Talk:Levi-Civita symbol

Too sloppy

This is much too superficial: A symbol is not the same as a tensor. This obscures a very simple abbreviation. --Peter Schmitt 01:40, 2 January 2011 (UTC)

I've modified the wording slightly, and introduced a sub-heading. According to the cited sources, the Levi-Civita symbol also is used to denote the alternating tensor or the completely antisymmetric tensor with three indices in three dimensions. Does the rewording meet your approval? John R. Brews 17:29, 2 January 2011 (UTC)

Though the L-C symbol and the L-C tensor are closely related, I think that the advanced topic (tensor) and the elementary one (symbol) should be treated separately. Thus I moved the tensor part.

By the way, common notions (that appear in many sources) need no reference, I would say.

--Peter Schmitt 00:13, 3 January 2011 (UTC)

I've rearranged the text a bit; no changes in content. I filled in some entries on the meta page and added a reference or two. John R. Brews 04:27, 3 January 2011 (UTC)

Applications

This article could benefit from some examples and applications. John R. Brews 15:55, 3 January 2011 (UTC)

Cyclic order

Cyclic order is a common (elementary) concept. References are not intended to provide such explanations. The right place to explain concepts are pages devoted to these concepts. And they need no cited source, either. --Peter Schmitt 00:07, 4 January 2011 (UTC)

References

Basic (common) facts and terms need no source in CZ. (A single, randomly selected source does not prove that it is commonly used, either.) Therefore I removed your reference. --Peter Schmitt 00:57, 4 January 2011 (UTC)

Explanatory footnote

Repeated from Peter Schmitt's Talk page:

As for the footnote on the sign of permutations: Either leave it unexplained, or explain it (briefly) in the text. (I agree with the cited guidelines.) --Peter Schmitt 01:19, 5 January 2011 (UTC)

Peter: According to CZ:Article_Mechanics_Complete#References "An informational note may be included as a reference in order to make important clarifications of the text, when including the clarification in the text itself would break the flow of the discussion." I'd say this footnote falls under this provision. John R. Brews 04:28, 5 January 2011 (UTC)

John, I don't claim that such footnotes are banned. But I think they should be avoided where easily possible.

Why do you think that a footnote is better than an inline explanation? (If the explanation is needed at all.)

In this case, it would not hurt to omit the explanation because whoever knows about even and odd permutations will also know about the sign of a permutation, and vice-versa. Who does not know the terms will have to read about permutations.

--Peter Schmitt 19:09, 5 January 2011 (UTC)

I'd guess that when the article on permutations is written, a link to that article would suffice. But in the meantime, and even after, a parenthetic explanation is helpful to some readers. This whole article on the Levi-Civita symbol arose in just this way: it was red-linked all over the place for a long time and no-one wanted to write a page about it. It's like eating popcorn, eh? One bite leads to the next and so on and so on. John R. Brews 19:33, 5 January 2011 (UTC)

Bibliography

Sorry, John, I do not agree with your bibliographic items. It may be nitpicking, but ...

The McCurdy book (for cyclic order) is from the 19th century (not necessarily bad!) but seems not be available online (only as a commercial reprint). Why recommend it? I wouldn't mention it even for cyclic order. But for the Levi-Civita symbol? Cyclic order is not an issue here -- it is only used for 3 indices, a case that more easily can be dealt with by direct enumeration. Why bother those who do not know what cylcic order is?

The numbers and symmetry book is also not available online. It is one of dozens (hundreds) of books that contain some section on permutations. I don't know it, but I checked its review and I doubt that it is to be recommended for permutations. (They are only a side issue!) Why cite it here? For this issue any readily available book treating permutations can be used.

A reader interested in the sign of a permutation should look at permutation group and literature recommended there.

--Peter Schmitt 19:36, 5 January 2011 (UTC)