Talk:Lower envelope
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[edit]It seems that the word "envelope" (lower envelope, convex envelope, etc) is usually used in the context of families of functions, not of a finite number of them (see for example Aliprantis and Border, Stromberg, Choquet, etc). That's why I think it would be useful to slightly rewrite the article to emphasize "lower envelope"/"pointwise infimum" of a family of functions, and then mention the special case of a finite number of functions, where it becomes "pointwise minimum".
Also when I first saw the title of the article, I thought "where is the article about upper envelope?". It would probably be better to rename the article "Lower and upper envelope" and have redirects for each of lower and upper envelope. What do you think? PatrickR2 (talk) 02:47, 19 November 2021 (UTC)
- You seem to have left off an important qualifier for your "usually": by people who are not computational geometers. For people who are computational geometers, it is the finite families that are usually of interest. Given that half of the current two references are from computational geometry, I think that might be relevant. —David Eppstein (talk) 07:33, 19 November 2021 (UTC)
- I did not realize this was mainly in the context of computational geometry. Fair enough then, although some words to that effect could be useful. PatrickR2 (talk) 22:52, 19 November 2021 (UTC)
- I'm not sure "mainly" is the right word; certainly lower envelopes of the infinite kind have significant contributions that are not computational. (It may be relevant to note that the use of Davenport–Schinzel sequences, later prevalent in computational geometry as a way of analyzing the combinatorial complexity of finite lower envelopes, actually originally came from a very non-discrete part of mathematics, the study of differential equations.) Anyway, as for whether it should be "lower and upper" in the article title: Upper set chooses one rather than having both. Infimum and supremum has both in the title, as does Maxima and minima. I think it could go either way, as long as we're clear that there should be only one article, rather than trying to have a separate upper envelope article. —David Eppstein (talk) 23:39, 19 November 2021 (UTC)
- Agree completely about having a single article. PatrickR2 (talk) 00:56, 20 November 2021 (UTC)
- I'm not sure "mainly" is the right word; certainly lower envelopes of the infinite kind have significant contributions that are not computational. (It may be relevant to note that the use of Davenport–Schinzel sequences, later prevalent in computational geometry as a way of analyzing the combinatorial complexity of finite lower envelopes, actually originally came from a very non-discrete part of mathematics, the study of differential equations.) Anyway, as for whether it should be "lower and upper" in the article title: Upper set chooses one rather than having both. Infimum and supremum has both in the title, as does Maxima and minima. I think it could go either way, as long as we're clear that there should be only one article, rather than trying to have a separate upper envelope article. —David Eppstein (talk) 23:39, 19 November 2021 (UTC)
- I did not realize this was mainly in the context of computational geometry. Fair enough then, although some words to that effect could be useful. PatrickR2 (talk) 22:52, 19 November 2021 (UTC)