Sage 3.2.3 Release Tour

Sage 3.2.3 was released on FIXME. For the official, comprehensive release notes, see sage-3.2.3.txt.

Algebra

• Powers of polynomial variables (Alex Ghitza) -- Report an error message when a determinate of a (multivariate) polynomial is raised to a fractional exponent. Previously, raising a polynomial determinate to a fractional power has the effect of rounding the exponent to an integer. As yet, fractional powers is not supported.

• Extensions of finite fields (Alex Ghitza) -- Implements methods random_element() and order() for quotients of polynomial rings. The method random_element() returns the number of elements of a quotient ring, and order() returns a random element of a quotient ring.

• Conjugates for integer, rational and real numbers (Alex Ghitza) -- Implements trivial conjugate() methods for elements over the integers, rationals, and reals. Conjugates work (trivially) for matrices over rings that embed canonically into the real numbers.

• Square roots of Galois field elements (John Cremona, William Stein) -- Improve the square root of an element of a Galois field GF(2^e), where e > 15. Previously, this works fine except for the square root of 1, where 1 is an element of GF(2^e) for e > 15.

Build

• Upgrade ATLAS in Sage to version 3.8.2 (Michael Abshoff) -- An update of the ATLAS spkg to the upstream version 3.8.2. This upstream version now provides: (1) better detection of Pentium D and E; (2) detect more Core2Duos cores; and (3) properly detect Dunnington cores. Versions 3.8.x for x < 2 sometimes detect a modern CPU architecture as an older architecture, hence causing a massive blow up in the time it takes to compile ATLAS on systems like Xeon core 2 quad, Itanium 2, and Xeon E5420.

• Update optional Sage package polymake (Michael Abshoff) -- The updated optional Sage package is polymake-2.2.p5. Earlier versions hard coded spkg versions of cddlib and gmp, and could cause polymake to break in Sage versions 3.0.3 and 3.0.4.

Coercion

• Fix performance regression in eisenstein_submodule.py (Robert Bradshaw) -- Performance regression in eisenstein_submodule.py was due to cyclotomic coercion. Previously, it would take about 73.3 seconds to run all doctests in eisenstein_submodule.py. Now, the performance is substantially increased such that all dotests in eisenstein_submodule.py should now take about 3.4 seconds.

Commutative Algebra

Doctest

Documentation

Graphics

Interfaces

Linear Algebra

Miscellaneous

Modular Forms

Notebook

Number Theory

Optional Packages

Packages

Solaris