|
|
|
|
|
|
by halma
3409 days ago
|
|
|
I remember this and other tricks are implemented in Gaigen (a code generator for geometric algebra). 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/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. |
|
|