Differences between revisions 1 and 9 (spanning 8 versions)

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

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.

Diff for "ReleaseTours/sage-3.4.1"