Sage 3.3 Release Tour

Sage 3.3 was released on FIXME. For the official, comprehensive release notes, see sage-3.3.txt. The following points are some of the foci of this release:

• Clean up various doctest failures from 3.2.3
• Fix some build issues from 3.2.3 on the new set of supported images
• Merge small to medium sized patches ready to go in

• Switch to eMPIRe for multi-precision integers and rationals

• Switch to ecl for a Common Lisp implementation

• Update Python to 2.5.4 upstream release

• Update Pari to 2.3.4svn upstream release

• Switch to FLINT for univariate polynomial arithmetic over Z/nZ

• Update NetworkX to version 0.99 upstream release

• Update cddlib to version 0.94f upstream release

• Some improvements to the lrs spkg

• PyNaC interface enhancements

• Update the readline spkg

• Update the ATLAS spkg

Here's a summary of features in this release, categorized under various headings.

Algebra

• Transitivity for permutation groups (William Stein) -- In the permutation group module permgroup.py, the query function is_transitive() returns whether or not the group is transitive on [1..G.degree()]. A few surrounding docstrings are fixed and doctest coverage for the file sage/groups/perm_gps/permgroup.py is now 100%.

• Update the ATLAS spkg (Michael Abshoff).

Algebraic Geometry

• Improved precision and performance when calculating analytic rank (William Stein) -- When calculating the analytic rank of an elliptic curve, the default is to use Cremona's gp script, where the precision is automatically doubled until it doesn't fail. The precision is started at 16 rather than the previous default precision. The computation is now about 3 times faster usually by starting off using this smaller precision.

Basic Arithmetic

• ivalue field in integer_mod.pyx is no longer public (Craig Citro) -- The ivalue field for IntegerMod_int is no longer public. This gives about a 1.5 to 2X speedup when multiplying IntegerMod_ints.

• Some fixes for is_perfect_power and bessel_J(0,0) (Craig Citro, Robert Bradshaw, Robert Miller) -- A temporary work around for an upstream bug in GMP when using is_perfect_power(). Resolved a Pari interface bug when using bessel_J(0,0).

• Improved performance for generic polynomial rings, and for univariate polynomial arithmetic over Z/nZ[x] (Yann Laigle-Chapuy, Martin Albrecht) -- Improved performance when performing modulo arithmetic between elements of a generic polynomial ring. Univariate polynomial arithmetic over Z/nZ[x] now has considerable speed-up at approximately 20x.

• Deprecate the function sqrt_approx() (David Roe) -- To obtain a numerical approximation of the square root of a ring element (integers, polynomials over GF(2^x), rationals), users are advised to use the function sqrt() with a given number of bits of precision instead.

• Use Pohlig-Hellman for generic discrete logarithm (Yann Laigle-Chapuy) -- This results in significant improvement in performance and less memory foot print.

• Exact division syntax in finite fields of prime order (David Roe) -- Support the division operator // for finite fields of prime order.

• Consistent integer hashing (Craig Citro).

Build

• 64-bit OSX (Michael Abshoff) -- Fixed 64-bit OSX build support for f2c, added 64-bit OSX build support for tachyon, added 64-bit OSX build support for flintqs, and added persistent Sage 64-bit building switch on OSX and Solaris.
• Update readline spkg (Michael Abshoff) -- The updated readline spkg allows readline-5.2 to be built on the 64-bit version of OpenSUSE 11.1.

Calculus

• LaTeX output (Mike Hansen) -- Added LaTeX output for ceiling, floor, and derivative functions, and LaTaX'ing of powers of negative numbers.

• Make bernoulli_polynomial independent of Maxima (Craig Citro) -- A rewrite of bernoulli_polynomial to avoid using Maxima completely in computing Bernoulli polynomials. This gives roughly a factor of 10 speedup.

• Support integration without explicit variable declaration (Karl-Dieter Crisman).

• CPU time of a Maxima session (Martin Albrecht) -- The new function cputime() in interfaces/maxima.py returns the amount of CPU time used by a Maxima session.

• PyNaC interface enhancements (Burcin Erocal) -- New enhancements to the PyNaC interface include:

  • Add the method operator() to sage/symbolic/expression.pyx to return the topmost operator in an expression.

  • Allow PyNaC symbolic variables as arguments to factorial() and binomial().

  • Iterator support to sage.symbolic.expression.Expression.

  • Allow substituting more than one variable in PyNaC expressions.

  • New function collect_common_factors to sage.symbolic.expression.Expression.

  • LaTeX printing.

  • Allow PyNaC symbolics to be used in CallableSymbolicExpressions.

Coding Theory

• Weight distribution for binary codes (Robert Miller) -- A weight distribution algorithm for binary codes using Robert Bradshaw's bitsets. This implementation in Cython gives a 19 to 20 times performance speed-up over the previous GAP/Guava implementation.

Coercion

• Ring coercion for polynomials over finite fields (William Stein).
• Move univariate polynomial rings to new coercion model (Robert Bradshaw).

Combinatorics

• Bell polynomials (Blair Sutton) -- New function bell_polynomial() in combinat/combinat.py returns the Bell polynomial.

• Covering design (Daniel Gordon) -- New module combinat/designs/covering_design.py adds basic support for covering design. The function best_known_covering_design_www() is an interface to the online database of best known covering design at the La Jolla Covering Repository.

Commutative Algebra

• Multivariate polynomials over residue fields of number fields (Nick Alexander) -- Fixed an infinite loop bug when working with multivariate polynomials over residue fields of number fields. Previously in hashing "large" characteristic residue fields, the hash method would try to hash an ideal of the residue field itself, which in turn would try to hash its parent, and so on ad infinitum. At no point has a residue field with cardinality a very large prime been created in Sage.
• GCD of polynomials over finite fields (Martin Albrecht) -- Previously when using ibsingular to compute the GCD of two (multivariate) polynomials over finite fields, Sage would segfault whenever the base rings are not identical.

• Deprecate Ideal.reduced_basis (John Perry) -- The previous name Ideal.reduced_basis is misleading as it suggests that it can be used for computing the reduced Gröbner basis, when in fact it returns the interreduced basis. Thus Ideal.reduced_basis() is now deprecated and users are encouraged to use Ideal.interreduced_basis() instead.

• Factoring multivariate polynomials over non-prime finite fields (William Stein) -- The factoring algorithm works as follow. If f is a polynomial over a non-prime finite field, factoring f is reduced to factoring over a prime field and using GCD over the non-prime field.

• Groebner bases over any field (John Perry) -- Support for computing the dimension of fields of large prime characteristics via the method dimension() in the module rings/polynomial/multi_polynomial_ideal.py. The default is to use the functionalities of Singular to do so. However, if the characteristic of the field is larger than what Singular can handle, the method falls back on a toy implementation of Buchberger to compute the Groebner basis, and finally using the algorithm described in Chapter 9, Section 1 of the following text:

  • David A. Cox, John B. Little & Donal O'Shea. "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra" 3rd edition. Springer, 2007.

Distribution

• GAP configuration file (Matthias Meulien) -- A user's local GAP configuration file is usually named $HOME/.gaprc. When such a file already exists and Sage is compiled from source, using the Sage interface to GAP, e.g. gap._eval_line('1+3;'), can result in gibberish. This is now fixed so that the GAP interface would output a comprehensible message/answer as a result of some GAP calculation.

Documentation

Geometry

• Polyhedral improvements (Marshall Hampton) -- Added more built-in Archimedean solids and some new methods such as the Gale transform, bipyramid construction, edge truncation, and perspective projection with (optionally) hidden faces invisible. The Schlegel projection code has also been somewhat refactored to make it more general in the future.

Graph Theory

• Equality testing in graphs (Robert Miller) -- The "weighted" property or edge label is taken into account when testing for equality in graphs.

• Update NetworkX to version 0.99 (Robert Miller, Michael Abshoff).

Graphics

• Plotting a region (Arnaud Bergeron) -- Plot a region where a system of equations/inequalities were true.

• Consistency in variable range (Mike Hansen, Jason Grout) -- The variable range of parametric_plot is now consistent with that of plot, namely (var, min, max).

• Polar plot syntax (Jason Grout) -- Polar plot now accepts the syntax (t, 0, 2*pi) for the interval.

• Added a density_plot() function and improve colour map handling (Arnaud Bergeron) -- The density_plot takes a function of two variables and plots contour lines of the function over two specified ranges. Some improve on how colour map is handled.

• 3-D polygon (Arnaud Bergeron) -- The new function polygon3d() allows for plotting of 3-D polygons.

Group Theory

• Added an is_cyclic method (David Joyner) -- The is_cyclic method for (finite) groups is currently not as optimized as it should be. Given a finite abelian group, one can test to see whether or not it is cyclic, a test that depends on calculating the elementary divisors of the group. As correctness is the main concern in the current implementation of elementary_divisors(), performance is not taken into account. However, the docstring for elementary_divisors() describes an algorithm communicated by Robert Miller for speeding up this method.

Interfaces

• Magma interface (William Stein) -- Fixed a problem in Sage's interface to Magma so that now the Magma .sig files in extcode are no longer written there by Magma itself. The current behaviour is that the first (and only first) time a Magma interface is started in a given session, files in data/extcode/magma are copied to a temporary directory.

• GAP interface (Mike Hansen) -- Ensured that the GAP interface handles keyboard interrupt gracefully, that GAP output would be printed, and that multi-line input and comments are handled as expected.
• Sage preparser (Robert Bradshaw) -- Some simplification of the Sage preparser, together with improved handling of literal numbers.

Linear Algebra

• Multiplication of sparse matrices over finite fields (William Stein, Craig Citro) -- Significant performance improvement when multiplying two sparse matrices over the same finite field. In some cases, performance is about 37 times faster than previously.

• Minimum polynomials for GF(p) (Alex Ghitza).

• Matrix exponential for general matrices (Jason Grout) -- Added a generic matrix exponential that depends on Maxima's matrix exponentiation function. If the matrix has floating point numbers, these will be rounded automatically to rational numbers during the computation. For numerical approximations to the exponential, one can first convert the matrix to RDF or CDF.

• 100% doctest coverage for matrix/constructor.py, matrix/misc.pyx, matrix/matrix_generic_dense.pyx (William Stein) -- Apart from the full doctest coverage, calculating the lift of a matrix is now 20 times faster than previously.

• Improved performance for method density() in matrix/matrix_modn_sparse.pyx (Craig Citro).

• Added a kernel method for sparse integer matrices (John Palmieri).

Miscellaneous

• Rewrite of the function __getitem__ (Jason Grout, Craig Citro) -- A rewrite of the function __getitem__ in matrix/matrix0.pyx to better support slices, negative indices, and improved performance.

• Function get_memory_usage() now return a float on all platforms (William Stein).

• The function CremonaDatabase().number_of_curves() now works even when the optional Cremona database isn't installed (Alex Ghitza).

• Set iteration for finite sets (Robert Miller) -- Set iteration is now implemented for finite sets.

Notebook

• Interact cells in the notebook are not automatically evaluated (Mike Hansen).
• Clear browser cache when restarting the worksheet (Mike Hansen).
• Update jsmath to version 3.6 (Jason Grout).

• In-line WYSIWYG editor for text cells using TinyMCE (Jason Grout).

• Automatic indentation (Alexander Hupfer, Tom Boothby) -- Automatic indentation for Python code after colons and same level identation. Currently, up to four levels of identation are supported.

Number Theory

• Number field ideal utilities (John Cremona, Maite Aranes) -- New function invertible_residues() for iterating through only the invertible residues modulo an integral ideal. New function element_1_mod() such that A.element_1_mod(B) returns some a in A such that 1 - a is in B.

• New function random_element for returning a random element of a number field (Alex Ghitza).

• Elliptic curve function integral_points() misses some points (John Cremona) -- Francois Glineur reported that for the elliptic curve 20160bg2, the output of integral_points() misses the points x = 168 and x = 381. This problem has been narrowed down to the function point_preprocessing(), and the bug is now fixed.

• Elliptic curve (Robert Bradshaw) -- Support for the construction of an elliptic curve via a Weierstrass equation. The Weierstrass equation can be passed as an argument to EllipticCurve().

• Separating relative number fields from generic/absolute number fields (Nick Alexander) -- Functionalities in the module rings/number_field/number_field.py that deal with relative number fields are now wrapped inside the new module rings/number_field/number_field_rel.py.

• Cremona's database of elliptic curves (William Stein) -- Improved handling of the case 990h.

• Manin constant (William Stein) -- New function manin_constant() to compute the Manin constant of an elliptic curve. This function only works if the curve is in the installed Cremona database. By default Sage includes a small databases, whereas the full database must be installed as an optional package. WARNING: The result is _not_ provably correct in the sense that when the numbers are huge, isogenies could be missed due to precision issues. The newly implemented function can be found in the module schemes/elliptic_curves/ell_rational_field.py.

• Bach bound (William Stein) -- New function bach_bound() to compute the Bach bound associated to a number field. Assuming the General Riemann Hypothesis, the Bach bound is a bound B such that every integral ideal is equivalent modulo principal fractional ideals to an integral ideal of norm at most B. The newly implemented function can be found in the module rings/number_field/number_field_base.pyx.

Optional Packages

• Modular polynomials database (Alex Ghitza) -- Remove the use of polydict in databases/db_modular_polynomials.py.

• lrs.spkg improvements (Marshall Hampton) -- Further tests added to the makefile of the package lrs. This optional package implements the reverse search algorithm for vertex enumeration and convex hull problems.

Packages

• Switch gmp to eMPIRe svn1555 (Michael Abshoff) -- The package eMPIRe.spkg is a drop in for the previous package gmp-4.2.1.spkg.

• Upgrade GMP-ECM to version 6.2.1 (Michael Abshoff).

• Move jquery into its own spkg (Jason Grout).

• Upgrade Mercurial to version 1.1.2 (Mike Hansen).

• OS X 64-bit (Michael Abshoff) -- Added 64-bit build support for PyNaC, R, GHMM, and Boehm GC. Also added fortran-OSX64-20090120.spkg to the experimental spkg repository.

• Upgrade IPython to version 0.9.1 (Mike Hansen).

• Update cddlib to version 0.94f upstream release (Sebastien Barthelemy).

Porting

• OS X 64-bit (Michael Abshoff) -- Added proper libcsage build support, and Singular is now built using the flag "--with-malloc=system".

Solaris

• Upgrade libgcrypt to version 1.4.3 and force the function get_memory_usage() to fall back to using top when not on Linux (Michael Abshoff).

User Interface

• Added a hg_examples Mercurial wrapper for the examples repository (Mike Hansen).

Website/Wiki

• The trac server now displays the comments of a Mercurial diff (Robert Bradshaw).