By: deleva (deleva) - 2007-05-30 03:05 |
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https://www.euclideanspace.com/maths/algebra/clifford/d3/arithmetic/index.htm#calc The calculator does not seem to perform correctly a simple geometric product ab where a and b are orthogonal(which should be numerically equivalent to an outer product a ^ b and to a cross product a x b). The calculator gives ab = - a x b. However, every book and web page that I have seen agree that (a x b) * e123 = a ^ b, which means that the coefficients c1 c2 c3 of a x b = c are the same as the coefficients d23 d31 d12 of a ^ b = d because e1 * e123 = e23 e2 * e123 = e31 e3 * e123 = e12 Do you agree? Paolo |
By: Martin Baker (martinbaker  ) - 2007-06-15 01:34 |
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Paolo, Yes I agree, I tried it myself and got, e1 * e2 = -e12 I'll correct it to agree with the multiplication table on the same page: e1 * e2 = e12 Thanks very much for pointing this out I'll correct it as soon as I can. Cheers, Martin |
By: Martin Baker (martinbaker ) - 2007-06-18 11:03 |
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Paolo, I've fixed it, it took me a while as some of the 'a' and 'b' operands were reversed, both in the javascript and some of the web page content. Hopefully its all correct now, I've tested it as much as I can, but if anyone else would like to try it please let me know what you find. Thanks again for letting me know about this. Martin |
