GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content. TeXmacs can also be used as an interface to many external systems for computer algebra, numerical analysis, and statistics. New presentation styles can be written by the user and new features can be added to the editor using Scheme.
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. It provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.
Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Theano features tight integration with numpy, transparent use of a GPU, efficient symbolic differentiation, speed and stability optimizations, dynamic C code generation, and extensive unit-testing and self-verification. Theano has been powering large-scale computationally intensive scientific investigations since 2007. But it is also approachable enough to be used in the classroom (IFT6266 at the University of Montreal).
Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. Integer, floating point, and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Various matrix decompositions are provided through optional integration with LAPACK and ATLAS libraries. A delayed evaluation approach, based on template meta-programming, is used (during compile time) to combine several operations into one and reduce or eliminate the need for temporaries.
TRIP is a general computer algebra system dedicated to celestial mechanics. It includes a numerical kernel and has interfaces to gnuplot and xmgrace. Computations can be performed with double, quadruple, or multi-precision. Users can dynamically load external libraries written in C, C++, or Fortran. Parallel computations on multivariate polynomials can be performed.
The Java Penrose Empires Package allows you to compute the empires (forced tiles) for an arbitrary initial patch of tiles. Tilings may be saved for later, and may be exported to PDF, EPS, or PNG. This software represents a new method of computing forced tiles. Rather than using a "growth" approach (where some tiles are randomly forced), this system only shows the forced tiles in the system, leaving all unforced areas blank.