Tag: linear algebra
Few days ago I decided to create a C++ implementation of the Simplex algorithm, which is a tool for solving Linear Programming problems. One of my motivations could have been my recent encounter with the Eigen linear algebra library, which really surprised me with its beautiful syntax and easy usage. So I wanted to gain a little experience with Eigen, although some factorization-related project might have suited this purpose better. Another motivational factor was a not yet published project of mine, which might get finished in 1 or 2 months, and would give LP a real application.
This post features two examples of algebraic manipulation and their relation to the symmetry of the matrices representing the expressions. The algebraic expressions we investigate are quadratic, multivariate and can be written in the matrix form:
Making matrix representations of graphs always takes a lot of time. For practicing algebraic or spectral graph theory on computer algebra systems, one has to create a lot of graphs. A handy tool can make this easy, which allows to draw graphs and generate code e.g. for Maple with one click. Well I couldn’t find a tool like that, so I made one on the weekend in C#. With it, you can draw custom graphs, including: arbitrary loops, parallel edges, directed edges, etc. and can generate code for these computer algebra systems: Maple, MATLAB, Maxima. Then the code can be