At its core is a carefully tuned implementation of Grobner basis methods for manipulating systems of polynomial equations. Macaulay 2 - A new software system devoted to supporting research in algebraic geometry and commutative algebra. Mathscribe - Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included. MuPAD - Free, Open Source computer algebra system for symbolic and numerical computations.
Library routines for linear algebra, integration, polynomials, graphics and more.
Can generate and be called from C or Fortran code. Started in 1989 and used worldwide. Over 20 years old. Comes with full source code. Free download, documentation.