugfixes.
• hashs and matrix pickling was much improved (Martin Albrecht)

Before

sage: A = random_matrix(GF(2),10000,10000)
sage: A.set_immutable()
sage: %time _ = hash(A)
CPU times: user 3.96 s, sys: 0.62 s, total: 4.58 s
sage: A = random_matrix(GF(2),2000,2000)
sage: %time _ = loads(dumps(A))
CPU times: user 4.00 s, sys: 0.07 s, total: 4.07 s

After

sage: A = random_matrix(GF(2),10000,10000)
sage: A.set_immutable()
sage: %time _ = hash(A)
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
sage: A = random_matrix(GF(2),2000,2000)
sage: %time _ = loads(dumps(A))
CPU times: user 1.35 s, sys: 0.01 s, total: 1.37 s

• dense matrices over \mathbb{F}_2 can now be written to/read from 1-bit PNG images (Martin Albrecht)

New PolyBoRi Version (0.5) and Improved Interface

• PolyBoRi was upgraded from 0.3 to 0.5rc (Tim Abbott, Michael Abshoff, Martin Albrecht)

• mq.SR now returns PolyBoRi equation systems if asked to

• support for boolean polynomial interpolation was added

Example

First we create a random-ish boolean polynomial.

sage: B.<a,b,c,d,e,f> = BooleanPolynomialRing(6)
sage: f = a*b*c*e + a*d*e + a*f + b + c + e + f + 1

Now we find interpolation points mapping to zero and to one.

sage: zeros = set([(1, 0, 1, 0, 0, 0), (1, 0, 0, 0, 1, 0), \
                   (0, 0, 1, 1, 1, 1), (1, 0, 1, 1, 1, 1), \
                   (0, 0, 0, 0, 1, 0), (0, 1, 1, 1, 1, 0), \
                   (1, 1, 0, 0, 0, 1), (1, 1, 0, 1, 0, 1)])
sage: ones = set([(0, 0, 0, 0, 0, 0), (1, 0, 1, 0, 1, 0), \
                  (0, 0, 0, 1, 1, 1), (1, 0, 0, 1, 0, 1), \
                  (0, 0, 0, 0, 1, 1), (0, 1, 1, 0, 1, 1), \
                  (0, 1, 1, 1, 1, 1), (1, 1, 1, 0, 1, 0)])
sage: [f(*p) for p in zeros]
[0, 0, 0, 0, 0, 0, 0, 0]
sage: [f(*p) for p in ones]
[1, 1, 1, 1, 1, 1, 1, 1]

Finally, we find the lexicographically smallest interpolation polynomial using PolyBoRi .

sage: g = B.interpolation_polynomial(zeros, ones); g
b*f + c + d*f + d + e*f + e + 1

sage: [g(*p) for p in zeros]
[0, 0, 0, 0, 0, 0, 0, 0]
sage: [g(*p) for p in ones]
[1, 1, 1, 1, 1, 1, 1, 1]

QEPCAD Interface

Developer's Handbook

• John H Palmieri rewrote/rearranged large parts of the 'Programming Guide' (now 'Developer's Guide') which should make getting started easier for new developers.

Improved 64-bit OSX Support

Fast Numerical Integration

GAP Meataxe Interface

• In the module matrix_group, the method module_composition_factors interfaces with GAP's [http://www.gap-system.org/Manuals/doc/htm/ref/CHAP067.htm Meataxe] implementation. This will return decomposition information for a G-module, for any matrix group G over a finite field.

Better SymPy Integration

• Ondrej Cetrik implemented more conversions from Sage native types to SymPy native types.

Faster Determinants of Dense Matrices over Multivariate Polynomial Rings

• Martin Albrecht modified Sage to use Singular

Before

sage: P.<x,y> = QQ[]
sage: C = random_matrix(P,8,8)
sage: %time d = C.det()
CPU times: user 2.78 s, sys: 0.02 s, total: 2.80 s

After

sage: P.<x,y> = QQ[]
sage: C = random_matrix(P,8,8)
sage: %time d = C.det()
CPU times: user 0.09 s, sys: 0.00 s, total: 0.09 s

• a discussion about this issue can be found on [http://groups.google.com/group/sage-devel/browse_thread/thread/7aa1bd1e945ff372/ sage-devel]

Real Number Inputs Improved

• Robert Bradshaw improved real number input so that the precision is preserved better:

Before

sage: RealField(256)(1.2)
1.199999999999999955591079014993738383054733276367187500000000000000000000000

After

sage: RealField(256)(1.2)
1.200000000000000000000000000000000000000000000000000000000000000000000000000