I remember this and other tricks are implemented in Gaigen (a code generator for geometric algebra). https://sourceforge.net/projects/g25/?source=directory htt

I remember this and other tricks are implemented in Gaigen (a code generator for geometric algebra). https://sourceforge.net/projects/g25/?source=directory https://sourceforge.net/projects/g25/?source=directory The XOR trick is close to slide 16 of http://www.science.uva.nl/research/ias/ga/gaigen/files/20020219_talk.pdf http://www.science.uva.nl/research/ias/ga/gaigen/files/20020... ... How to compute the geometric product of unit orthogonal basis blades (3/3) If we represent each basis vector with a specific bit in a binary number (e1 = 001b, e2 = 010b, e3 = 100b), computing the geometric product of basis blades is exactly the xor operation on binary numbers! (e1^e2)(e2^e3) = e1^e3 011b xor 110b = 101b We have to take care of the signs though: - basis vectors have to be rearranged into a specific order before they can annihilate each other (this rearranging causes a sign change in the result). This can also be computed binary. - signature of annihilated basis vectors can change the sign as well.