GATL: Geometric Algebra Template Library. GATL is a C++ library for Euclidean, homogeneous/projective, Mikowski/spacetime, conformal, and arbitrary geometric algebras. Geometric algebra is a powerful mathematical system encompassing many mathematical concepts (e.g., complex numbers, quaternions algebra, Grassmann-Cayley algebra, and Plücker coordinates) under the same framework. Geometric algebra is mainly based on the algebraic system called Clifford algebra, but with a strong emphasis on geometric interpretation. In geometric algebra, subspaces are treated as primitives for computation. As such, it is an appropriate mathematical tool for modeling and solving geometric problems in physics, chemistry, engineering, and computer science. GATL uses template meta-programming to implement the lazy evaluation strategy. This way, GATL is capable of performing some optimizations on the program at compile time. In other words, GATL is designed to automatically execute low-level algebraic manipulation in the procedures described by the users with geometric algebra operations, leading to more efficient programs.

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