"Physicists employ a miscellaneous
assortment of mathematical tools in ways that contribute to a fragmentation of knowledge. " - David Hestenes
There does not seem to be any mention of the mathematical notation system developed by Dr. David Hestenes and known as Universal Geometric Algebra or Geometric Calculus. This seems like a major oversight to make in 2016. I found a few references to Clifford Algebra but nothing for multivectors.http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/clifford_algebra.html
"Research on the design and use of
mathematical systems provides a guide for designing a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight." D. Hesteneshttp://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
Some of the competitors are MAPLE, C++ and Java libraries, Mathematica/CLIFFORD and the no longer supported Matlab/GABLE prototype. This software usually doesn't use the notation system developed and used by Dr. Hestenes and is often confined to the narrow specialty of Clifford Algebra and quadratic forms.
Geometric Calculus Internationalhttp://erkenntnis.icu.ac.jp/gcj/gc_int.html