So Gene, you've given us a nice description of how to compute the
complement for arbitrary dimension and grade. Now how about the wedge
product between pairs of multivectors of arbitrary dimension (and
possibly different) grades? Graham, feel free to chime in here too. :-)
... Thanks very much for these. Please don't be offended by my attempts to translate some parts in a way that I imagine might be more easily comprehended by...
So Gene, you've given us a nice description of how to compute the complement for arbitrary dimension and grade. Now how about the wedge product between pairs...
... Certainly, to find the wedge product of two wedgies x an y: Initialize the result to the empty wedgie. Take every distinct basis element of x in turn (by...
That's great Graham. I think I get it now. Let me try feeding it back in a different way so you can tell me if I've got it right, and so others may have...
... Thanks Gene. I'll bet there were lots of mathematical nits you could have picked, with my presentation, so I really appreciate a simple response like this....
... i've already done it here: http://sonic-arts.org/dict/wedge-product.htm Gene, can you give me the rigorous mathematical definition as well? -monz...
It would be nice to have a shortcut to avoid actually doing all those index position swaps to find the sign of each product of scalars. We already have such a...
I think I've found one shortcut. But there may yet be a simpler one. Given that the indexes of the two coefficients are respectively I = {i1 i2 i3 ...} and J =...
... I think that's equivalent to the one I'm using, which I got from a group theory book. (Actually, the book gave a slightly different algorithm, presumably...
... Right, but if you use a fixed-length bitset implementation of the compound indices (e.g. 32 bits) then there's no requirement for sorting. You just OR them...
... You mean I shouldn't take your thing as Gospel just yet? ... http://tinyurl.com/wiz6 So, can we get a version of your Gospel with this rolled in? -Carl...
... Lets first take the simplest case worth considering. The wedge product of two 3-limit (2D) vectors. [a1 a2> ^ [b1 b2> The procedure is to first list every...
... Yes. Disturbing isn't it? It occurs only for all odd grades in all even dimensions (where the dimension is the index of the limiting prime). So the...
... http://www.ses.swin.edu.au/homes/browne/grassmannalgebra/book/bookpdf/ TheComplement.pdf Then the dual must not be the same thing as the Euclidean...
... complement ... it's the ... analogous to ... always ... that's easy -- in 3-dimensional space, the dual of e1^e2^e3 is 1, while the dual of 1 is -e1^e2^e3....
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