Initially, Grassmann.jl and Cartan.jl introduced the DirectSum formalism into computational language design for differential geometric algebra, thus enabling the construction of custom algebras through metaprogramming.Grassmann.jl pioneered a novel type system design along with its syntax and semantics, which has undergone significant refinement through many years of development and continuous improvement.Cartan.jl represents a groundbreaking extension of capabilities offered by Grassmann.jl, marking a pioneering fully realized implementation of numerical differential geometric algebra, based on TensorField representations over a FrameBundle and the ImmersedTopology of the FiberBundle.Grassmann.jl and Cartan.jl build on Julia's multiple dispatch and metaprogramming capabilities, presenting a new computational language design approach to interfacing with differential geometric algebra based on a new sector integral theorem.This pioneering design not only actualizes but also elevates computational language syntax to new heights using the foundations of Grassmann.jl and Cartan.jl.The Grassmann.jl and Cartan.jl packages introduce pioneering computational language designs, having inspired imitation projects and thereby validating the project's relevance as significant advance in computational mathematics.