Numerical Computing with Sage¶
This document is designed to introduce the reader to the tools in Sage that are useful for doing numerical computation. By numerical computation we essentially mean machine precision floating point computations. In particular, things such as optimization, numerical linear algebra, solving ODE’s/PDE’s numerically, etc. or the first part of this document the reader is only assumed to be familiar with Python/Sage. In the second section on using compiled code, the computational prerequisites increase and I assume the reader is comfortable with writing programs in C or Fortran. The third section is on mpi and parallel programming and only requires knowledge of Python, though familiarity with mpi would be helpful. Finally the last section is about 3d visualization in Sage.
In the current version of this document the reader is assumed to be familiar with the techniques of numerical analysis. The goal of this document is not to teach you numerical analysis, but to explain how to express your ideas in Sage and Python. Also this document is not meant to be comprehensive. Instead the goal is to be a road map and orient the reader to the packages relevant to numerical computation and to where they can find more information.