Talk:Geometric algebra: Difference between revisions
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:Put differently: all of the implementations here which I have inspected use index 0 to represent the "scalar part" of the "multivector". However, the scalar part of the multivector is not orthogonal to the elements of the orthogonal basis. Specifically, in these implementations, e(0) here corresponds to index 1 of the multivector, e(1) corresponds to index 2 of the multivector, e(2) corresponds to index 4 of the multivector, e(3) corresponds to index 8 of the multivector and e(4) corresponds to index 16 of the multivector. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 17:14, 19 October 2015 (UTC) |
:Put differently: all of the implementations here which I have inspected use index 0 to represent the "scalar part" of the "multivector". However, the scalar part of the multivector is not orthogonal to the elements of the orthogonal basis. Specifically, in these implementations, e(0) here corresponds to index 1 of the multivector, e(1) corresponds to index 2 of the multivector, e(2) corresponds to index 4 of the multivector, e(3) corresponds to index 8 of the multivector and e(4) corresponds to index 16 of the multivector. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 17:14, 19 October 2015 (UTC) |
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== This task is a mess == |
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I'm considering going back to verifying the axioms. I would add a verification that <math>\mathcal{V}</math> is of dimension at least 5, though. That should prevent implementations of trivial algebras and re-use of the quaternion. |
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In order to verify the contraction rule, I would require the test to be done on a large number of random vectors. |
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Possibly also displaying the multiplication table, as in the echolisp solution. |
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--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 14:54, 21 October 2015 (UTC) |
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