# Sage 3.2 Release Tour

Sage 3.2 was released on November 20th, 2008. For the official, comprehensive release notes, see the HISTORY.txt file that comes with the release. For the latest changes see sage-3.2.txt.

## Subspace generation

Robert Miller: generate all subspaces of a vector space/projective space

## New Symbolics

William Stein, Burcin Erocal: high level integration of pynac into Sage

## General group algebras class

David Loeffler: general group algebras class

## Elliptic Curve Doctesting

Paul Zimmermann: much improved elliptic curve doctests and some bug fixes

## Modular Forms

Craig Citro: huge number of small fixes to modular forms code. David Loeffler: eta product modular functions. Craig Citro: massively speed up Victor Miller basis code.

## Magma Interface

William Stein: much improved Magma interface with 100% doctests

## Generalized Bernoulli Numbers

William Stein: massively optimized generalized Bernoulli numbers

## Modular Composition

Martin Albrecht, Paul Zimmermann: improve modular composition in GF(2)[x]

## Polyhedral Improvements

Marshall Hampton: Schlegel diagrams, standard polytopes, multiplication, polars

## Notebook

Timothy Clemans: notebook templatization work

## Sage Build

William Stein: make it so "sage -br" does the cythonization in parallel using pyprocessing. Robert Bradshaw, Gonzalo Tonaria, Craig Citro: massively cleaned up and faster setup.py. Robert Bradshaw: update to Cython 0.10.

## libSingular

Simon King, Martin Albrecht: fix memory leaks in libsingular's reduce()

## Numerical Linear Algebra

Jason Grout: make numpy the backend for matrices over CDF and RDF

## Graph Theory

Jason Grout: much more robust planarity testing code for graphs