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Rewrite of Section 12
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A short working note by Phil dated 2.25.12, part of the support files for his tensor document on curvilinear systems. He concludes that C = curl B is a vector density of weight -1, so C = J^-1 Σ C'n en, and edits Section 12 by replacing C'n with J^-1 C'n. No results change. He defers an alternative curl derivation and a similar edit of the vector Laplacian section; the rewrite was installed into the main document.
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Rewrite of Section 12 PhL 2.25.12
I am today convinced that C = curl B is a vector density of weight -1, and this means that Section 12 has to be edited somewhat. The main implication is that, for such a vector (see "expansions of tensor..")
C = J-1 ΣnC'nen for C = curlB
where we have a new J-1 factor sitting there. So I will copy the whole section here and try to edit it.
Log of comments and changes. Well, I did the whole thing with a few comments in red. Luckily not a single result changes!! It went pretty fast. Basically all I had to do was replace C'n → J-1 C'n everywhere it appeared, and all changes cancelled out.
I think nowadays I could do an "alternative" derivation of the curl in an added section, as I did with the divergence. I will add this at some point, but don't want the huge digression it would require right now. Save it.
I think an edit of the vector Laplacian section will be similar to what I have done here. I put that off as well.
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the rewrite that was right here has now been installed into tensor doc.