Sage 3.2.1 Release Tour

Sage 3.2.1 was released on December FIXME, 2008. For the official, comprehensive release notes, see sage-3.2.1.txt.

Algebra

• Division over integers (Robert Bradshaw) -- A much simpler and faster algorithm for the divisors function over integers. The new optimized code is faster than a similar integer divisor function in the version of PARI/GP that's bundled with Sage 3.2.1, as well as outperforming a similar integer divisor function found in the version of Magma that Sage 3.2.1 interfaces with.
• Finite field operations (John Palmieri) -- A few methods for finite field elements including additive order, p-th power, and p-th root where p is the characteristic of the field.

Basic arithmetic

• Polynomials over a field (Burcin Erocal) -- Improving the user interface of polynomial classes.
• Polynomial square roots (John Palmieri, Carl Witty) -- A method to test whether a polynomial is square over the field it is defined. If the polynomial is square, then the method has the option of returning a square root.

Build

• Problematic CPU flags (William Stein, Michael Abshoff) -- Binary distributions of Sage for Linux (e.g. Ubuntu) may not work properly once installed. The following CPU flags are known to prevent Sage from running properly: sse, 3d, mmx, pni, and cmov.

Calculus

• Gamma and factorial functions (Mike Hansen, Burcin Erocal, Wilfried Huss) -- Symbolic gamma and factorial functions.

• Update to sympy-0.6.3 (Ondrej Certik) -- Update to the latest upstream of SymPy (sympy-0.6.3), which is a Python library for symbolic mathematics. For more information about SymPy, please visit http://code.google.com/p/sympy/.

• Numerical trigonometry (Robert Bradshaw) -- Optimized floating point evaluation of trigonometric functions such as sine and cosine. For example, numerical calculation of sine via _fast_float_ is now twice as fast as math.sin.

Combinatorics

• Coding theory (David Joyner) -- Several changes in linear_codes.py which should speed up (and in some cases do:-) some coding theory computations considerably. It adds interfaces to Cython and C functions of Robert Miller, CJ Tjhal, and Jeffery Leon. Speed up of minimum_distance (for codes over GF(2) and GF(3)), the spectrum (=weight_distribution), and permutation_automorphism_group are expected and in most cases achieved. (Also a new function is_permutation_equivalent was added, which interfaces with Robert Miller's double coset partition refinement code.)
• Incidence structures and block designs (David Joyner) -- Beginning of an incidence structure class and an implementation of some basic block design algorithms. A few functions require GAP's Design package (which is included in gap_packages-4.4.10_6.spkg) but calling GAP or GAP's Design was only done when the corresponding Sage functionality was missing. Robert Miller's recent code on computing the automorphism group of a non-linear binary code was used to implement the automorphism group of a block design.