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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. |
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== 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 |
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* provides much improved performance for multiplication, | * provides much improved performance for multiplication (see [http://m4ri.sagemath.org/performance.html M4RI's "performance" page]), |
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* hashs and matrix pickling was much improved * dense matrices over $\mathbb{F}_2$ can now be written to/read from 1-bit PNG images |
* hashs and matrix pickling was much improved (Martin Albrecht) |
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== Doctest Coverage Hits 60% == * Mike Hansen wrote doctests for almost all pexpect interfaces, which will ensure greater stability across the board. |
'''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) |
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* PolyBoRi was upgraded from 0.3 to 0.5rc | * PolyBoRi was upgraded from 0.3 to 0.5rc (Tim Abbott, Michael Abshoff, Martin Albrecht) |
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'''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] }}} |
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* Ondrej Cetrik implemented more conversions from Sage native types to SymPy native types. | |
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== Hidden Markov Models == | == Faster Determinants of Dense Matrices over Multivariate Polynomial Rings == * Martin Albrecht modified Sage to use Singular |
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== Faster Determinants of Matrices over Multivariate Polynomial Rings == | '''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] |
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* 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 }}} == Arrow drawing improved == * Jason Grout redid the arrows to look nicer and behave better with graphs: {{{ sage: g = DiGraph({0:[1,2,3],1:[0,3,4], 3:[4,6]}) sage: show(g) }}} == Eigen functions for matrices == * Jason Grout added a few standard functions to compute eigenvalues and left and right eigenvectors, returning exact results in QQbar. {{{ sage: a = matrix(QQ, 4, range(16)); a [ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11] [12 13 14 15] sage: a.eigenvalues() [0, 0, -2.464249196572981?, 32.46424919657298?] sage: a.eigenvectors_right() [(0, [ (1, 0, -3, 2), (0, 1, -2, 1) ], 2), (-2.464249196572981?, [(1, 0.3954107716733585?, -0.2091784566532830?, -0.8137676849799244?)], 1), (32.46424919657298?, [(1, 2.890303514040928?, 4.780607028081855?, 6.670910542122782?)], 1)] sage: D,P=a.eigenmatrix_right() sage: P [ 1 0 1 1] [ 0 1 0.3954107716733585? 2.890303514040928?] [ -3 -2 -0.2091784566532830? 4.780607028081855?] [ 2 1 -0.8137676849799244? 6.670910542122782?] sage: D [ 0 0 0 0] [ 0 0 0 0] [ 0 0 -2.464249196572981? 0] [ 0 0 0 32.46424919657298?] sage: a*P==P*D True }}} |
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
Arrow drawing improved
- Jason Grout redid the arrows to look nicer and behave better with graphs:
sage: g = DiGraph({0:[1,2,3],1:[0,3,4], 3:[4,6]}) sage: show(g)
Eigen functions for matrices
- Jason Grout added a few standard functions to compute eigenvalues and left and right eigenvectors, returning exact results in QQbar.
sage: a = matrix(QQ, 4, range(16)); a [ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11] [12 13 14 15] sage: a.eigenvalues() [0, 0, -2.464249196572981?, 32.46424919657298?] sage: a.eigenvectors_right() [(0, [ (1, 0, -3, 2), (0, 1, -2, 1) ], 2), (-2.464249196572981?, [(1, 0.3954107716733585?, -0.2091784566532830?, -0.8137676849799244?)], 1), (32.46424919657298?, [(1, 2.890303514040928?, 4.780607028081855?, 6.670910542122782?)], 1)] sage: D,P=a.eigenmatrix_right() sage: P [ 1 0 1 1] [ 0 1 0.3954107716733585? 2.890303514040928?] [ -3 -2 -0.2091784566532830? 4.780607028081855?] [ 2 1 -0.8137676849799244? 6.670910542122782?] sage: D [ 0 0 0 0] [ 0 0 0 0] [ 0 0 -2.464249196572981? 0] [ 0 0 0 32.46424919657298?] sage: a*P==P*D True