Yes, in fact there already is such a formalism: http://faculty.luther.edu/~macdonal/ http://faculty.luther.edu/~macdonal/ From the first page: "Geometric alge

Yes, in fact there already is such a formalism: http://faculty.luther.edu/~macdonal/ http://faculty.luther.edu/~macdonal/ From the first page: "Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering."