Differences between revisions 1 and 2
Revision 1 as of 2009-03-22 03:51:27
Size: 1090
Editor: Minh Nguyen
Comment: Lay out general structure of release tour for Sage 3.4.1
Revision 2 as of 2009-03-24 02:06:43
Size: 6545
Editor: Minh Nguyen
Comment: Summarized #5537, #5460, #5569, #5570, #5519, #5223
Deletions are marked like this. Additions are marked like this.
Line 12: Line 12:
 * 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 the following system info:
 {{{
kernel: 2.6.24-1-686
CPU: Intel(R) Celeron(R) 2.00GHz
RAM: 1.0GB
 }}}
here are some 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
 }}}

Line 18: Line 86:
 * Speed-up in dividing a polynomial by an integer (Burcin Erocal) -- Dividing a polynomial by an integer is now up to 7x faster than previously. On the machine sage.math, 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: 231 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: 32.4 µs per loop
 }}}

Line 33: Line 118:
 * New function {{{weil_restriction()}}} on multivariate ideals (Martin Albrecht) -- The new function {{{weil_restriction()}}} computes the [[http://en.wikipedia.org/wiki/Weil_restriction|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
 }}}

Line 54: Line 153:
 * 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
 }}}

Line 60: Line 179:
 * 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 1.5% faster. On the machine sage.math, one can see the following improvement in computation time:
 {{{
# BEFORE
sage: mat = random_matrix(Integers(256), 30)
sage: timeit("Integers(256)(mat.lift().det())")
25 loops, best of 3: 9.53 ms per loop
sage:
sage: mat = random_matrix(Integers(256), 200)
sage: timeit("Integers(256)(mat.lift().det())")
5 loops, best of 3: 779 ms per loop
sage:
sage: mat = random_matrix(Integers(2^20), 500)
sage: timeit("Integers(256)(mat.lift().det())")
5 loops, best of 3: 13.5 s per loop


# AFTER
sage: mat = random_matrix(Integers(256), 30)
sage: timeit("Integers(256)(mat.lift().det())")
25 loops, best of 3: 10 ms per loop
sage:
sage: mat = random_matrix(Integers(256), 200)
sage: timeit("Integers(256)(mat.lift().det())")
5 loops, best of 3: 762 ms per loop
sage:
sage: mat = random_matrix(Integers(2^20), 500)
sage: timeit("Integers(256)(mat.lift().det())")
5 loops, best of 3: 13.3 s per loop
 }}}

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 the following system info:

  • kernel: 2.6.24-1-686
    CPU: Intel(R) Celeron(R) 2.00GHz 
    RAM: 1.0GB

here are some 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 7x faster than previously. On the machine sage.math, 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: 231 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: 32.4 µs per loop

Build

Calculus

Coercion

Combinatorics

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

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 1.5% faster. On the machine sage.math, one can see the following improvement in computation time:

    # BEFORE
    sage: mat = random_matrix(Integers(256), 30)
    sage: timeit("Integers(256)(mat.lift().det())")
    25 loops, best of 3: 9.53 ms per loop
    sage: 
    sage: mat = random_matrix(Integers(256), 200)
    sage: timeit("Integers(256)(mat.lift().det())")
    5 loops, best of 3: 779 ms per loop
    sage: 
    sage: mat = random_matrix(Integers(2^20), 500)
    sage: timeit("Integers(256)(mat.lift().det())")
    5 loops, best of 3: 13.5 s per loop
    
    
    # AFTER
    sage: mat = random_matrix(Integers(256), 30)
    sage: timeit("Integers(256)(mat.lift().det())")
    25 loops, best of 3: 10 ms per loop
    sage: 
    sage: mat = random_matrix(Integers(256), 200)
    sage: timeit("Integers(256)(mat.lift().det())")
    5 loops, best of 3: 762 ms per loop
    sage: 
    sage: mat = random_matrix(Integers(2^20), 500)
    sage: timeit("Integers(256)(mat.lift().det())")
    5 loops, best of 3: 13.3 s per loop

Miscellaneous

Modular Forms

Notebook

Number Theory

Numerical

Optional Packages

Packages

Quadratic Forms

Symbolics

User Interface

Website / Wiki

ReleaseTours/sage-3.4.1 (last edited 2009-12-26 14:48:37 by Minh Nguyen)