We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

中文翻译：

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射影几何代数作为共形几何代数的子代数

我们证明，如果在数学上正确的意义上，如果射影几何代数（PGA），即具有简并签名（n，0，1）的几何代数被理解为共形几何代数（CGA）的子代数，则平面图元共享相同的在PGA和CGA中具有代表性。特别是，我们在CGA框架中对待PGA中的对偶性。这导致PGA和CGA原语的统一，这对于软件实现和符号计算尤其重要。