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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

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

DSage

FIXME: summarize #5824

Factorization

FIXME: summarize #5928

Geometry

Graph Theory

FIXME: summarize #5914

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

Diff for "ReleaseTours/sage-3.4.2"