Sage 3.4.2 Release Tour

Sage 3.4.2 was released on FIXME. For the official, comprehensive release note, please refer to sage-3.4.2.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

• FIXME: summarize #5820
• FIXME: summarize #5921

• Coercing factors into a common universe (Alex Ghitza) -- New method base_change(self, U) in the module sage/structure/factorization.py to allow the factorization self with its factors (including the unit part) coerced into the universe U. Here's an example for working with the new method base_change():

  sage: F = factor(2006)
  sage: F.universe() 
  Integer Ring
  sage: P.<x> = ZZ["x"]
  sage: F.base_change(P).universe() 
  Univariate Polynomial Ring in x over Integer Ring

Algebraic Geometry

Basic Arithmetic

• Enhancements to symbolic logic (Chris Gorecki) -- This adds a number of utilities for working with symbolic logic:

  1. sage/logic/booleval.py -- For evaluating boolean formulas.

  2. sage/logic/boolformula.py -- For boolean evaluation of boolean formulas.

  3. sage/logic/logicparser.py -- For creating and modifying parse trees of well-formed boolean formulas.

  4. sage/logic/logictable.py -- For creating and printing truth tables associated with logical statements.

  5. sage/logic/propcalc.py -- For propositional calculus.

  Here are some examples for working with the new symbolic logic modules:

  sage: import sage.logic.propcalc as propcalc
  sage: f = propcalc.formula("a&((b|c)^a->c)<->b")
  sage: g = propcalc.formula("boolean<->algebra")
  sage: (f&~g).ifthen(f)
  ((a&((b|c)^a->c)<->b)&(~(boolean<->algebra)))->(a&((b|c)^a->c)<->b)
  sage: f.truthtable()
  
  a      b      c      value
  False  False  False  True   
  False  False  True   True   
  False  True   False  False  
  False  True   True   False  
  True   False  False  True   
  True   False  True   False  
  True   True   False  True   
  True   True   True   True

• New function squarefree_divisors() (Robert Miller) -- The new function squarefree_divisors(x) in the module sage/rings/arith.py allows for iterating over the squarefree divisors (up to units) of the element x. Here, we assume that x is an element of any ring for which the function prime_divisors() works. Below are some examples for working with the new function squarefree_divisors():

  sage: list(squarefree_divisors(7))
  [1, 7]
  sage: list(squarefree_divisors(6))
  [1, 2, 3, 6]
  sage: list(squarefree_divisors(81))
  [1, 3]

Build

Calculus

Coercion

Combinatorics

• Make cartan_type a method rather than an attribute (Dan Bump) -- For the module sage/combinat/root_system/weyl_characters.py, cartan_type is now a method, not an attribute. For example, one can now invoke cartan_type as a method like so:

  sage: A2 = WeylCharacterRing("A2")
  sage: A2([1,0,0]).cartan_type()
  ['A', 2]

Commutative Algebra

• Improved performance in MPolynomialRing_libsingular (Simon King) -- This provides some optimization of the method MPolynomialRing_libsingular.__call__(). In some cases, the efficiency is up to 19%. The following timing statistics are obtained using the machine sage.math:

  # BEFORE
  
  sage: R = PolynomialRing(QQ,5,"x")
  sage: S = PolynomialRing(QQ,6,"x")
  sage: T = PolynomialRing(QQ,5,"y")
  sage: U = PolynomialRing(GF(2),5,"x")
  sage: p = R("x0*x1+2*x4+x3*x1^2")^4
  sage: timeit("q = S(p)")
  625 loops, best of 3: 321 µs per loop
  sage: timeit("q = T(p)")
  625 loops, best of 3: 348 µs per loop
  sage: timeit("q = U(p)")
  625 loops, best of 3: 435 µs per loop
  
  
  # AFTER
  
  sage: R = PolynomialRing(QQ,5,"x")
  sage: S = PolynomialRing(QQ,6,"x")
  sage: T = PolynomialRing(QQ,5,"y")
  sage: U = PolynomialRing(GF(2),5,"x")
  sage: p = R("x0*x1+2*x4+x3*x1^2")^4
  sage: timeit("q = S(p)")
  625 loops, best of 3: 316 µs per loop
  sage: timeit("q = T(p)")
  625 loops, best of 3: 281 µs per loop
  sage: timeit("q = U(p)")
  625 loops, best of 3: 392 µs per loop

Distribution

Doctest

Documentation

• FIXME: summarize #5610

Geometry

Graph Theory

• Default edge color is black (Robert Miller) -- If only one edge of a graph is colored red, for example, then the remaining edges should be colored with black by default. Here's an example:

  sage: G = graphs.CompleteGraph(5)
  sage: G.show(edge_colors={'red':[(0,1)]})

Graphics

Group Theory

Interfaces

• FIXME: summarize #5111

Linear Algebra

• FIXME: summarize #5886

Miscellaneous

Modular Forms

• FIXME: summarize #5876

Notebook

• FIXME: summarize #5912
• FIXME: summarize #2740
• FIXME: summarize #5880

Number Theory

• FIXME: summarize #5130
• FIXME: summarize #5822
• FIXME: summarize #5704
• FIXME: summarize #4193
• FIXME: summarize #5890
• FIXME: summarize #5856

Numerical

Packages

• FIXME: summarize #5803
• FIXME: summarize #5849

• Move DSage to its own spkg (William Stein) -- The Distributed Sage framework (DSage) contained in sage/dsage is now packaged as a self-contained spkg. DSage allows for distributed computing from within Sage.

P-adics

• FIXME: summarize #5946

Quadratic Forms

Symbolics

Topology

User Interface

Website / Wiki