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$\begingroup$ Thanks for reminding me of Penros & Rindler. Will have a look later. For the graphical notation, the shuffle product would need an extra graphical widget. The problem with it is: How to notate a variable amount of stuff, e.g. drawing n derivatives (not just 3). --- I found a PDF file of Noll's book. It is impossible to browse with all the fancy names and notation and no linked index. And I haven't even found the table of contents. Anyhow, methinks it has not more to offer than plain readable Serge Lang. Next time in the library I'll browse a plain paper copy. :-) Alas the library is far... $\endgroup$

Martin Gisser
– Martin Gisser

2015-10-20 22:24:07 +00:00
Commented Oct 20, 2015 at 22:24
$\begingroup$ Noll's is probably the nicest coordinate free approach, has some significant innovations. (Altho one can as well use abstract indices diagrammatically and put a circle around a set of operations with a line coming from it, index N next to it saying how many such lines, each being everything in that circle, and operate with them as usual, to define theorems recursively.) $\endgroup$

Gottfried William
– Gottfried William

2015-10-20 23:41:33 +00:00
Commented Oct 20, 2015 at 23:41
$\begingroup$ Noll 1987 has three detailed indices. One general, another for theorems, and one more for each piece of notation, the various functors. (Pp. 376-393). I'd suggest printing the book. The one on Carnegie Mellon's website is missing the table of contents ... but exist pdfs scans online on `elsewhere' without anything missing. Btw, Noll, W & Chiou, S. 1995. Geometry of differentiable manifolds, chapter 4, section 41, is relevant too but it was not published, only math.cmu.edu/~wn0g/book4.pdf. $\endgroup$

Gottfried William
– Gottfried William

2015-10-21 00:00:12 +00:00
Commented Oct 21, 2015 at 0:00
$\begingroup$ Looks like Noll represents the paradigmatic anti-antithesis (sic) to the "debauch of indices", the "debauch of formalism". This is not what I intend with the primacy of the total product rule. My mind refuses to waste most of its meagre IQ with such a huge tangle of garlands around what is the plain calculus product rule. Maybe that's why it took a dimwit like me to discover the plain proof of the general Leibnz formula... I have caught masters not seeing the product rule for the forest of formalism. --- I am now sufficiently sure that nobody else (except Gavrilov) has ever seen the formula. $\endgroup$

Martin Gisser
– Martin Gisser

2015-10-22 18:43:54 +00:00
Commented Oct 22, 2015 at 18:43
$\begingroup$ Have you considered getting Gavrilov to coauthor with you a semiexpository article in an MAA or AMS journal that publishes those? One way to get more people interested in it. Compare it with another approach in two pages and it'll certainly get published again. $\endgroup$

Gottfried William
– Gottfried William

2015-10-23 20:09:11 +00:00
Commented Oct 23, 2015 at 20:09

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