Talk:Euler's totient function/Archive 1: Difference between revisions

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:The TeX version is an uppercase [[phi (letter)|phi]], &Phi;. The lowercase phi can also be generated, <code>\varphi</code> <math>\varphi</math>. There are HTML-versions for both uppercase and lowercase phis too, <code>&amp;Phi;</code> &Phi; and <code>&amp;phi;</code> &phi;. I don't know for sure but I think the uppercase phi is the "official" symbol used to denote the Euler's totient function and thus that should be used. Currently all articles I have seen referring to this article unfortunately use the lowercase phi. But of course it would be simple to convert them into uppercase phis if so is agreed. --[[User:ZeroOne|ZeroOne]] (<small>[[User talk:ZeroOne|talk]]</small>&nbsp;|&nbsp;<small>[[Special:Emailuser/ZeroOne|@]]</small>) 17:33, 2 November 2006 (UTC)

::The TeX <ttcode>\phi</ttcode> is ''not'' an uppercase phi; <ttcode>\Phi</ttcode> is. Both <ttcode>\phi</ttcode> and <ttcode>\varphi</ttcode> denote a lowercase phi, just differently styled. [[User:Fredrik|Fredrik Johansson]] 17:40, 2 November 2006 (UTC)

:::Confusing. Uppercase TeX phi: <math>\Phi</math>. So you are saying that Euler's totient function should be denoted with a lowercase phi, then? --[[User:ZeroOne|ZeroOne]] (<small>[[User talk:ZeroOne|talk]]</small>&nbsp;|&nbsp;<small>[[Special:Emailuser/ZeroOne|@]]</small>) 18:37, 2 November 2006 (UTC)

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here we saw that 0 < k < 5 <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Yourskadhir|Yourskadhir]] ([[User talk:Yourskadhir|talk]] • [[Special:Contributions/Yourskadhir|contribs]]) 06:29, 5 March 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:Even if this were accurate and sourced, it still wouldn't seem helpful. — [[User:Arthur Rubin|Arthur Rubin]] [[User talk:Arthur Rubin|(talk)]] 01:56, 11 March 2015 (UTC)

==The name of the function==

I am an American number theorist, and I cannot find a single book in my shelves that calls the Euler phi function the "totient" or "Euler totient" function. It is in all cases referred to as the Euler phi function. I think for a function as well-used as this one, especially by undergraduates, we should use standard terminology. It is hard to cite all the references -- please look at any number theory book on your shelf. I am curious about what other readers think.[[User:Jaatex|Jaatex]] ([[User talk:Jaatex|talk]]) 19:19, 11 April 2015 (UTC)

I am an American number theorist, and in no reference on my shelf is the Euler phi function called the totient function or the Euler totient function. With a function as well-used as this, especially by undergraduates, shouldn't we use the standard name? I'm curious how others feel. [[User:Jaatex|Jaatex]] ([[User talk:Jaatex|talk]]) 19:27, 11 April 2015 (UTC)

: I am also a number theorist, and have very often heard the phi function called the "totient function", or "Euler totient function". The term was apparently invented by Sylvester. It is mentioned by Niven and Zuckerman (3rd edition, p.22). In the "Handbook of estimates in the theory of numbers" (B. Spearman, K.S. Williams, Carleton Mathematical Lecture Note 14, 1975), on the definition p. 4, phi is called "Euler's totient function". If you search on MathSciNet, you will find that the number of articles containing in their titles "Euler totient function" is 34 (73 for "Euler phi function"), and that the number of referee's reports citing "Euler totient function" is 386 (225 for "Euler phi function"). (Searching for just "totient function" is misleading: there are many other totient functions). [[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 20:57, 11 April 2015 (UTC)

::Thanks for the research. As you found, two-to-one in titles it is referred to as the Euler phi function. My bookshelf research: Ireland and Rosen, "A Classical Introduction to Modern Number Theory" and Pierre Samuel (translated from French), "Algebraic Theory of Numbers"; Kenneth H. Rosen "Elementary Number Theory"; Joseph H. Silverman, "Number Theory"; David M. Burton, "Elementary Number Theory" (the only reference where "totient" is mentioned: "The function \phi is usually called the \it {Euler phi-function} (sometimes, the \it indicator or \it totient)"); Serge Lang, "Algebra"; and "Andre Weil, "Number Theory, An approach through history...". In the above references, totient is neither in the index nor the text (except as noted in Burton, where it is not in the index). I understand that totient function terminology is sometimes used, and that it is historical. My point is that it is not commonly used. If a student tries to look up the totient function in a standard text, they will find nothing. I'm not sure why totient was chosen for the title of this article. I would like to change it to the more common name. [[User:Jaatex|Jaatex]] ([[User talk:Jaatex|talk]]) 14:39, 15 April 2015 (UTC)

:::In the past, this page was named "Euler's phi function". It is not clear when the name has changed, but the first line has been changed in 2003, apparently without any discussion, by this edit [https://en.wikipedia.org/w/index.php?title=Euler%27s_totient_function&diff=613055&oldid=604106]. In any case, as both [[Phi function]] and [[Euler's phi function]] redirect to this article, the reader searching for this article will find it easily. Personally, I have no opinion on the best title nor for the name that should be used in the article (as far as both names appear in the first sentence). [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 15:23, 15 April 2015 (UTC)

::::Thank you for this information. This is my first attempt to edit a Wikipedia page. I see the edit from 2003, thanks for pointing it out. I do not see why the change was made. How was the change made without discussion? How does one go about getting it changed back? Do people vote? :-) [[User:Jaatex|Jaatex]] ([[User talk:Jaatex|talk]]) 15:54, 15 April 2015 (UTC)

:::::In Wikipedia, decisions are taken by consensus, as described in details in [[WP:CON]]. However, few people have given their opinion. One could start a [[WP:request for comments]]. But, as nobody disagrees formally with you, and your arguments are convincing, I have self-reverted my revert of your edits. The change of title (called [[WP:moving a page|move]] in WP) seems less important than editing the content, because the title you suggest exists as a [[WP:redirect]]. For technical reasons, it may be done (in this case) only through a [[WP:move request]]. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 19:12, 15 April 2015 (UTC)

== Totient numbers ==

This section contains {{tq|there are infinitely many nontotients, and indeed every odd number has an even multiple which is a nontotient}}, the word "even" being added by a recent edit. In both versions, this sentence is a nonsense, as every odd number greater than 1 is a nontotient; thus no need to consider multiples. I guess that the correct assertion should be {{tq|every totient has a multiple (by an odd number) that is a nontotient}}. However this needs to be checked on the source. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 09:59, 25 April 2015 (UTC)

: As you say, odd numbers greater than 1 are trivially nontotients, so what is of interest is the existence of even nontotients. I imagine the previous writer meant "there are infinitely many even nontotients, and indeed..." but just forgot the "even". I've checked the paper and in fact it proves that any number (even or odd) has a multiple which is a nontotient. If n is odd then the nontotient multiple of 2n gives an even nontotient multiple of n, so this is equivalent to saying any number has an even nontotient multiple. I'll make those changes. [[User:Especially Lime|Especially Lime]] ([[User talk:Especially Lime|talk]]) 08:54, 20 May 2016 (UTC)

== Unexplained revert of style improvement ==

My edit in [[Euler's totient function#Euler's product formula]] has been reverted by an IP user, without any explanation. My edit consisted in

*Removing, per [[MOS:HEADINGS]] the redundant reference (through a formula) to the article title.

*Replacing a heading consisting of a technical formula by a less technical phrase (the formula was redundant, as reproduced in the body

*Avoiding the confusing term "modulo-and-coprime", which is nowhere defined in Wikipedia

*Linking [[coprime]]

All are style improvements that does affect in any way the content of the article. As I cannot find any valid reason for rejecting these edits, I have restored them. Please, if I have missed something, please discuss here before a second revert. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 15:52, 13 January 2017 (UTC)