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Do you have a Physics background by any chance? Anyway, I believe the module might be named after the mathematician, not the number system called after the same
by contravariant 6y ago
Do you have a Physics background by any chance? Anyway, I believe the module might be named after the mathematician, not the number system called after the same mathematician.
Regardless the name Grassman is tied to exterior algebras (and therefore geometric algebras), which are implemented by this library and which can be used to solve matrix equations (although I couldn't recommend using the geometric algebra approach for higher dimensions, unless you can do so symbolically).
- deltasquared 6y agoI do have a bit of physics in my background. I read about Grassmann recently in a game programming book. Foundations of game engine development Volume 1 By Eric Lengyel ends with a nice explanation of Grassmann algebra. The road to reality by Roger Penrose also has a treatment of Grassmann algebra in physics context. I agree the library is likely a reference to the mathematician.
- contravariant 6y agoInteresting. Yeah it's nothing too important it's just that I've only ever seen physicists use Grassman numbers, whereas mathematicians tend to work with the exterior algebra directly (which works in much the same way except the wedge operator is used explicitly, IMHO this makes things clearer).
- DreamScatter 6y agoGrassmann algebra and exterior algebra are the same thing, regardless of whether a mathematician or physicist uses them.
- contravariant 6y agoSure, but the Grassman numbers are a bit of an odd model of Grassman algebra with its own notation. They live in some anonymous vector space that is effectively defined in terms of the Grassman numbers, whereas mathematicians usually have some vector space they're interested in and construct an exterior algebra from its elements. The differences are minor but they're two clearly distinct approaches. Like I said it's nothing terribly important but it's still an interesting difference.
- deltasquared 6y agoI agree, the subtle difference between the physics and math mindset is interesting. I wound up on the sidelines as a computer scientist who worked in a physics lab.