Vector products: Difference between revisions
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=={{header|J}}== |
=={{header|J}}== |
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Perhaps the most straightforward definition for cross product in J uses rotate multiple and subtract: |
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Based on [[j:Essays/Complete Tensor]]: |
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<lang j>cross=: (1&|.@[ * 2&|.@]) - 2&|.@[ * 1&|.@]</lang> |
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However, there are other valid approaches. For example, a "generalized approach" based on [[j:Essays/Complete Tensor]]: |
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<lang j>CT=: C.!.2 @ (#:i.) @ $~ |
<lang j>CT=: C.!.2 @ (#:i.) @ $~ |
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ip=: +/ .* NB. inner product |
ip=: +/ .* NB. inner product |
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cross=: ] ip CT@#@[ ip [</lang> |
cross=: ] ip CT@#@[ ip [</lang> |
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Note that there are a variety of other generalizations have cross products as a part of what they do. |
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An alternative definition for cross (based on finding the determinant of a 3 by 3 matrix where one row is unit vectors) could be: |
An alternative definition for cross (based on finding the determinant of a 3 by 3 matrix where one row is unit vectors) could be: |
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<lang j>cross=: [: > [: -&.>/ .(*&.>) (<"1=i.3) , ,:&:(<"0)</lang> |
<lang j>cross=: [: > [: -&.>/ .(*&.>) (<"1=i.3) , ,:&:(<"0)</lang> |
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