User talk:D.Lazard/Archive 1

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Welcome

Welcome!

Hello, D.Lazard, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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I hope you enjoy editing here and being a Wikipedian! Please sign your messages on discussion pages using four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question on this page and then place {{helpme}} before the question. Again, welcome! Wikipelli ^Talk 11:57, 26 May 2010 (UTC)

Cubic function

Hi, I reverted your edit to Cubic function. Rationale, see edit summary. If you'd like to discuss, please do so on article talk page. Cheers - DVdm (talk) 16:31, 28 October 2010 (UTC)

I have edited (in line with wp:MOS) and moved/shortened your latest contribution to the lead of the article. Please aquaint yourself with our manual of style? Thanks. DVdm (talk) 18:18, 28 October 2010 (UTC)

Gröbner basis

Gröbner writes in, §2, p72: "Das Mittel aber, die Eliminationstheorie frei von diesem Mangel aufzubauen, liefert die Idealtheorie"; afterward he defines "das erste Eliminationsideal" (p.73) and performs his study completely in terms of "Idealtheorie" (p.73). Gröbner also suggests a geometrical interpretation of a constructed ideal as an algebraic manifold (p.74), and this is as close as he comes to any vector space. The generator systems of ideals are described on the p.75-76.

Obviously, the words "Gröbner basis" do not appear in the text: Gröbner introduced them but his student Buchberger named them "Gröbner basis" in his PhD thesis where he implemented existing algorithm as an effective computer program. This fact is widely known, e.g. Buchberger has got The Paris Kanellakis Theory and Practice Award for "developing the theory of Gröbner bases into a highly effective tool in computer algebra".

Heisuke Hironaka who independently developed analogous conception for local rings has got Fields Medal.

If you do not know German - you can find the English translation of the original Gröbner's paper here:

http://www.ricam.oeaw.ac.at/Groebner-Bases-Bibliography/do_search.php?query_option1=&search_title=&search_author=813&search_type=-1&search_keywords=&search_on=0&viewoption=0 —Preceding unsigned comment added by 90.146.117.12 (talk) 12:50, 27 December 2010 (UTC)

Trigonometric tables

Hipparchus of Rhodes compiled trigonometric tables in the first century AD, so the answer to your question "Trigonometric tables in 11th century?" is "Yes, certainly." JamesBWatson (talk) 16:47, 6 November 2011 (UTC)

But do you have any source showing that 1/ Omar Khayyám did use them 2/ use them in connection with his geometric solution? I think that more credible that he intended to use his solution to build abaci, that is to compute graphically the solutions. As I am unable to source my opinion and I have not read the texts of Omar Khayyám, the best is to simply remove the assertion on trigonometric tables as unsourced. D.Lazard (talk) 17:14, 6 November 2011 (UTC)

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Algebraic geometry

Thank you for the heads-up! Tous les meilleurs voeux! Garald (talk) 10:41, 4 January 2012 (UTC)

PS. We are neighbours, aren't we? Garald (talk) 10:41, 4 January 2012 (UTC)

Possible. Je n'ai pas décrypté votre pseudo. Moi je suis à Jussieu en info (LIP6). D.Lazard (talk) 11:35, 4 January 2012 (UTC)

Je suis au DMA (ENS). Garald (talk) 14:36, 16 January 2012 (UTC)

Hello! (and a question close to flat modules)

Hi, I had not realized you were that Lazard whose flat module results I have read about. Nice to meet you! I hope you find the chance to visit the eastern US sometime. Do you happen to have the time to address some basic questions on flat modules (and their candidate dual notions)? Rschwieb (talk) 14:18, 21 January 2012 (UTC)

I am afraid that I will be of few help on flat modules: I have not worked on this subject since more than 35 years. Since then I am working on Computer algebra and specifically on Polynomial system solving and computational algebraic geometry. Sincerely. D.Lazard (talk) 15:07, 21 January 2012 (UTC)

Doh, that's too bad :( No matter, say hi anytime! Rschwieb (talk) 15:38, 21 January 2012 (UTC)

Algebraic structure

Hi, I've recently been starting changes to Algebraic structure. Some sort of distinction has arisen that I want to be clear on. The problem is that order seems both algebraic and topological to me. Here is the question I've been asking myself and the answer I've been giving myself:

• Q: A lattice can be defined algebraically, and the order structure creates a topology, which is non-algebraic. Is the nature of a lattice algebraic or non algebraic?
• A: The lattice structure is algebraic. This structure can be used to create a topology, however that will involve quantifying over subsets of the set, so the topology itself is not algebraic.

Does this seem consistent with the definition of "algebraic object" you offered earlier, where only first order logic was involved? Thanks for any feedback. Rschwieb (talk) 13:56, 2 March 2012 (UTC)

Hi, Here is my opinion, but it is essentially OR. I do not know any mathematician who has tried to define properly what is algebraic and what is not. This is probably as impossible as to define precisely the limits of a scientific area. And this changes with scientific progresses. Here are some hints for answering to your question.

• The general definition of a topology is certainly non algebraic, as it involves quantifiers on infinite subsets.
• Nevertheless, some topologies may be defined algebraically. This is the case of the topology of the rational numbers Q: The open intervals are a basis of the topology and an open interval is defined by, at most, two rationals. Similarly the notion of limit may be defined by a first order formula. This seems also true for the topology of the real numbers, but is not because the set of real numbers itself may not be defined algebraically.
• Some questions about a given topology, which is algebraically defined may not be asked by a first order formula, and are thus not algebraic. This is the cases of the completeness. But the non completeness may be proved algebraically, as "∃ an infinite sequence" may be replaced by giving explicitly an infinite sequence.

Conclusion: A topology is not an algebraic structure, but some specific topologies may be defined algebraically (I think that it is the case of that of the lattices, but I do not remember exactly this definition). When it is the case, as long as one uses only first order formulas, the introduction of the topology is only for the comfort of thinking and language, as every reasoning could be done without using topology.

By the way, I remark that the page Algebraic structure does not consider ordered sets and graphs as algebraic structures. In my opinion, they are as both are are sets equipped by a binary operation with values in {true, false] (the ordering relation or the property to be joined by an edge).

D.Lazard (talk) 16:22, 2 March 2012 (UTC)

It's strange that order would be nonalgebraic and lattices would be algebraic. Rschwieb (talk) 19:47, 2 March 2012 (UTC)

I can explain: Lattices may be defined as a structure involving only one set, while orders involve two sets (one set and the booleans). Probably the authors of algebraic structure did not have in mind the definition of "binary relation" which is standard in computer science and is not even cited in relation (mathematics): A binary relation is a bivariate boolean valued function. In fact this is the only definition which is compatible with a constructivist point of view. D.Lazard (talk) 11:17, 3 March 2012 (UTC)

Yes that seems to be the case. I just found it a little surprising! Thanks for the thoughts Rschwieb (talk) 15:08, 3 March 2012 (UTC)

hyphenation

Hi, I noticed you recently converted many instances of "noncommutative" to "non-commutative" in the article ring theory. I'm changing all of these back for two reasons.

• One is that the unhyphenated version seems to be far more common in the literature. Using mathscinet for example, "noncommutative" appears in 4367 titles and "non-commutative" in 1509. A similar 3:1 ratio arises if you use the two adjectives in the "anywhere" field. Using googlebooks in title search function, there are ~6000 hits with the hyphen, and ~16600 hits without the hyphen.
• Secondly, it seems like most article titles in wikipedia use the unhyphenated version, so it'd be nice to match them.

I did note the presence of numerous subsections using a hyphenated version, but I'm not really sure if there is some merit I am overlooking. Rschwieb (talk) 13:12, 30 March 2012 (UTC)

This is not a problem for me. The main object of my edit was to clarify the relationship between commutative algebra, algebraic geometry and number theory. Indeed the previous version presented wrongly algebraic geometry as a subfield of commutative algebra. I have inserted the hyphens because it makes reading easier and I have learned recently that, normally, non is hyphenated. But as non native English speaker, I am not sure of myself for such a question. D.Lazard (talk) 13:41, 30 March 2012 (UTC)

You definitely clarified what was there. Writing a lead for such an article must be challenging... it seems like a very broad experience is required! Rschwieb (talk) 15:04, 30 March 2012 (UTC)

Degree of a monomial

Hello! Thanks for assuming my edit on the "Monomial" page (regarding multivariate degree) was in good faith. I agree that my "this definition is seldom used" was overly strong.

That said, I suppose I meant "This definition is seldom used outside of a graduate and post-graduate context." I've done a better job of revising the page now, so as to be much more objective. Let me know what you think.

As far as original research, my justification for my claim consists of spending an hour perusing the online literature, and finding no other context for why one would define the degree of a multivariate monomial thusly. Hence my conclusion that it was most useful in the circumstances I stated. How would I cite this, given that I'm largely raising the fact that there's an absence of evidence otherwise?

71.201.199.149 (talk) 23:13, 21 April 2012 (UTC)

I think that your online research gave a biased answer, because the degree of a multivariate monomial can not be dissociate to the degree of a multivariate polynomial. Thus the usage of "degree of a monomial" is most of the time implicit. I have edited the article for explaining this. I have removed the reference to monomial ordering, because of wp:DUE, keeping it would either need to add a lot of other examples or make an artificial distinction between "degree of a monomial" and "degree of a polynomial". D.Lazard (talk) 12:23, 22 April 2012 (UTC)

Ha, I agree with you that my latest edit did place undue weight on using monomial degree for monomials only -- because I was treating its use in the polynomial case as so implicit as to be basic! Your edits, pointing out how the degree definition is used implicitly, are well-taken. I've added back in a link to the Gröbner basis page as an example of a more explicit use. I don't think it's too minority of a viewpoint so as not to be featured. Cheers. 71.201.199.149 (talk) 15:50, 22 April 2012 (UTC)

Historical revision on symbolic integration is false

The symbolic integration scheme based on the exploitation of special functions was pioneered by Maple and certainly not by Axiom, a system whose implementastion of this approach of integration came AFTER Maple. The method was shown at the MIT conference and emulated by the systems whose representatives attended the conference. TonyMath (talk) 23:04, 3 June 2012 (UTC)

To reiterate, definite integrals from special functions did exist in a limited way in systems older than Maple, like Macsyma, but the method pioneered by developers of Maple involved, for example, derivatives of special functions with respect to its parameters and providing a much more varied class of integrals. Axiom emulated the method because a couple of developers for Maple had become developers of Axiom. If you insist that the method as stated in the references was really invented earlier by developers of Macysma or Reduce, then you should provide proof with an older reference to a peer-reviewed paper. TonyMath (talk) 23:26, 3 June 2012 (UTC)

A suggestion for Diophantine approximations

It looks to me like the section Measure of the accuracy of approximations should come immediately after the introduction -- it sort of sets up the analysis in the rest of the article, and explains why in the "best approximations" we focus on the denominator q. However, there's a small amount of rewriting that would have to take place as a result (the talk of convergents is not explained until later, for example), and I'm not comfortable doing it myself. What do you think? --JBL (talk) 20:02, 1 July 2012 (UTC)

The ordering of the sections is a matter of taste. I have left "Best approximation" at the beginning for several reasons:

• It was there and I did not see why changing this.
• It is the section for which the proofs are the easiest, and WP:MOS recommend to order the sections by increasing difficulty
• Before measuring something, it is better to know it
• Section "Measure" is clearly an introduction to the sections on bounds. It would be strange if an introducing section would be followed by a section that is not introduced by irt.
• This section is used by for upper bounds (at least implicitly), but not for lower bounds. Thus, to put it just after Section "Measure" would imply to exchange the places of "upper bounds" and "lower bounds. I am not willing to proceed to such an exchange, because lower bound results are IMHO more notable and more useful for the applications to transcendence theory and Diophantine equations.

Again, this is somewhat a matter of taste. If the question is asked on the task page, and if there is a consensus for another organization of the sections, I would accept it. D.Lazard (talk) 09:27, 2 July 2012 (UTC)

(Also, another minor comment: currently three separate things are denoted by φ in the article; are there other standard or acceptable choices for any of them?) — Preceding unsigned comment added by Joel B. Lewis (talk • contribs) 20:07, 1 July 2012 (UTC)

In fact, there are only two meanings for φ: either the golden ration, for which it is a standard notation, or a unspecified function of the denominator. This is why I used \varphi for the latter (note that \varphi and φ have the same shape, which is different of that of \phi, used for the golden ratio). It is probably better to use f for an unspecified function. D.Lazard (talk) 09:27, 2 July 2012 (UTC)

Thanks for your reply! On the first point, I am happy to defer to you. On the second, I had changed \varphi to \phi yesterday because the symbol {{math|''φ''}} appeared the same as \phi on the computer I was using at the time; however, at my present computer it appears the same as (or at least similar enough to) \varphi. Any idea what could be causing this/how it can be avoided? --JBL (talk) 12:42, 2 July 2012 (UTC)

Elementary algebra GA Review

Thank you for you input to the situation, I have given you a barnstar for it. Contrary to that what you said and what I said and believe is that this article is "quickfail" since it is sourced with books and no websites and nothing can really be verified, and furthermore it sounds like a Wikiversity page and is confusing to beyond repair. If so, I will quickfail this article. Obtund^Talk 04:14, 5 August 2012 (UTC)

		The Barnstar of Diligence
		Thank you for your input to the situation, I really appreciate it. ObtundTalk 04:14, 5 August 2012 (UTC)

Credo Reference

I'm sorry to report that there were not enough accounts available for you to have one. I have you on our list though and if more become available we will notify you promptly.

We're continually working to bring resources like Credo to Wikipedia editors, and this will very hopefully not be your last opportunity to sign up for one. If you haven't already, please check out WP:HighBeam and WP:Questia, where accounts are still available. Cheers, Ocaasi 19:11, 22 August 2012 (UTC)

Reversion of "Klein 4 ring" comment

The original poster appears to have been talking about this, which is nothing like the endomorphism ring of the Klein 4 group. At any rate, the main thing I objected to was the terminology and the use of a ring without identity, so your fix seems ok. Rschwieb (talk) 14:35, 7 November 2012 (UTC)

I did not notice that. In any case the "Klein 4 ring" is a subring of the endomorphisms of the Klein 4 group: the matrices with zero second column, when the endomorphisms are represented by matrices over the field with 2 elements. D.Lazard (talk) 15:20, 7 November 2012 (UTC)

Since our convention is to favor rings with identity, and the matrix ring you describe is far easier and nicer to describe, I'm glad you used it there. At any rate, the term "Klein 4-ring" appears to have been coined by an author on Planet Math, and nowhere else: I couldn't let it stand :) Rschwieb (talk) 16:26, 7 November 2012 (UTC)

"In Galois theory,....."

Please see this edit. I don't think the phrase "In Galois theory,..." succeeds in informing the lay reader that mathematics is what the article is about. "Algebra", on the other hand is a word that everybody knows. Michael Hardy (talk) 18:25, 8 November 2012 (UTC)

I agree. In fact, I have created this stub by copying three lines I had written sometimes ago in the dab page resolvent, because this well established topic was not even mentioned in this page. Recently an aficionado of MOS:DAB has removed these lines and replaced them by links redirecting to their source. The creation of the stub was the best way to solve the problem while respecting MOS:DAB (see talk: Resolvent). As I do not like not understandable texts, I have added some details and, now, a complete definition. D.Lazard (talk) 22:15, 8 November 2012 (UTC)

(Non) speedy deletion of Mathomatic

I've replied to your message on my talk page. I hope my comments will be helpful to you. Feel free to keep in touch on this, if you like. JamesBWatson (talk) 15:18, 12 November 2012 (UTC)

Comparison of computer algebra systems

After this [1] I am inclined to think that discussion at the talk page is needed before either of you make further reverts. Deltahedron (talk) 17:29, 17 November 2012 (UTC)

OK D.Lazard (talk) 17:52, 17 November 2012 (UTC)

Terminology

I have answered your question [2] at Talk:Diophantine approximation#Terminology. In general, please don't try to conduct conversations through edit summaries: take a moment to post your question on the relevant talk page where others are more likely to see it and will find it easier to respond. Deltahedron (talk) 07:43, 18 November 2012 (UTC)

Algebraic curve

I have reverted your edit because the left superscript for the h of the homogenization was intended: A right superscript could be confusing with exponentiation, and, mainly, is not compatible with the prime of the derivative. The \mbox{} is for a correct spacing after "=" (otherwise "h" appears as an exponent of the "=". D.Lazard (talk) 11:05, 19 November 2012 (UTC)

May be correct, but if Wikipedia won't render it, it is of no use. Incompatible subscripts are better than broken but compatible tex. But I see that you've found a new markup. Great, thanks. -lethe ^{talk +} 13:13, 19 November 2012 (UTC)

Rank conditions on augmented and unaugmented matrices

For my future reference, is the following statement true regardless of the numbers of equations, independent equations, and unknowns?

A system of linear equations Ax = b is consistent if and only if the rank of the augmented matrix [A b] equals the rank of the unaugmented matrix A, and is inconsistent if and only if the rank of the augmented matrix is greater than the rank of A.

I want to put this or a corrected version into overdetermined system, underdetermined system, augmented matrix, and System of linear equations#Consistency. Duoduoduo (talk) 01:13, 22 November 2012 (UTC)

Never mind, I found it in Rank (linear algebra)#Applications. Duoduoduo (talk) 01:44, 22 November 2012 (UTC)

Möbius group is isomorphic to PGL(2,C)

I believe your reversion of my correction at Möbius transformation is wrong because your have misunderstood the notation. PGL(2,C) does indeed act on the complex projective line which has dimension 1, but it is called PGL(2,C) because it is a projection of GL(2,C). PGL(1,C) (if that notation is ever used) would be the projection of GL(1,C), and so would be the trivial group. To confirm that the Mobius group is indeed isomorphic to PGL(2,C), see the section Projective matrix representations further down in the article, or projective linear group which says "the projective linear groups therefore generalise the case PGL(2,C) of Möbius transformations (sometimes called the Möbius group), which acts on the projective line" or Google "mobius pgl" for numerous sources. Gandalf61 (talk) 16:34, 15 December 2012 (UTC)

You may be right. I have not checked on the literature, but Projective group and Fano plane use the same convention as you. I'll revert my edit. D.Lazard (talk) 18:54, 15 December 2012 (UTC)

Thank you. Gandalf61 (talk) 19:06, 15 December 2012 (UTC)

Jean-François Monteil wanted to contact D.Lazard

(84.100.243.163 (talk) 14:33, 20 December 2012 (UTC))

More spam?

Re this: did you have a look at recent Special:Contributions/Mrjohncummings? Not sure, but more of the same, it somewhat seems. Cheers - DVdm (talk) 22:34, 2 January 2013 (UTC)

Speedy deletion declined: Differential equationsof mathematical physics

Hello D.Lazard. I am just letting you know that I declined the speedy deletion of Differential equationsof mathematical physics, a page you tagged for speedy deletion, because of the following concern: Not a recently created redirect - consider WP:RfD. Thank you. — Malik Shabazz ^Talk/_Stalk 04:31, 31 January 2013 (UTC)

Projective module

Thanks for working with the recent edit I made about the diagram there involving torsion-free modules. I had asserted that the right-to-left implication was true for domains only because I was having trouble tracking down a citation for the general statement.

The most general definition of a torsion-free module that I'm aware of is this: "M is torsion-free if the following holds: for any element x of R which is not a right zero divisor, right multiplication by x is injective on M." I don't have access to Matlis' book atm, but the recent contributions make it look like Matlis uses a version of this with just regular elements.

If memory serves, I have seen definitions of "Dedekind ring" that were not necessarily domains, and I am wondering if the "torsion-free implies flat" conclusion might hold for them. Rschwieb (talk) 15:24, 3 February 2013 (UTC)

For my edit I have used WP definitions: Dedekind rings and Dedekind domains are defined as synonymous. For torsion-free modules, I have the feeling that, for the editor who has written the previous version, "torsion-free" is defined only over a domain. I believe that the same is true for many people. Therefore my "however". For Dedekind rings that are not domains, I think that the best thing is to exclude this case. This could be done by editing the figure to replace "Dedekind ring" by "Dedekind domain". But I do not know how to do that. D.Lazard (talk) 17:30, 3 February 2013 (UTC)

I think you're right. As an aside, I don't know if you enjoy any of Carl Faith's works, but in the fun book "Rings and Things" he gives such a definition (for commutative rings). I'm not saying this should be included, I just wanted to point you to where I saw it. Thanks! Rschwieb (talk) 22:41, 3 February 2013 (UTC)

N-ary associativity

Hello, D.Lazard, and thank you for your contributions!

An article you worked on N-ary associativity, appears to be directly copied from http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Associativity.html. Please take a minute to make sure that the text is freely licensed and properly attributed as a reference, otherwise the article may be deleted.

It's entirely possible that this bot made a mistake, so please feel free to remove this notice and the tag it placed on N-ary associativity if necessary. MadmanBot (talk) 21:54, 17 February 2013 (UTC)

Context

I fear that the lay reader, seeing the sentence below, will not know whether the article is about psychology, jurisprudence, chemistry, medicine, diplomacy, comparative religion, theory of banking, computer science, or tennis.

Associativity can be generalized to n-ary operations.

I've changed it so that it tells the reader at the outset that algebra is what it's about. Michael Hardy (talk) 23:35, 22 February 2013 (UTC)

I have not written this sentence. I have simply moved this paragraph from associative property (where it was too technical) to create this stub. IMO the notability of the topic does not deserve a WP article, but I am not sure of that. I have created this article, because it was the easiest way to remove this paragraph from associative property without fighting.D.Lazard (talk) 23:45, 22 February 2013 (UTC)

Additional Revision to Ring (Mathematics) Example

I see the concept regarding the additive inverse in "Detailed example I: the ring Z₄" thanks to you, but believe it may still be confusing to readers. Would a revision more along the lines of

The additive inverse of $x$ is $y$ if $x+y=0$. In Z₄, the sum of ${\overline {x}}+{\overline {y}}=0$ if the remainder of $x+y$ (as integers) when divided by 4 is 0. Therefore $(4-{\overline {x}})\mod 4=$ the additive inverse of ${\overline {x}}$

be appropriate? I leave this to your discretion... :) — Preceding unsigned comment added by Critical Reason (talk • contribs) 21:07, 25 February 2013 (UTC)

Adequality

Hi, Thanks for your effort to engage the new editor in dialog at adequality. I wanted to make a comment in response to what you wrote there, but the discussion got so voluminous that the comment will be lost in the verbiage. My comment is that the term "adaequalitat" should not be analyzed in terms of its Latin meaning, and in particular the meaning of the Latin prefix "ada". This is because the original mathematical term is Diophantus' "parisotes" in Greek, and "adaequalitat" is merely Bachet's calque from "parisotes". Therefore what is more relevant is the meaning of the Greek prefix "para" which combined with "isotes" (equality) gives "parisotes". However, this meaning seems to be ambiguous, and one has to go to the mathematics to understand Diophantus' intention. Tkuvho (talk) 18:30, 20 February 2013 (UTC)

Thanks again for putting in the effort. By the way, you should sign your recent post at User:Klaus Barner's page. I wanted to make a quick comment concerning algorithms. Fermat's applications of the technique often go beyond the algorithm that's described in the page. He adds subtle physical and geometric considerations that allow him to derive powerful applications of the method. One such example is the application to transcendental curves. The technique as described in the page only applies to polynomials, therefore clearly additional input is needed to treat the cycloid, for example, as Fermat does. After looking at the variety of applications it is clear that they go far beyond the simple algorithm. Tkuvho (talk) 20:49, 2 March 2013 (UTC)

I wanted also to respond to your comment that In my opinion, the only thing whose analysis is relevant is the nature and the significance of e. In fact, Fermat computed with it as it were a number, but it is not a number because, at some point it was supposed to be zero, and just after, it is put to zero. I am convinced that Fermat considered it as some kind of "imaginary number" (the modern meaning was not yet invented). The question "what is e?" is double. The first question is "what intuition of e had Fermat?". The second is "what modern meaning may be given to e to make his algorithm provable?" One relevant article here is that by Stromholm in 1968. Stromholm specifically argues against the idea that Fermat sets e "equal to zero". Stromholm illustrates how Fermat bends over backwards by carefully choosing a variety of terms to emphasize that e is being discarded rather than set to zero. In fact, as the term parisotes/adequality suggests, Fermat is working with a binary relation R which is not an equality but rather an approximate equality, so that one would have 2x+e R 2x (of course Fermat never calculated derivatives and did not have the notion of local slope). Tkuvho (talk) 21:06, 2 March 2013 (UTC)

What is from a computational point of view (and from a formal point of view also) the difference between putting e to 0 and removing e? The difference lies only in the informal (intuitive) description for which the accuracy of the terminology is not very important. D.Lazard (talk) 22:49, 2 March 2013 (UTC)

First, Fermat's contribution is not limited to a computational algorithm. For example, his treatment of the cycloid involves clever geometric arguments involving a mutual replacement of a point on the curve and a nearby point on the tangent line (both points being close to the point of tangency), as an instance of "adequality". This is not part of the formal kernel as outlined in the article but rather a nontrivial additional piece of geometric data. From the conceptual point of view, it is important that Fermat does not commit the logical fallacy of first assuming that e is nonzero and then setting it equal to zero at the end of the proof. For the simplest examples involving polynomials this does not matter because everything can be done purely algebraically using the idea of the "double root" as in Pappus and Viete. However, Fermat's nontrivial applications involve additional nontrivial ideas beyond the algorithmic kernel. Tkuvho (talk) 13:32, 3 March 2013 (UTC)

I also wanted to comment on your remark that It may be infinitesimal in non-standard analysis sense. I think it is clear that Fermat's "E" cannot be viewed as an "infinitesimal in non-standard analysis sense". The construction of infinitesimals in non-standard analysis requires means and techniques that were utterly beyond the reach of 17th century mathematicians. Thus, such a construction requires algebraic results such as the existence of maximal ideals that were not only inaccessible but also inexpressible, since the relevant concepts have not been introduced. Furthermore, 17th century concepts were not precise enough to be identifiable with modern notions. Therefore any formalisation in terms of modern mathematics is also an interpretation. Modulo these remarks, one can interpret and formalize Fermat's E as such infinitesimals, much as one would interpret and formalize the definitions of the derivative and the integral by Leibniz, Newton, Euler, and Lagrange. Tkuvho (talk) 14:04, 3 March 2013 (UTC)

Integrals of absolutes

Hi!

How are you? Hope fine... I wanted to discuss with you the disputed formula in the section Lists of integrals#Absolute value functions.

Cosine

The absolute cosine formula there is partly incorrect. The correct anti-derivative which is continuous as well, is:

$\int |\cos {ax}|\,dx={2 \over a}\left\lceil {\frac {2ax-\pi }{2\pi }}\right\rceil +{1 \over a}\operatorname {sgn}(\cos {ax})\sin {ax}+C$

The problem with this is that I have derived this equation myself and have verified it, both graphically and numerically, but have no external reference or citations. If this equation is eligible to enter that article, do you think it suitable to replace the old, incorrect one with this?

—Sγεd Шαмɪq Aнмεd Hαsнмɪ (тαʟк)

01:55, 10 April 2013 (UTC)

Normally this kind of questions is better placed in the talk page of the relevant article. The rule of Wikipedia is that citation must exist for every assertion. But WP:CALC says "Routine calculations do not count as original research". Here we are (in my opinion) in a limit case, because the derivation of such formulas is routine computation only for rather experimented mathematicians. This is why I have added the tag "citation needed" to the formula for |sin| and I'll add it to your formula (or to any similar one) if it is inserted.

Nevertheless your formula is not fully correct if the usual definition of the sign function (sgn(0)=0). To be correct, one have to choose sgn(0)=1. On the other hand, the floor function is more usual than the ceil function, and I would prefer the similar formula with the floor function (which would imply sgn(0)=-1) This is a personal opinion, that does not really matter.

All these considerations may be useful to many readers. Therefore, I'll add comments to the section to emphasize on this question of continuity. D.Lazard (talk) 08:26, 10 April 2013 (UTC)

Thanks for pointing that problem with the sgn function... A solution to this could be replacing $\operatorname {sgn}(f(x))$ by $\operatorname {sgn} \left(\operatorname {sgn}(f(x))+{\frac {1}{2}}\right)$, whose output is 1 when x≥0 and is -1 otherwise.

This solves the problem with the usual definition of the sgn function. How about considering this instead of a redifinition of sgn?

—Sγεd Шαмɪq Aнмεd Hαsнмɪ (тαʟк) 11:20, 10 April 2013 (UTC)

Quartics

If you are interested, you could help us improve the article on quartic functions, as you did with the cubic ones. The general formula for roots obviously fails to cover the special cases when either t or Delta or u + v are 0. — 79.113.242.231 (talk) 00:50, 7 May 2013 (UTC)

IMO, the priority for this article is to rewrite all the material after the general formula to have something coherent, in particular for a description of how to derive the formula, which is compatible with both Ferrari solution and the correct formula you have given. I have done this some time ago for the cubic case, and partly for the quintic case (the structure of this article is not yet clear). I'll not have the time to do this for the quartic in the near future, being busy with other articles that are more important (for me) to improve (like Gröbner basis) and other articles related to computer algebra, a field badly covered by WP). D.Lazard (talk) 08:57, 7 May 2013 (UTC)

Question

What was wrong with this suggestion? 94.116.38.81 (talk) 14:09, 7 May 2013 (UTC)

1. The author of this suggestion is suspected of WP:Sockpuppetry, and this is the main reason to delete this comment. If it is wrong, then you are invited to post a comment at Wikipedia:Sockpuppet investigations/Echigo mole#Comments by other users to give evidence that it is wrong. If it will be considered to be true, then the account will be blocked indefinitely.
2. There are already many recommendations about writing math articles at MOS:MATH. Proposing further recommendations has not any sense without reference to this manual of style.

D.Lazard (talk) 15:48, 7 May 2013 (UTC)

Your comments to WP:AE

Hello. In my capacity as an administrator responding to requests at WP:AE, I have removed your recent comment, because, as you said, it was entirely unrelated to the appeal being discussed. An appeal discussion is not the place to bring forward unrelated accusations against others. If you have problems with another user, please use the normal dispute resolution process (WP:DR). Thanks,  Sandstein  13:24, 14 May 2013 (UTC)

Hi, I noticed your comment at AE that Sandstein removed. While Sandstein is right that The Devil's Advocate's appeal is not the right time or place to raise that issue, I or TDA might make an arbitration request about Mathsci sometime in the future, and it would be appropriate to raise the Deltahedron issue there. If you want, whenever the request happens you can be included as a party so you can present evidence about it. Akuri (talk) 20:41, 14 May 2013 (UTC)

Echigo mole socks

Hi there; you seem to be taking a stand against the blocking of socks of Echigo Mole. While it of course true that you can edit exactly as you wish, could I ask that ib the case of this multiple sockpuppeteer you do so with extreme caution? He is quite evasive, and can be difficult to detect. Supporting him can damage the encyclopedia. Before you ask, no, I am not a skilled mathematician. But I am very experienced in Wikipedia.--Anthony Bradbury^"talk" 20:51, 19 May 2013 (UTC)

I am not against the blocking of socks of Echigo Mole. But I am definitively against blocking a good faith editor who is not a sockpuppet. In the case of Hyperbaric oxygen, nothing in his edits suggests that he is a sockpuppet. On the contrary, all his edits are constructive. In the SPI of this case, I understand the checkusers comments as no evidence of sockpupperty. Thus the accusation of sockpuppetry relies only on the conviction of a single editor who gives a description of Hyperbaric oxygen's edits that do not correspond to their real content. IMHO, the assertions of this editor are not credible, not only for the reasons that I gave in my posts at user talk:Hyperbaric oxygen, but also for his recent behavior here (section Hurwitz's theorem and related articles) and here (section Conjugation and real inner product on the quaternions), where his systematic WP:personal attacks has pushed an excellent editor (Deltahedron) to retire from wp. This has already damaged Wikipedia. D.Lazard (talk) 23:01, 19 May 2013 (UTC)

+1! Rschwieb (talk) 13:49, 20 May 2013 (UTC)

Given Anthony Bradbury's explanation, this response is not helpful. First of all I have an extremely long record of creating mathematical content. The incident being discussed above is stale now. It was in the end about minor and trivial notational issues within wikipedia not in mathematics. Secondly, and far more significantly, the disruptive editing by Echigo mole with multiple simultaneous socks is not something that is open to debate. The disruption falls within the category long term abuse, is not something new (it started in 2009) and does not have to be explained three or four times to ech person previously unaware if it. Just today an ipsock of Echigo mole was blocked by Future Perfect at Sunrise after posting here on this user talk page and on User talk:AGK. It was exactly the same user as Hyperbaric ozygen from one of the usual IP range he uses in Britain: 92.40.206.158 (talk · contribs · WHOIS) Because of the disruption caused by this particular banned user, a motion was passed by the arbitration committee about their edits and the enabling of their edits by others.[3] After coordinated editing from other socks plus a clear explanation from an admnistrator, any further attempts to argue for an unblock of this particular sock would probably lead to an enforcement request at WP:AE. That has never happened before after over 250 socks and ipsocks. Mathsci (talk) 15:07, 20 May 2013 (UTC)

"Would probably lead to an enforcement request at WP:AE": Is that a threat against me? D.Lazard (talk) 16:41, 20 May 2013 (UTC)

Request now at WP:AE

An enforcement request has been made concerning you at WP:AE. Mathsci (talk) 07:02, 21 May 2013 (UTC)

Premature closing of MathSci's RfE against D.Lazard by Future Perfect at Sunrise?

I wish to notify you of a discussion that you were involved in.[4] Thanks. A Quest For Knowledge (talk) 15:42, 22 May 2013 (UTC)

In "Quartic function" please restore "Ferrari's solution in the special case of real coefficients"

In the article on the Quartic function you made this edit http://en.wikipedia.org/w/index.php?title=Quartic_function&diff=556862583&oldid=556860306 which removed the section: "Ferrari's solution in the special case of real coefficients" with this justification: "Remove a misplaced section, which is WP:OR".

The section you removed is _not_ Original Research since the published, verifiable source that the section quotes provides all the information found in the section.

Please restore this section to the article at your earliest convenience.

Thank you.

Lklundin (talk) 18:57, 26 May 2013 (UTC)

Could you help me ?

I know that you're very busy, and have very little time on your hands, but I have absolutely NO idea how to prove this without retorting to Euler's beta function, or an equivalent thereof:

$\sum _{k=0}^{p}{(-1)^{k}\ {\frac {n}{n+k}}\ C_{p}^{k}}\ =\ {\frac {p!\ n!}{(p+n)!}}\ =\ {\frac {1}{C_{p+n}^{n}}}\ =\ {\frac {1}{C_{p+n}^{p}}}$

I've asked this question on the Math Reference Desk here at Wiki, but all the answers that I've got so far are more-or-less unsatisfactory (beta functions, hypergeometric functions, Cauchy matrixes, Möbius inversion formula, Taylor series, finite differences, etc). I personally would want to find a simple proof based probably on induction, or perhaps on something even more basic than that. — 79.113.237.30 (talk) 19:40, 11 June 2013 (UTC)

I do not know much of combinatorics (indeed, this is a question on combinatorics). I believe that the state of the art for these question is the book "A=B" (http://www.math.upenn.edu/~wilf/AeqB.html). Its goal is more automatic proofs than simple proofs. But automatic proofs requires a deep understanding of the problems, and this should provide simple proofs if any. D.Lazard (talk) 08:32, 12 June 2013 (UTC)

Thanks! Somebody else recommended to me the exact same book a few days ago. It generally deals with hypergeometric functions, and indeed, if the sum would not alternate, i.e. if the (-1)^k term were missing, the sum does become an expression in ₂F₁. It also contains a theorem and an algorithm detailing how to transform such sums into recursive equations by dividing two of its consecutive terms. On a different note, I've arrived at the problem in question by noticing the following:

$\int _{0}^{1}{\left(1-{\sqrt[{k}]{x}}\right)^{n-k}}\ dx\ =\ {\frac {1}{C_{n}^{k}}}\ ,\qquad \qquad \int _{0}^{\infty }{e^{-{\sqrt[{k}]{x}}}}\ dx\ =\ k!\ ,\qquad \qquad e^{-{\sqrt[{k}]{x}}}\ {\xrightarrow[{\text{Taylor series}}]{\quad {\sqrt[{k}]{x}}\ \to \ 0\quad }}\ 1-{\sqrt[{k}]{x}}$

The first integral above has already been studied by John Wallis three or four centuries ago (see here, on page 49), and its expression becomes that of Euler's beta function by making the simple substitution ${\sqrt[{k}]{x}}\ \to \ t.$ The second one becomes the expression of Euler's famous gamma function when making the same substitution. Furthermore, the first integral above shows the connection between factorials, combinations, and geometric shapes described by equations of the form x^m + y^p = 1 (if we make both k and n - k smaller than 1), as well as elliptic integrals and arithmetic-geometric means (for algebraic arguments of the form $a+b{\sqrt {c}},$ as shown by Borwein and Zucker in the early `90's, who also mention that some of those expressions were already known to Gauss two centuries ago: see Gauss's constant). — 79.113.242.174 (talk) 17:51, 12 June 2013 (UTC)

Diophantine approximation

I thought that the additional condition and the '<' would be right because it is written in this way in the book of Khinchin. Also the current definition for best approximation of the second kind does not exactly fit the ones given in the cited books of Lang and Cassels. I think that the difference in the definitions do not matter for irrational alpha anyway, but for rational alpha some care is needed. Compare also

A best rational approximation to a real number x is a rational number n/d, d > 0, that is closer to x than any approximation with a smaller or equal denominator.

in Continued_fraction#Best_rational_approximations and §15 in Perron's book. -- KurtSchwitters (talk) 19:54, 13 June 2013 (UTC)

I agree that both definitions are equivalent for irrational numbers, and that the one with strict inequalities may be better sourced. However, the main reason of my revert was the additional condition ${\frac {p}{q}}\neq {\frac {p'}{q'}}$, which may be confusing, and has confused me, suggesting that non-irreducible fractions are considered and inserting a single latex formula inside a sentence in which the other formulas are in HTML. Therefore, I'll not be opposed that you revert my revert, if you replace this condition by simply saying "for every rational number p'/q' different of p/q and such that 0< q' ≤ q ". D.Lazard (talk) 14:23, 14 June 2013 (UTC)

Thanks. I am not used to the way {{math| is used here. That was the reason I used the latex formula. As it is not urgent to change it, I will think about it for a while and update the paragraph on Monday. -- KurtSchwitters (talk) 16:50, 14 June 2013 (UTC)

Not Solvable Through Radicals

Uhm... Silly question, but I have to ask: What does it mean that certain equations (like the quintic) are "not solvable through radicals" ? I thought it meant that although such radical expressions do theoretically exist, their formulas cannot be guessed or deduced merely by looking at their coefficients (as in the case of linear, quadratic, cubic, or quartic ones). I mean, if a number would not even be expressible through radicals, then it would have to be transcendent, right ? And, as such, it couldn't obviously be the solution to an algebraic equation, no ? Or ? — 79.113.242.1 (talk) 17:34, 17 June 2013 (UTC)

This means that for some (in fact almost all) polynomials of degree 5 or higher, there can not exist any expression for the roots (formula for the roots) that may be constructed from the integers and the coefficients by using only the following operations: addition, subtraction, multiplication, division and nth root extraction for an integer n. This is Abel-Ruffini theorem. The simplest equation that cannot be solved in terms of radicals is $x^{5}-x\pm 1=0.$ D.Lazard (talk) 08:02, 18 June 2013 (UTC)

So what you're telling me is that there really are algebraic (non-transcendental) numbers which simply cannot be written as combinations of integers (or even rationals), +, -, ×, /, and ⁿ√ ? (If so, then does this weird sub-class of algebraics bear a name ?) — 79.113.230.120 (talk) 16:22, 18 June 2013 (UTC)

Yes, this is exactly what the Abel-Ruffini theorem says. As far as I know, the only specific usual name is radical extension for a field extension generated by algebraic numberrps that may be expressed in terms of radicals. Note that if one restricts oneself to square roots instead of nth roots one gets the algebraic numbers that may be constructed with compass and straightedge. D.Lazard (talk) 16:39, 18 June 2013 (UTC)

Wow! This all seems so shockingly surreal... :-| It's definitely "news" to me... Thanks! — 79.113.230.120 (talk) 18:20, 18 June 2013 (UTC)

$x={\sqrt[{5}]{x+1}}\ <=>\ x={\sqrt[{5}]{1+{\sqrt[{5}]{1+{\sqrt[{5}]{1+...}}}}}},$ similar to $\phi ={\sqrt {1+{\sqrt {1+{\sqrt {1+...}}}}}}.$ — 79.113.231.88 (talk) 23:29, 18 June 2013 (UTC)

This is true, but Abel-Ruffini theorem concerns finite formulas. In fact such infinite formulas express the solutions as a limit and are not algebraic. Moreover, every transcendental numbers may be represented by this kind of infinite formulas. That is the purpose of continued fractions theory. D.Lazard (talk) 09:09, 19 June 2013 (UTC)

Yes, I know, I wasn't implying anything, I was just happy to come up with something prettier-looking than a Bring radical... :-) On a somehow related note, are there some interesting or relevant conclusions to be drawn from the fact that the graphic of the zeta function so closely resembles that of a hyperbole of equation (x-1)(y-1) = 1 ? I'm asking this because $\scriptstyle f(x)={\sqrt[{x}]{1+{\sqrt[{x}]{1+{\sqrt[{x}]{1+...}}}}}}$ also approximates the same hyperbolic function. — 79.113.238.19 (talk) 15:26, 19 June 2013 (UTC)

Real multivariable function

Considering your post at Wikipedia talk:WikiProject Mathematics‎#A wild idea: multi-tiered maths articles to match the target audience?, I had a try starting this article, currently written starting from pure mathematics and ending in physics and engineering. It seems you were looking for an article on this and I couldn't find one either. By all means edit if inclined. Thanks and regards, M∧Ŝc²ħεИ_τlk 14:21, 26 June 2013 (UTC)

A Suggestion

I'm trying to come up with a single-letter name for the set of algebraic numbers that can be expressed as combinations of radicals, fractions, subtractions, sums, and products of integers. I thought of V for the combinations containing irreducible radicals (since the letter's shape reminds me of the symbol for the radical sign), but I don't really know what to call the reunion of V and Q. Any suggestions ? — 79.113.225.23 (talk) 21:01, 5 August 2013 (UTC)

Big oops

Thank you very much for having detected the confusion between radical and root. The fr:Duplication du cube involves the cubic root of two, and this is a radical while it's not a constructible number. I should have paid attention to that. I rephrased the whole section to focus on square roots instead of generic radicals (which can even be complex, as you pointed out). --MathsPoetry (talk) 12:07, 14 August 2013 (UTC)

Union? What union? Where is the union?

"The angle is not the intersection of the two rays, but their union.."

Tell me, where in "In geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle." is there a union? I was trying to add that thought which you took away. I might not have the best way of stating it, but please don't just revert it without editing it yourself to where it reads better. John W. Nicholson (talk) 13:02, 10 September 2013 (UTC)

The sentence that I have restored asserts correctly that an angle consists in two rays and their intersection at their common endpoint (the vertex), all together. Thus, when drawing an angle, you are representing the set theoretic union of the two rays. The edit that I have reverted asserted wrongly that an angle consists in the intersection of the two rays. This is wrong because the intersection of the two rays is not the angle; it is its vertex. If you think that the given definition is incorrect or unclear, you have to explain why in the talk page before inserting your WP:OR thought. D.Lazard (talk) 16:27, 10 September 2013 (UTC)

Theorem in commutative algebra

Hi there: been a while since we talked :) Might you be able to help out with this question?

Thank you for quoting this link. However, I cannot help here: I have never read this part of Eisenbud's book and I have not it at hand. More, I do not even know if Eisenbud's proof is mine, Govorov's one or a new proof. D.Lazard (talk) 17:33, 3 September 2013 (UTC)

OK, thanks for looking anyway! I notice now that someone pointed out that the poster is correct in his concerns, and that Eisenbud corrected it in some errata. See you around! Rschwieb (talk) 13:38, 23 September 2013 (UTC)

Books and Bytes: The Wikipedia Library Newsletter

Books and Bytes

Volume 1, Issue 1, October 2013

by The Interior (talk · contribs), Ocaasi (talk · contribs)

Greetings Wikipedia Library members! Welcome to the inaugural edition of Books and Bytes, TWL’s monthly newsletter. We're sending you the first edition of this opt-in newsletter, because you signed up, or applied for a free research account: HighBeam, Credo, Questia, JSTOR, or Cochrane. To receive future updates of Books and Bytes, please add your name to the subscriber's list. There's lots of news this month for the Wikipedia Library, including new accounts, upcoming events, and new ways to get involved...

New positions: Sign up to be a Wikipedia Visiting Scholar, or a Volunteer Wikipedia Librarian

Wikipedia Loves Libraries: Off to a roaring start this fall in the United States: 29 events are planned or have been hosted.

New subscription donations: Cochrane round 2; HighBeam round 8; Questia round 4... Can we partner with NY Times and Lexis-Nexis??

New ideas: OCLC innovations in the works; VisualEditor Reference Dialog Workshop; a photo contest idea emerges

News from the library world: Wikipedian joins the National Archives full time; the Getty Museum releases 4,500 images; CERN goes CC-BY

Announcing WikiProject Open: WikiProject Open kicked off in October, with several brainstorming and co-working sessions

New ways to get involved: Visiting scholar requirements; subject guides; room for library expansion and exploration

Read the full newsletter

Thanks for reading! All future newsletters will be opt-in only. Have an item for the next issue? Leave a note for the editor on the Suggestions page. --The Interior 20:44, 27 October 2013 (UTC)

SMath Studio

I would like to ask you a few questions, D.Lazard, regarding your Oct 28 2013 edit:

1. Why did you delete link to the official site?

2. Why do you insist that SMath Studio doesn't meet noteability guidelines and the artcile should be deleted?

3. What is it you find wrong about the feature remark (since you deleted it as well)?

Regards, Andy Monakov (talk) 09:04, 29 October 2013 (UTC)

1. The deletion of the link to the official site is a side effect of the revert. I'll not oppose if you reinsert it again.
2. Notability guideline says "if no reliable third-party sources can be found on a topic, then it should not have a separate article". For the moment, no such reliable third-party source is provided, although asked for since about one year.
3. The feature remark is an editor's opinion, not supported by any reliable source. As such it is WP:original research, and is forbidden by Wikipedia policy.

D.Lazard (talk) 10:50, 29 October 2013 (UTC)

2. Well, are you aware that over the years SMath Studio was covered in multiple reviews? Or do you perceive it as insufficient?

3. I'm afraid you didn't look well at the edit at all. By definition, opinion is a person's subjective judgment, and the remark doesn't contain anything of the sort. Andy Monakov (talk) 14:19, 29 October 2013 (UTC)

Free graph theory software

I want to discuss adding a link in the article "graph theory" to the website of "Free graph theory software". It was recently deleted with the following argument: "There are any number of free graph software libraries out there; what makes this one special?".

I want to correct a misunderstanding. "Free graph theory software" is no library. It is a free graph theory software tool to construct, analyse, and visualise graphs for science and teaching. It has a graphical user interface and works online without installation.

Why it is less special than other external links, that are not deleted? E.g., In "Free graph theory software" you can import an arbitrary list of graphs in graph6 format and choose graphs from it, by entering their graph parameters, which i consider a really useful feature. I do not know any other software that has this function. And it has a lot of other features listed on the website.

The intention of "Free graph theory software" is to help scientists and students all over the world. It is a graph theory software that may be used for free by everyone. Why should it not deserve an external link in the article "graph theory" of wikipedia? — Preceding unsigned comment added by Yloreander (talk • contribs) 15:24, 8 November 2013 (UTC)

Please read WP:What Wikipedia is not and more specifically WP:ADVOCATE. Your arguments supporting "Free graph theory software" look like advocacy. For the Wikipedia policy about external links, see WP:ELNO. There are many graph theory software, free and not free. To be linked to, a software needs to be notable, and its notability must be attested by reliable secondary sources. This is apparently not the case for "Free graph theory software". D.Lazard (talk) 15:43, 8 November 2013 (UTC)

Reducible polynomials

Is the definition of a polynomial be reducible over the integers the only one. For instance in Stewart's Galois Theory, Third Edition (Definition 3.10) he writes

"A polynomial over a subring R of C is reducible if it is a product of two polynomials over R of smaller degree. Otherwise it is irreducible."

He then goes on to give an example of a polynomial that is irreducible over Z(t) of 6t+3=3(2t+1). This was the basis for the change that I made on the irreducible polynomial page that you reverted back. If different books use different definitions then shouldn't this be included in the article. — Preceding unsigned comment added by Uwhoff (talk • contribs) 20:18, 17 November 2013 (UTC)

I have answered in Talk:Irreducible polynomial#Irreducibility aver the integers. However, I did not answered about this particular example. Are you sure that he wrote "the polynomial 6t+3=3(2t+1) is irreducible over Z[t]" (which is incorrect) and not "the polynomial 6t+3=3(2t+1) (defined) over Z[t] is irreducible over Q[t]" or "the polynomial 6t+3=3(2t+1) (defined) over Z[t] is irreducible" (which are both correct, if one considers only the irreducibility over a field). The place of "over" is essential. D.Lazard (talk) 14:30, 18 November 2013 (UTC)

Modular arithmetic

"(Reverted good faith edits by Jtle515 (talk): Translating the latin ablatif as "by" is not sourced and WP:OR. (TW))"

Knowing another language counts as original research now? Huh? --Jtle515 (talk) 06:25, 23 November 2013 (UTC)

It is not the knowledge of Latin which is original research, but the choice of translating ablatif, in this particular case, by "by". This choice is controversial. D.Lazard (talk) 10:18, 23 November 2013 (UTC)

What else could it be, in context? --Jtle515 (talk) 11:02, 23 November 2013 (UTC)

For a mathematician, "modulo" means "up to modulus". However I do not know if this translation is linguistically correct. D.Lazard (talk) 11:12, 23 November 2013 (UTC)

The Wikipedia Library Survey

As a subscriber to one of The Wikipedia Library's programs, we'd like to hear your thoughts about future donations and project activities in this brief survey. Thanks and cheers, Ocaasi ^{t | c} 15:14, 9 December 2013 (UTC)

Javascript Exetended Euclidean Algorithm

Hello!

I think the pseudocode is not so clear on the page Extended Euclidean algorithm, so I put a implementation in Javascript.

But you revert my edits.

I see that on the talk page there are more people talking it, so I think that it could bee good put some "real" code there. I am not saying that we need put the Javascript code, but, some code.

What do you think about?

Tks

Lp.vitor (talk) 12:53, 1 December 2013 (UTC)

The pseudo-code is be very close to Pascal or Maple code. Therefore Javascript of other codes seem not useful for the article. In fact, the difference with Pascal code lies only in the absence of "end" keywords and in multiple assignations. Maybe, it would be clearer if they would be split in pairs of simple assignations, which is complicated by the need an auxiliary temporary variable. D.Lazard (talk) 16:41, 1 December 2013 (UTC)

Or maybe someone could explain how the multiple assignations works... Lp.vitor (talk) 21:51, 1 December 2013 (UTC)

Done in the article D.Lazard (talk) 15:21, 9 December 2013 (UTC)

All right

	Diligent work
	Ok, no links, I'm sorry Ignacitum (talk) 20:26, 18 December 2013 (UTC)

Reverted my edit

Hi, you reverted my edit on "Algebra" today. I made an svg version of an equation that was a png, in line with the guidance here. Was there a reason to undo the edit? Could the svg be improved? I'm fairly new to editing Wikipedia so any help would be... well... helpful. Thanks Jamietwells (talk) 20:03, 14 January 2014 (UTC)

@Jamietwells: The only reason of my revert was that the copyright status of the image is not fixed. The file is tagged with "This file does not have information on its copyright and licensing status. Unless the copyright and licensing status is provided, the image will be deleted after Tuesday, 21 January 2014. Please remove this template if a correct copyright license tag has been added." When the copyright status will be clarified, there will be no problem to reinsert the svg version. D.Lazard (talk) 21:18, 14 January 2014 (UTC)

Ok, yeah, I made the image so I had already fixed it, but I don't know how to get rid of the copyright notice thing. I don't think you can copyright a formula anyway, It think they're all public domain (at least, the quadratic equation is). Can I put the image back then? Jamietwells (talk) 22:28, 14 January 2014 (UTC)

January 2014

Hello, I'm BracketBot. I have automatically detected that your edit to Computer algebra system may have broken the syntax by modifying 1 "[]"s. If you have, don't worry: just edit the page again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on my operator's talk page.

List of unpaired brackets remaining on the page:

• common divisor]]s is systemically used for the simplification of expressions involving fractions]].

Thanks, BracketBot (talk) 16:40, 16 January 2014 (UTC)

Hello, I'm BracketBot. I have automatically detected that your edit to Complex dimension may have broken the syntax by modifying 1 "()"s. If you have, don't worry: just edit the page again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on my operator's talk page.

List of unpaired brackets remaining on the page:

• x^2+y^2+z^2=0</math> is a variety of (complex) dimension 2 (a surface), but of real dimension 0 — (it has only one real point, (0, 0, 0).

Thanks, BracketBot (talk) 14:47, 28 January 2014 (UTC)

From user Arpan Mathur

Hi, I am Arpan Mathur. You have reverted my edit on article Derivative today. I agree with you that the example put by me was too technical. But, having more than one example will clarify the process of differentiation by first principles as is used in the first example. So, i have posted another example which is simpler to understand than the previous one. I hope you will agree with me. Arpan Mathur (talk) 15:27, 4 February 2014 (UTC)

Derivation

I think this move was too abrupt, too important to be made without consensus, and incidentally a mistake. Please discuss at the article talk page. Deltahedron (talk) 20:05, 15 February 2014 (UTC)

Perspective

Hi D.Lazard, I thought you may want to know that dab page sections don't have WP:primary topics. We can indent the other entries but I'm failing to see why we should on this. I also left a message at Talk:Rotation group (disambiguation). WP:MOSDAB may help. Widefox; talk 02:20, 20 February 2014 (UTC)

Reopening discussion

You are re-opening a discussion that should remain closed there. I am all the more surprised, because your argument is incomplete. It is good, if you acknowledge restriction to the function R⁺ × R → R : (x,y) ↦ exp(y log x), in which case the inclusion of (0,0) is not only inappropriate by your argument, but it also has no utility: this is not the function in use when we want x⁰ = 1 for x = 0. The distinct function R × Z → R : (x,n) ↦ xⁿ (with removal of x = 0 for n < 0) can sensibly include (0,0) in its domain. I am surprised at the failure to acknowledge this fundamental and crucial point by pretty much everyone involved. I have pointed this out there, and the fact that the whole debate vanishes as a consequence. It's like watching a bunch of kids squabbling about whether St Niklaus wears green or red. —Quondum 15:47, 4 March 2014 (UTC)

You are right: In some contexts, it is perfectly legitimate to attribute some value to 0⁰. But we write an encyclopedia and we cannot hope that the layman reader will care if the exponent is integer or not. Therefore, if we will try to avoid reader's errors, we must define 0⁰ as undefined. On the other hand, I have written this post essentially for emphasizing that the substitution is an operation which is not as simple as it appears ("simple substitution" is used in the preceding post). I became convinced of this by my experience in computer algebra, where the substitution is a fundamental operation. A large part of errors done by beginner users of a computer algebra system are misuses of this operation. D.Lazard (talk) 16:33, 4 March 2014 (UTC)

I agree that we need to be sensitive to the fact that this is an encyclopedia. It is a small matter to document the two distinct uses of the same notation, and to sensitize the reader that they are distinct and appropriate to distinct uses. It would be very unencyclopedic to perpetuate the misconception that the distinct operations may be regarded as a single function, when in fact their use is in fact distinguished everywhere that it is used, albeit implicitly. My own OR generalizes this to two broader classes of function, which makes the divide between and irreconcilability of the two crystal clear, and hence also the folly of trying to merge them. The article is currently written from the perspective of how do we calculate the function given the domains, rather than from the perspective of from being given the applicable function definition. I think you'll agree that if the notation for the two distinct cases had been kept different, none of this confusion would even have occurred. From a purely encyclopedic perspective then, we can tell the reader that he must determine a priori which of the two cases applies, and the article could then develop each separately; it can be a matter of editorial choice. Such a choice does not depend on integer/real considerations, but certain contexts do make this choice obvious: a series with integer exponents invariable means the one. Who would ever interpret a Taylor series or binomial expansion as using the two-argument analytical version? Especially since the exp function is frequently defined in terms of one, and circularity here would be anathema? On your point of substitution, agreed, but this is entirely circumvented if the two functions are fundamentally distinguished; focusing on substitution in your post merely distracts from the real issue. —Quondum 18:11, 4 March 2014 (UTC)

Summation

Perhaps a better solution to the hatnote would be to move the article to a clearly unambiguous title like finite summation. Any thoughts? Sławomir Biały (talk) 15:29, 14 March 2014 (UTC)

Maybe finite summation could be confusing for the layman because "infinity" is not an easy concept, even if it is so familiar to experimented mathematician that it appears to be "trivial". On the other hand, during the recent discussion about minus one twelfth, I had to read the whole article to remark that the article does not contain any mention of infinite sums outside its lead. Apparently, this had not been remarked by the other users participating to the discussion. Thus the present title is confusing for mathematicians. This is the reason for which I have introduced the hatnote. IMO, the present title has to be kept, as the content is about the primary topic for "summation". On the other hand, as finite and infinite summations are distinct topics, which are only related by the fact that an infinite sum is a limit of a sequence of finite sums. Moreover, the readers of Summation are not supposed to know anything about limits, and the two topics, although related, are quite different. Thus, this corresponds exactly to the last sentence of WP:RELATED, which is "This guideline does not discourage the use of disambiguation hatnotes in a situation where separate topics are related, but could nonetheless be referred to by the same title and would thus qualify for disambiguation, such as a book and its film adaptation". Here, it is a basic concept and its wide generalization. Thus, I find convenient both the present title and the hatnote. D.Lazard (talk) 18:18, 14 March 2014 (UTC)

I generally don't like hatnotes unless absolutely necessary, and the article does mention the case of infinite summation in the (overly long) lead. But your argument is quite reasonable, and I'll defer to your judgment. Sławomir Biały (talk) 19:33, 14 March 2014 (UTC)

Were you going to make an update to Critical point (mathematics)?

Hello D. Lazard. In a comment here you mentioned making a recent edit to Critical point (mathematics). Since I was trying to figure out if I could close the move discussion at Talk:Mathematical singularity#Requested move it would assist me if I knew what you were referring to. I didn't notice any recent edit by you at the critical point article. Thanks, EdJohnston (talk) 17:23, 24 March 2014 (UTC)

Time is going faster than I thought (sorry if this sentence is not correct English). In fact, I edited this article from August to October 2013. Here [5] is the difference between the state of the article before my first edit and the last one (there are few minor edits in between by other editors). As you can see, many different aspects of the notion are now presented as a unified notion. Several were lacking or sketched in a non-understandable way in the older version. I believe that a similar work is possible for Singularity (mathematics), although probably harder: for critical points, the dominant point of view is that of differential geometry and manifolds, although it extends to algebraic geometry. I see two difficulties for the singularities: by definition, manifolds are non-singular. Thus, in differential geometry, the concept occurs (primarily) for intersections of singularities, which is a less elementary level than the one I have considered for critical points. The second difficulties arises with differential equations, which have two notions of singularity: singular equations and singular solutions. I believe that all these notions may be presented in an unified way, but I have to think more to understand how to do that. D.Lazard (talk) 18:52, 24 March 2014 (UTC)

Thanks for your reply. One possibility is to close the discussion (for now) as No Consensus with the hope that some editors will work on the content issue in the meanwhile. If we rename Mathematical singularity to Singularity (mathematics) it is puzzling that the DAB page at Singularity shows eight other meanings (e.g. in complex analysis) that also belong to mathematics. This suggests that only mathematicians can dig us out of the problem. However, you are still on record as supporting the move, so perhaps you don't consider the difficulties to be too severe. EdJohnston (talk) 21:08, 24 March 2014 (UTC)

Polynomials

Quote: "Unsourced and wrong (there are implemented algorithms for testing if a multivariate polynomial has real zeros)"

Hi, could you provide a link to an algorithm which determines if a multivariate polynomial f(x,y,z,...)=0 has no real roots. i.e. the surface does not cross the horizontal plane? I need to find this algorithm. You say it exists. — Preceding unsigned comment added by 5.68.85.46 (talk) 21:44, 21 April 2014 (UTC)

The best (as far as I know) software is RAGLIB (http://www-salsa.lip6.fr/~safey/RAGLib/ ). The main contributor for this kind of algorithms is Safey el Din, Mohab. D.Lazard (talk) 22:58, 21 April 2014 (UTC)

About link from Hermite matrix to Row echelon form

Hi D.Lazard Hello, well I found a better way for your link described in the title, it should be: Hermite matrix -> Hermitian matrix can you redirect the link please? — Preceding unsigned comment added by Fjnplx (talk • contribs) 16:45, 8 May 2014‎

To editor Fjnplx:: Please, sign your posts in talk pages with four tildes (~}. I have never edited, nor read before you post, the page Hermite matrix. Therefore, it is not "my" link, in any way. Hermite matrix is an orphan, which means that no page is linked to it. It follows that one can come to this page only by searching its title. As I do not know any mathematical concept called "Hermite matrix", the target of the redirect is unclear. I know two kinds of matrices named after Hermite: Hermite normal form and Hermitian matrix. There is no relation between these concepts. As someone typing "Hermite matrix" is searching "Hermitian matrix" with higher probability, I'll follow your suggestion. D.Lazard (talk) 20:31, 8 May 2014 (UTC)

Real numbers

Hi D. Lazard. Could you be so kind as to look at Real number#Vocabulary and notations. Some edits made there a few days ago specifically talk about notational preferences in French mathematics. Even though this is referenced, I am having a hard time believing that these statements are universally true. If the statements are accurate could you put this POV in context for me? Thanks, Bill Cherowitzo (talk) 18:33, 11 May 2014 (UTC)

I agree with you, this terminology and notation are common, but are not a rule. I have edited the article by simply adding "commonly". D.Lazard (talk) 20:47, 11 May 2014 (UTC)

BRR editing

This edit, being a repeat of your own change which had been reverted, does not conform to WP:BRD. The editor who uses the pseudonym "JamesBWatson" (talk) 14:08, 13 May 2014 (UTC)

On reflection, I think both versions are likely to be unhelpful to most readers. Better would be:

an expression of the form $a_{0}+a_{1}x+\cdots +a_{n}x^{n},\quad a_{n}\not =0$

because that is what a polynomial is, not a pair of expressions connected by an equals sign. I, and presumably you, will in the context read "an expression p = XYZ " as a short hand for "an expression XYZ, which will be referred to as p for convenience of reference", but most non-mathematicians are likely to read it as meaning exactly what it says. Correcting in this way would have the drawback of needing a second sentence to introduce the notation p (or, as I would prefer, p(x)), but that is a small price to pay for reducing the risk of misleading readers. Any thoughts? The editor who uses the pseudonym "JamesBWatson" (talk) 14:20, 13 May 2014 (UTC)

I do not remember why I have repeated my edit without discussing in the talk page. Maybe by for saving some time or because I guessed that the edit summary was sufficient. It is also possible that it is because I do not like the misconception of many editors that functional notation is mandatory for polynomials.

In fact, it appears from my edit history, that soon after this edit, I have added a new section Notation and terminology to Polynomial, for explaining why both notations p and p(x) are correct for the same polynomial. Probably, I intended to explain my revert to the talk page and I have forgotten to do it after having introduced the new section.

Nevertheless, I agree with your suggestion of avoiding equation in the first displayed formula and finding a simple formulation for introducing p in the next sentence. For the moment, I have no good suggestion. I'll think about it. D.Lazard (talk) 19:40, 13 May 2014 (UTC)

OK, I have made the change. Naturally, if you can think of a better way of wording it, that will be fine. For what it's worth, I fully agree with you about "the misconception of many editors that functional notation is mandatory for polynomials", but most people are introduced to the subject via the "p(x) = " notation, rather than the "p = " notation, and I think that articles on elementary mathematical topics should be written in ways that make them as far as possible accessible to the majority of readers, who are not mathematicians. Having thought more about it, I no longer feel that in this particular case it is likely to matter much, but I feel very strongly that in general we should give accessibility to lay readers priority over strict correctness from the point of view of mathematicians, especially in a case such as this, where it is a mere question of notational convention, rather than logical soundness. (I emphasise that I am referring to articles on topics elementary enough that it is reasonably likely that non-mathematicians will consult them. It is a different matter when it comes to writing on topics sufficiently advanced that nobody below the level of post-graduate mathematical studies is likely to even be able to understand what the topic of the article means.) I know of intelligent and educated people who frequently use Wikipedia to look up information on numerous scientific topics, but not mathematical topics, because so many mathematical articles are incomprehensible to anyone without a degree in mathematics. Most mathematical articles are heavily edited by research mathematicians more concerned with making everything strictly correct from the point of view of someone with an advanced knowledge of the subject than making it comprehensible to non-mathematicians. Having spent much of my life teaching mathematics to non-specialists, I am acutely aware of how much difference it can make. Having said all that, however, I accept that in this case it probably isn't as important as I initially thought. The editor who uses the pseudonym "JamesBWatson" (talk) 09:31, 14 May 2014 (UTC)

Misplaced talk page post

I don't know if you already know, but I see that in January an editor posted a message on your user page instead of here. By now it may well be too late for any reply to be helpful, but I thought I'd let you know just in case. The editor who uses the pseudonym "JamesBWatson" (talk) 09:34, 14 May 2014 (UTC)

I have not seen this post previously. In fact, I have moved a post of this user from the top to the bottom of talk:operator (mathematics) and notified him of this move. The post on my talk page was an answer to this moving. As the original post of this user is rather confusing for me, I have not replied to it, and this post remains without any answer or comment. D.Lazard (talk) 10:11, 14 May 2014 (UTC)

Thanks

... for this. There was a source, but I wasn't at all sure whether it was sound. I more or less counted on you to verify . Cheers - DVdm (talk) 19:14, 21 May 2014 (UTC)

Euclidean domain

Greetings! In your recent edits of Euclidean domain#Examples, you appended an unmatched ] to the end of the second line. This appears to have been a typographical error, but I am not certain of what you intended, so I am not going to change it. Would you please take a look at it? Thanks! And by the way, thank you for adding all the examples. I always like to see lots of examples that are helpful and appropriate! — Anita5192 (talk) 20:15, 22 May 2014 (UTC)

Thanks. I do not understand how I have introduced this in a line that I have not edited. Probably by hitting wrongly one of the keys <alt.gr>, <ctrl>, <shift> instead of another (on my keyboard, ] needs <alt.gr>). This kind of typos has frequently unpredictable consequences. D.Lazard (talk) 03:41, 23 May 2014 (UTC)

A barnstar for you!

	The Original Barnstar
	how r u Janifer akhtar (talk) 06:02, 21 June 2014 (UTC)

Thanks. However, I would pleased to know for which edit(s) I got this barnstar. D.Lazard (talk) 08:26, 21 June 2014 (UTC)

Draft 1/∞ Article

Hello, I have addressed some of your concerns about this draft article after having performed some initial research, I would appreciate your comments...thank you!YWA2014 (talk) 05:02, 14 July 2014 (UTC)

Euclidean algorithm

You haven't responded on my talk page. If MathJax alt= is busted, then it should be fixed or people should stop using MathJax. Squelching attempts to accomodate disabilities seems to be poor form. Glrx (talk) 17:54, 15 July 2014 (UTC)

I agree that MathJax bug must be fixed, but I have not the competence for doing that. About requiring people to stop using MathJax, it is against Wikipedia consensus, as shown by the recent discussion at Wikipedia talk:WikiProject Mathematics/Archive/2014/Jun#A challenge from Jimbo Wales. If you want to make Wikipedia unreadable for MathJax users, please ask before to Wikiproject Mathematics. D.Lazard (talk) 13:26, 16 July 2014 (UTC)

Credo

Hello! You have received preliminary approval for access to Credo. Please fill out this short form so that your access can be processed. MediaWiki message delivery (talk) 22:50, 16 July 2014 (UTC)

Alleged irrelevance

On 24/1/2014, you deleted a condition as an "irrelevant sentence" in the article on Euler's totient function. Perhaps you would like to tell us how you decided that the clause is irrelevant.

Please, sign your post in talk pages, by inserting four tildes (~~~~) at the end.

The removed sentence was "If R(s) is bigger than 2." This sentence is grammatically incorrect and involves a function R that does not appear in the section. May be you wanted say that the equality is true only inside the domain of convergence. But the fact that the series is convergent if the real part of s is larger than 2 does not implies that the domain of convergent does not include values of s with a real part smaller than two. Moreover, the result should be better understood as "the two members define the same analytic function. Therefore, your grammatically incorrect and unclear sentence does not add anything to the article. D.Lazard (talk) 11:33, 22 July 2014 (UTC)

"R(s)" is a well known symbol for the real part of s and is used widely in analytic function theory and complex numbers generally. In point of fact the function {zeta(s-1)}/{zeta(s)} has a pole at s=2.

(talk page stalker) You're still not signing your posts here, as both requried and requested. Second, from what I see, D.Lazard was right in their removal. If you think it should be added, then it should be discussed on the article talkpage to obtain WP:CONSENSUS the panda ɛˢˡ” 12:55, 22 July 2014 (UTC)

Euclidean algorithm

Back in July, you changed or removed some alt tags in < math > expressions. It looks as if there are now some unclosed comments: " < ! - - " closed with "> - -", rather than the correct " - - >". Since some substantive changes were also made, I'm not sure I can recover what should be there. Could you look into it and see what happened? — Arthur Rubin (talk) 14:34, 16 August 2014 (UTC)

I do not find any comment closed with >--, only one ends with </math>-->. In fact my edits consisted in putting into comments the texts which appeared after the alt tag of the following formulas. This was motivated by the fact, with my configuration, MathJax put the text following the alt tag in place of the formula, where it appears as a long chain of words, without spacing between them. I have omitted to edit similarly the formula at the end of section "Computational expense per step". So you can see if this bug (of MathJax ?) appears for you.

IMO these text descriptions of rather complicated formulas, introduced by alt tags, are not understandable and thus not useful. I have kept them as comment, but it is probably better to remove them completely. What do you think? D.Lazard (talk) 15:50, 16 August 2014 (UTC)

Finally, I have removed these textual descriptions of formulas (either commented or appearing in alt tag) which are, in any case, less understandable than the latex source. D.Lazard (talk) 09:02, 17 August 2014 (UTC)

In theory, an alt tag representing the actual TeX code could be useful to a screen reader. The particular code you commented out appears not to be potentially useful, though, it appears to be an attempt to produce pronounceable words which might be someone's reading the formula. — Arthur Rubin (talk) 09:10, 17 August 2014 (UTC)

Field theory (mathematics)

Thank you for reverting my last edit; I was unsatisfied with it myself. I feel like this article needs major improvement, but I've been unable to find many references on Field Theory as its own subject of research. Most references containing the word "Field Theory" seem to refer to the basics of fields found in the article field (mathematics). Do you have any suggestions for improving this article, either by expanding sections or merging it into field (mathematics)?

Brirush (talk) 18:39, 25 August 2014 (UTC)

In general, for classifying subareas of mathematics, my main reliable source is the Mathematics Subject Classification. I have used it for Algebra#Algebra as a branch of mathematics. In the present case, I would not be against a merge with field (mathematics). D.Lazard (talk) 20:26, 25 August 2014 (UTC)

Your revert on RSA

I moved the image to the left due to Wikipedia:Manual_of_Style/Images#Horizontal_placement:

It is often preferable to place images of faces so that the face or eyes look toward the text. However, images of people ought not be reversed to make the person's face point towards the text, because faces are generally asymmetrical. Reversal may result in materially misleading the viewer (e.g., by making the subject of the article or section appear to have a birthmark on the left side of his face, when the birthmark is actually on the right side).

--RokerHRO (talk) 10:00, 2 September 2014 (UTC)

OK, I did not understood your edit summary. However, in this case, I am not convinced that putting the image on the left is a good thing: This emphasizes to much on one of the authors of RSA, and may be misleading by suggesting that he is more important than the others. Thus I prefer to keep the image on the right. However, I'll not revert you again if you put it on the left. D.Lazard (talk) 11:40, 2 September 2014 (UTC)

Trapezoidal Rule

Hello. You;ve reverted edit of trapezoidal rule, namely, deleted external link. I deleted this link by mistake, so I just reverted my actions. And now you deleted this link? Why this link wasn't deleted the first time? Is it spammy? I think, it directly contributes to Wikipedia article. — Preceding unsigned comment added by Simamura (talk • contribs) 06:49, 17 September 2014 (UTC)

I have answered on your talk page. D.Lazard (talk) 07:55, 17 September 2014 (UTC)

Curve

You removed an identity based on the fact that it was without a source and trivial. First, I derived this identity to solve a problem and did not find it in a book. However, it's a very simple yet useful identity and I'm pretty sure it has been published somewhere. We can allow the identity to remain in place and people can find references later. The point is that the result and its proof are correct.

The fact that it can be easily derived is the reason I included it in the original article and not a separate one. Note that someone who is looking for information about curves on Wikipedia is not someone who is already an expert on curves and is only looking for nontrivial results. People come here to learn, thus a simple derivation that illustrates relevant concepts in an orderly fashion is quite useful.

To summarize, I disagree with the edit. I am willing, however, to move this identity to another article (say, arc length) in a section titled "Examples". Thanks.

InfoTheorist (talk) 20:22, 3 October 2014 (UTC)

Please place the new threads at the end of the talk pages. This is easy, by using the button "new section" at the op of the talk pages.

"First, I derived this identity to solve a problem and did not find it in a book". This sentence contains two fundamental reasons to not accept your edit in Wikipedia. Firstly, as you have derived it by yourself, this is original research. Original research is not allowed in Wikipedia, as explained in details in WP:No original research. Secondly, as you have not found it in a book, this means that this identity, although true and well known, is not important enough to appear in books. This implies that it is also not important enough to appear in Wikipedia (see WP:Verifiability, WP:Notability and WP:Neutral point of view, WP:Neutral point of view for details on these questions). In my opinion, if this identity does not appear in books, this is because deriving the absolute value is rarely useful and often misleading or error prone, especially, in geometric questions, where derivatives of points and vectors are considered; this implies that derivatives are not scalars, but vectors, for which the absolute value is replaced by the square root of the norm. Thus, when derivatives are considered, it is usually better to replace the absolute value by the square root of the square. In fact, your identity is simply the derivative of the identity $|x|={\sqrt {x^{2}}}.$

In summary, your edits are welcome, but please, try to follow Wikipedia policies. D.Lazard (talk) 09:27, 6 October 2014 (UTC)

User:Thomas Walker Lynch needs some tutoring

I don't know if Thomas Walker Lynch (talk · contribs) intentionally deleted that comment, but he definitely needs some tutoring. Could you ask him about that edit on his talk page? --50.53.47.9 (talk) 23:05, 8 October 2014 (UTC)

I came to talk math, not to get pulled into petty bickering. I have a life you know. Look at my talk page and you can see a list of talk page entries ignored before deletes. I called the person involved a bully, on my talk page, seems to have riled the man up. Now here are a list of contributions I have made that were deleted in most cases without discussion. When I arrived on the page the first sentence was a circular definition from wholes and defined naturals as {1,2, 3... } etc. the fix was deleted, put back, deleted, and put back, finally put back by another editor. Other pages were not linked that dealt with topics when I added references they were deleted. The article said that indexing always started from 1. When edited and mentioned the convention used in a lot of CS, the whole topic was deleted (rather than have zero mentioned as a natural?). The article said that there was not 0 row in a matrix, well this is not true in the hard sciences, EE circuit theory as one example. When I edited the whole topic was deleted (rather than have zero mentioned as an index?) When I pointed out that zero is an additive identity needed in arithmetic, my edit was deleted. When I mention Von Neuman's definition used zero my edit was deleted. When I copied another editors comment that "The convention used by set theorists .." it was deleted and the other editors comment modified (or deleted and returned - not sure). These deletes were often when ignoring my talk page entries. Majorpants ignored six talk page entries and the confirmation of two editors when he deleted stuff, but I don't think he is the only one.

Yes I appreciate the tutoring. Though as I need tutoring it would appear that some others might need potty training. To be honest I was flabbergasted when 50.53 .. was actually friendly.

I've been asked to go find pointers to this stuff and to engage in a conversation on topic of who deleted what. I would rather have a dentist appointment before doing this. So yes, when Majorpants attempted to derail the new material I added on the definition of "a set of natural numbers" rather than "the set", which comes from material in the references I also added - and yes so I removed it. This refactoring on the talk page to keep the discussion on topic is allowed according to the Wikipedia rules. See, https://en.wikipedia.org/wiki/Wikipedia:Refactoring_talk_pages. Note that the point raised by Majorpants was already addressed in our talk pages *at length*, and further up in other sections - one of which should probably be factored out as well - as I explained to JRSpriggs on this talk page, after he reverted it. BTW, I do have a talk page, and JR did not come asking for clarification before hand. — Preceding unsigned comment added by Thomas Walker Lynch (talk • contribs) 03:33, 9 October 2014 (UTC)

translation of a quote from Abrégé d'histoire des mathématiques by Jean Dieudonné

Could you give us your translation of this quote from Abrégé d'histoire des mathématiques by Jean Dieudonné?

Note on page 333: "Dès le tome II de son Formulaire ([214], 1897-1899), Peano substitue l'ensemble N de tous les entiers naturels à celui N* des entiers positif non nuls, le 0 au 1 dans l'écriture des axiomes..."

Thomas Walker Lynch posted the quote on Talk:Natural_number in this edit.

--50.53.49.112 (talk) 03:59, 9 October 2014 (UTC)

"From volume II of his Formulaire ([214], 1897-1899) on, Peano substitutes the set N of all natural integers to the set N* of the nonzero positive integers, [and] the zero to the 1, ..."

The normal translation of "celui" would be "that", but I am not sure that "that N* of the positive integers" would be correct English. Adding "and" is required because of the truncation of the citation. D.Lazard (talk) 08:33, 9 October 2014 (UTC)

Note also the following: the fact that in French the set of natural integers contains zero does not imply that the same convention applies in English. The sentence contains an example where the English and French conventions differs: "nonzero positive integers" is redundant in English, not in French, where "positif" means "nonnegative". D.Lazard (talk) 08:48, 9 October 2014 (UTC)

Thanks. That's very helpful. I have copied the above to Talk:Natural number. --50.53.53.206 (talk) 11:12, 9 October 2014 (UTC)

I would like to move the "The distinction that you make between various kinds of numbers is wrong .."

I am planning to move the "The distinction that you make between various kinds of numbers is wrong .." discussion to the prior existing section "the current article appears to be confusing counting numbers with natural numbers" where it is apropos.

I moved the history discussion to the a section of its own, as others are probably not following the discussion on translation of the Peano material, and we would like to act on your suggestion.

Thank you very much for your comments. I know how we are all taking time from other work to be here. Thomas Walker Lynch (talk) 18:53, 11 October 2014 (UTC)

Please avoid such moves: your edits separate some posts from their answer. This makes impossible for other editors to understand the discussion. Thus I'll revert your moves. D.Lazard (talk) 20:29, 11 October 2014 (UTC)

An award for you!

		The Socratic Barnstar
		I must award this barnstar for your logical addition of content here and brilliant reason explained in the edit summary174.3.125.23 (talk) 12:01, 13 October 2014 (UTC)

In the future, please use {{cn}} or {{cn span}} to tag unsourced text, instead of removing it as "unsourced", so that editors have an opportunity to cite sources. --50.53.41.238 (talk) 15:18, 13 October 2014 (UTC)

To 50.53.41.238: Apparently you made a mistake and your post is not addressed to me but to 174.3.125.23, who made the removal that you cite. D.Lazard (talk) 17:18, 13 October 2014 (UTC)

My comment was not a mistake, as the link shows. It was directed to 174.3.125.23, who received a similar message on his talk page. If you want to remove it that would be fine with me. I apologize for any confusion. --50.53.240.29 (talk) 02:52, 14 October 2014 (UTC)

It appears you are starting an edit war.

We had agreed not to change the lede until there was a consensus. You changed another editors work despite this agreement. There are relevant open talk threads on the subject. Hence your change was reverted.

"In the first revert your edit summary was "There is no source saying these sets are identical." Indeed there is not. You have some dictionary level online sources stating convention that contradict other sources we have on mathematical definition. There is an ongoing talk thread on this.

"this revert without further comment" the reverts are discussed on the talk page, and made due to the agreement to leave the lede alone until there is consensus. There are open talk threads. Might I suggest a better approach would be to provide sources for your talking points instead of crying edit war. You have provided none yet. This has been common to all the responses you have provided save one (thanks for the Peano citation). And I do want to hear your thoughts .. but then you go and write in the talk page "this talk page is not a forum" when you had made it just that. As another example when discussing history dismiss an editor writing "This page is not a forum to discuss the history of mathematics", but then yourself opened a section to discuss history (again without citations) LOL. Like all of us you have vagaries of behavior on these pages, so please don't become mean spirited.

You write on my talk page: "This appears to be the beginning of an edit war. Normally, when two editors disagree about an edit, the normal process is, after the first revert, to start a discussion to reach a consensus (see WP:BRD)" --- that is so funny! You are the one who edited first without consensus, and now you complain, in a quite meanspirited manner that someone else did it!! LOL. (As for your comment about majority making it ok, note that consensus is not the same as majority. - Is it not exactly such imprecision in usage of terms we are discussing on the talk page right now? eh?)

Your recent editing history shows that you are currently engaged in an edit war. Being involved in an edit war can result in your being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly.

To avoid being blocked, instead of reverting please consider using the article's talk page to work toward making a version that represents consensus among editors. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

This is the second warning: now you have done three reverts of the same text.

Have a good one David, and I hope we can keep the conversation to the math. Particularly to the needed citations. 218.187.103.34 (talk) 17:34, 14 October 2014 (UTC)

Hello! There is a DR/N request you may have interest in.

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 Done

Thomas Walker Lynch at AN/I

There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Thank you.MjolnirPants Tell me all about it. 14:36, 17 October 2014 (UTC)

Clarification needed in Greatest common divisor

Could you take a look at this sentence? --50.53.60.41 (talk) 16:39, 27 October 2014 (UTC)

I have replaced it by a link to GCD domain. I have also notified its author, Arthur Rubin. D.Lazard (talk) 17:39, 27 October 2014 (UTC)

I was worried about it being WP:OR, but http://mathworld.wolfram.com/GreatestCommonDivisor.html mentions the concept of GCD of rationals, and it's not the same. It could be extended to GCD in the fraction field of a GCD domain, but I have only seen it over the rationals. I'm on my way out, I do not have time to update GCD at the moment. Maybe tonight, around 14 hours from now. — Arthur Rubin (talk) 17:54, 27 October 2014 (UTC)

To editor Arthur Rubin: IMO this concept of GCD of rationals is WP:OR by Mathworld. As far as I know, this concept has been used only to define the content of a polynomial with rational coefficients (see Factorization of polynomials#Primitive part–content factorization). As far as I remember correctly my readings, most books and articles, which defines this notion of content, define it directly, without extending the concept of GCD of numbers. In any case, to mention this in the lead requires that it would be mentioned in a specific section. IMO this extension of the GCD is not notable enough to be included in this article, unless if it appears in The Art of Computer Programming, which is the best encyclopedic reference for this kind of questions. D.Lazard (talk) 18:37, 27 October 2014 (UTC)

Thanks. That's much better. (I am going to overlook the word "notion" in that sentence.) --50.53.60.41 (talk) 19:21, 27 October 2014 (UTC)

Polynomial Calculator External Link

Hello Sirs, Thanks for the explanation. Those software are kind of charity provided for free usage of public. I believed could be helpful promoting them in a convenient place frequented by relevant pupils and scholars. I couldn't find any other way. Regards — Preceding unsigned comment added by 86.31.47.92 (talk) 20:16, 31 October 2014 (UTC)

Copyright checks when performing AfC reviews

Hello D.Lazard. This message is part of a mass mailing to people who appear active in reviewing articles for creation submissions. First of all, thank you for taking part in this important work! I'm sorry this message is a form letter – it really was the only way I could think of to covey the issue economically. Of course, this also means that I have not looked to see whether the matter is applicable to you in particular.

The issue is in rather large numbers of copyright violations ("copyvios") making their way through AfC reviews without being detected (even when easy to check, and even when hallmarks of copyvios in the text that should have invited a check, were glaring). A second issue is the correct method of dealing with them when discovered.

If you don't do so already, I'd like to ask for your to help with this problem by taking on the practice of performing a copyvio check as the first step in any AfC review. The most basic method is to simply copy a unique but small portion of text from the draft body and run it through a search engine in quotation marks. Trying this from two different paragraphs is recommended. (If you have any question about whether the text was copied from the draft, rather than the other way around (a "backwards copyvio"), the Wayback Machine is very useful for sussing that out.)

If you do find a copyright violation, please do not decline the draft on that basis. Copyright violations need to be dealt with immediately as they may harm those whose content is being used and expose Wikipedia to potential legal liability. If the draft is substantially a copyvio, and there's no non-infringing version to revert to, please mark the page for speedy deletion right away using {{db-g12|url=URL of source}}. If there is an assertion of permission, please replace the draft article's content with {{subst:copyvio|url=URL of source}}.

Some of the more obvious indicia of a copyvio are use of the first person ("we/our/us..."), phrases like "this site", or apparent artifacts of content written for somewhere else ("top", "go to top", "next page", "click here", use of smartquotes, etc.); inappropriate tone of voice, such as an overly informal tone or a very slanted marketing voice with weasel words; including intellectual property symbols (™,®); and blocks of text being added all at once in a finished form with no misspellings or other errors.

I hope this message finds you well and thanks again you for your efforts in this area. Best regards--Fuhghettaboutit (talk) 02:20, 18 November 2014 (UTC).

       Sent via--MediaWiki message delivery (talk) 02:20, 18 November 2014 (UTC)

Math Edits: Italics with Differential Operator

I have to admit that I'm not a fan of the italicized operator, but I do appreciate you showing me the style guide. Another person appears to be going in and redoing my edits, though. (Derivative) Ushakaron (talk) 16:35, 19 November 2014 (UTC)

Sorry ushakaron but dx in Leibniz's notation is not a "differential operator" as you put it. It's an infinitesimal increment. I can quote Leibniz on that. Tkuvho (talk) 18:50, 19 November 2014 (UTC)

The mathematical nature of d is not the point here. The point is its typographical appearance. It is me who has called it, for simplicity, "differential operator" in the edit summary of my revert at Derivative. D.Lazard (talk) 19:03, 19 November 2014 (UTC)

And I'm not saying dx is a differential operator; I'm saying d is a differential operator. d takes an infinitesimal increment of its argument, in that case, x. d is the operator; x is a variable. Therefore, according to ISO regulations, the d should not be italicized. Have a look at http://www.tug.org/TUGboat/Articles/tb18-1/tb54becc.pdf Ushakaron (talk) 20:53, 19 November 2014 (UTC)

I and others are of the opinion that ISO are wrong: d, like all single Roman letter functions, should be italicized. It's the same as f or g. But ultimately this is a matter of opinion: ISO is entitled to my opinion and I'm entitled to mine. Which is why we have WP:RETAIN. Ozob (talk) 02:47, 20 November 2014 (UTC)

Well User:Ushakaron, I understand you are claiming that d is a differential operator, but you are wrong. Here dx is an infinitesimal increment not analyzable into components. Tkuvho (talk) 09:14, 20 November 2014 (UTC)

I disagree: dx means here "infinitesimal increment of the variable x". Thus, d maps a variable to an increment and behaves as an operator. D.Lazard (talk) 09:31, 20 November 2014 (UTC)

Daniel, we are talking about Leibniz's notation. Leibniz thought of dx as an nonanalyzable increment. The operator viewpoint was obviously not developed until much later. If you wish to go by modern standards, the notation ${\frac {dy}{dx}}$ is nonanalyzable: neither is it a ratio nor is an operator being applied to anything, as far as ISO standards are concerned. We are not talking modern functional analysis but rather calculus. Tkuvho (talk) 09:34, 20 November 2014 (UTC)

This discussion is silly. There's more than one viewpoint on dx. In some of them it means d applied to x and in others d has no independent meaning and only appears together with x (e.g., if dx denotes Lebesgue measure). We are all agreed, however, that the d in dx should appear in italics. Ozob (talk) 14:32, 20 November 2014 (UTC)

Concerning a problem in Jacobson's book

Is this problem #4 attributed to you? link Rschwieb (talk) 21:57, 7 January 2015 (UTC)

It is probably attributed to me, as I remember that I have worked on the relationship algebraic properties of idempotents and topological properties of open-closed subsets of the spectrum. However, I do not remember of this particular result. If I have proved it, it should appear in chapter II of my Thèse d'État (Autour de la platitude. (French) Bull. Soc. Math. France 97 1969 81–128). D.Lazard (talk) 13:22, 9 January 2015 (UTC)

Very cool :) Did you ever consider ideals I such that R/I only has trivial idempotents? It's the first thing that came to mind. I can imagine it might be a quaint but unfruitful generalization of prime ideals... Rschwieb (talk) 13:43, 9 January 2015 (UTC)

If e is an idempotent, then V(e) is open and closed in the spectrum (the spectrum is the disjoint union of V(e) and V(1−e)). It follows that R/I only has trivial idempotents if and only if it spectrum is connected; that is this is the case if it only has one minimal prime. In other words, R/I only has trivial idempotents if and only if the radical of I is prime. If R is a polynomial ring, one may consider the graph defined on the set of the irreducible components of the algebraic set defined by I, by the relation "having a non empty intersection". Then R/I only has trivial idempotents if and only this graph is connected. If R = k[x, y, z], and the Krull dimension of R/I is one, then, generically, the irreducible idempotents of R/I correspond to the irreducible components of the algebraic set defined by I, but this is not always the case. D.Lazard (talk) 14:35, 9 January 2015 (UTC)

Saqi Books

The subject article was PRODed by yourself - it has been restored as a contested PROD. You may wish to consider WP:AfD in the light of this result. Ronhjones  ^(Talk) 00:15, 30 January 2015 (UTC)

Thanks!

		The Disambiguator's Barnstar
		For helping out with the tricky math-related disambigs. JaGatalk 01:51, 8 February 2015 (UTC)

Personal attacks by Purgatorio

You removed two remarks refering to one person which I made in the talk page of natural numbers. I concede, that both are not the most friendly kind, but their reason is a definitely more unfriendly one. I accept that the second remark is not factually based, but derived from repeated behaviour and indirectly from the method of argueing. So I assure you my regret for this one. The other one, however is a factual claim in which this person is involved as agent. I furthermore concede that the adverb brutally might be considered offensive, so I left it out of my citation in my edit of this talk page.

I do not know this person, I am in no way interested in battling around, but unluckily he really caught my eye by chance because he is involved in more than this case of reverting edits (I'm not talking of my negligibilities) by simple non-arguments. I do not consider it advantageous for the quality of Wikipedia to strengthen this not-invented-here syndrome.

Being bold against these guys is impossible! Best regards, Purgy (talk) 12:26, 27 February 2015 (UTC)

Purgy Purgatorio, please read (or read again) the lead of WP:No personal attack, and, specifically the first line: "Do not make personal attacks anywhere in Wikipedia. Comment on content, not on the contributor." If you are not happy with the behavior of an editor, the talk page is not the place to complain, the page WP:ANI is devoted for this. However, in this case Rick Norwood's, behavior is perfectly correct and respectful of all rules of Wikipedia, and I am pretty sure that the administrators will agree with me. D.Lazard (talk) 13:58, 27 February 2015 (UTC)

I want to point to the fact that I admitted personal atttack wrt the my second remark you edited and that I stated my regret for this (just above!). So I do not get it, why you made explicit the one word in the first remark which possibly could be considered offensive and which I explicitely did not cite and also made visible again the attacking phrase of the second remark.

I'm rather clueless, even after reading WP:No personal attack. Purgy (talk) 18:20, 27 February 2015 (UTC)

My Thanks Too!

I was up late all last night night writing, rewriting, and fretting over how I should (and did) word the bit about matrices and polynomials of a standard basis, and I eventually got so tired I had to quit and just submit the thing. Then I noticed overcomplications and other things wrong, and made a couple more edits.

Finally, I just had to give up, because I was too tired to keep working. I figured someone might come along and work on it further before I got back to it, and sure enough, you did. But I thought it would probably just be deleted (and my work wasted) because the way I put it didn't exactly fit well with the later generalizatinons.

I was wrong; you fixed it, and did an great job. I was so happy with your work that I decided to track down who did it (I usually don't bother), and I was just going to leave a short word of thanks but I couldn't help noticing the carefully chosen barnstar someone else gave you above.

I've never given a barnstar, partly because I just couldn't be bothered to spend the time picking an appropriate one. And frankly, I thought it was kind of silly. But I am so pleased with your work, I decided to do it: I picked the "original", since this is the first I've given. Here you go:

		The Original Barnstar
		for your absolutely beautiful work, which saved my disjointed hours-long work on standard basis

Thanks again, and have a wonderful day. (The code for this picture, by the way, was adapted from the box in WP:SPIDER, which is a quite humorous "policy in a nutshell" page—be sure to take a close look at the nut!—I happened to be reading at about this time. If you haven't seen it yet, I strongly suggest you do take a look...) --BlueGuy213 (talk) 14:09, 18 March 2015 (UTC)

And sorry for the several spelling and grammatical errors here too. I see them now, but I didn't notice them in the previews before I submitted. I didn't sleep much last night either... Anyhow, good day! BlueGuy213 (talk) 14:26, 18 March 2015 (UTC)

Isaac Asimov

Hi Daniel, I agree with your recent revert at point (geometry), but not for the reason you gave. While Isaac Asimov was primarily known as a science fiction author, he was a bit of a polymath and wrote a large number of non-fiction books in science and literature. These included at least two popularizations of elementary mathematics topics, Realm of Algebra and Asimov on Numbers that I am aware of. Bill Cherowitzo (talk) 18:37, 24 April 2015 (UTC)

To editor Wcherowi: I was aware of this aspect of Asimov works, and I would not have reverted a simple reference to him. But my edit summary was the best way that I have found for saying, in a short sentence, that emphasizing on "science fiction writer" is misplaced in this article. D.Lazard (talk) 21:01, 24 April 2015 (UTC)

An effort to understand your viewpoint

May I ask you a question? I'm trying to understand why the 0^0 conflict is so irresolvable. Different participants appear to have fundamentally different ideas on what formulas mean and how they should be interpreted. Suppose we are working over R, a commutative ring with identity. How do you read the binomial theorem?

$(x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}$

(a) x,y are place-holders, they can refer to any element of R

or

(b) the binomial theorem is not a formula that holds inside R, rather, it holds in the polynomial ring R[x,y]. In this ring, x is a non-zero polynomial and x^0 = 1. Substituting values for x,y is only OK after each x^0, y^0, (x+y)^0 have been replaced by 1

or

(c) some other interpretation.

Thanks in advance for your response. MvH (talk) 13:08, 29 April 2015 (UTC)MvH

To editor MvH: IMO the interpretation depends on the context. I would interpret interpretation (a) as an equality between functions from R to R (such an equality of functions is also called an identity, although I find this terminology old fashioned). Interpretation (b) is also valid; it should even be preferred to (a), as being stronger (in finite characteristic, the equality of two polynomial functions does not implies the equality of the polynomials). However, if one replaces "function from R to R" by "function from any ring containing R to itself", (a) and (b) becomes equivalent, as the polynomial functions are defined by substitution of the indeterminates.

However, for evaluating correctly the result, one requires a convention: either the convention that 0⁰ = 1 as soon as the exponents are restricted to non-negative integers (or more precisely to cardinal numbers) or the rule that substituting values and expanding the sum do not commute, and that sum expansion must be done before substitution. This evaluation rule is then usefully completed by the convention that substituting x by 0 in x⁰ gives 1.

My opinion is that we have here an example of a general problem that has been underestimated by mathematicians and becomes fundamental in computer algebra: that is well specifying the rules for transforming and simplifying formulas. It appears that most errors occurring when using a computer algebra system do not come from the computer algebra system, but from a misuse of simplification/evaluation rules. D.Lazard (talk) 14:58, 29 April 2015 (UTC)

To editor D.Lazard: In your interpretation of (a), the equality = in the above formula is then not an equality between elements of the set R, rather, it is an equality between elements of the set R^R. What if I wrote the equation explicitly as an equation between elements of R, with n a positive integer, would you then consider it to be a valid theorem, or invalid, or only valid in certain contexts? Here R is still a commutative ring with identity.

$\forall _{n\in \{1,2,\ldots \}}\forall _{x,y\in R}\ \ (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}$.

PS. I'm wondering if part of the reason we have not spelled out the rules for transformations is that perhaps we don't agree on what these rules are! And once we have found an internally consistent set of rules, and have successfully used them for a long time, it becomes very hard to imagine that other viewpoints might be internally consistent as well. MvH (talk) 16:29, 29 April 2015 (UTC)MvH

This is a valid theorem, as soon as one has defined the exponentiation with non negative exponent in a ring (that is x⁰ = 1, and xⁿ⁺¹ = x·xⁿ).

I have to apologize that I have not be clear that I did consider the point of view of the standard user (if this make sence) which is not customized with formal logic nor with working in a well specified structure. Such a user works with expressions, not with well-formed formulas, and may ignore that the meaning of a formula may depend on the nature of the objects represented by the variables. This is the context of my answer to Bo Jacoby. I tried to identify exactly his misconception and to make explicit where he is wrong. D.Lazard (talk) 17:44, 29 April 2015 (UTC)

To editor D.Lazard: Another thing I do not know is what exactly is meant by "context" and "nature of the objects". I have only one interpretation for these phrases but I think you mean something else. To start with an example, suppose someone says: "the meaning of the + symbol depends on the context", then I would agree with that, but I have only one interpretation for what that statement could mean, namely "the meaning of the + symbol depends on the choice of an additive group/monoid". But once it is clear which additive group has been selected, and one still uses a phrase like "depending on the context", then I no longer have an interpretation for that. So in this view, saying that "over the integers, 0^0 is 1 in some contexts" means the same as saying "over the integers, 0^0 is 1 in all contexts", because I have no idea what different "contexts" could mean after we've already selected the domain/field/ring/module/group/etc. MvH (talk) 20:05, 29 April 2015 (UTC)MvH

Here is one important "context": in complex analysis, $x^{y}$ is defined as an abbreviation for $\exp(y\log x)$ for all complex numbers (and for some branch of the logarithm). That definition makes $0^{0}$ undefined, because $\log 0$ is undefined. Complex exponentiation is, formally, an entirely different operation than natural number exponentiation, even though it is written with the same notation. So only context determines whether the expression $0^{0}$ indicates a natural number exponentiation or a complex exponentiation. But that choice makes a huge difference in trying to compute the value of $0^{0}$.

A key confusion of certain participants on the exponentiation talk page is that they are not comfortable with the idea that $0^{0}$ has a different definition when we think of 0 as a complex number than it does if we think of 0 as a natural number. A similar phenomenon happens, for example, if we compute $2^{-1}$ in $\mathbb {Q}$, $\mathbb {Z} _{5}$, $\mathbb {Z} _{7}$, and $\mathbb {Z} _{8}$, and find it has values 1/2, 3, 4, and "undefined", respectively. — Carl (CBM · talk) 01:22, 30 April 2015 (UTC)

Carl, I don't mean to be rude, but I'm really interested in Lazard's view. That's why I posted the question on his page. MvH (talk) 03:31, 30 April 2015 (UTC)MvH

For defining context, one needs a bit of epistemology: By considering the history of 20th century mathematics (before 20th century, mathematics were not clearly distinguished from their applications), it appears that a mathematical result, theory of concept is considered (by the mathematical community) as interesting only when it is used outside the theory in which it has been developed, the most interesting results being those that can be applied/used in various areas of mathematics, or may be studied from various point of views (this is a personal opinion, elaborated by observing the judgments of good mathematicians about other's work). For me the "context" is the framework in which a concept is used. When a mathematical concept is used, it is very common to not specify it completely. For example, variables are commonly used to represent numbers, but it is rarely specified if they are complex, real, rational or integers. The reason is that, when this is not specified, the reader may choose the domain of the variable as he want. Another example is the "operators" that appear in quantum theory: it is rarely specified on which space they operate. When I was a young mathematician, this made quantum theory very difficult for me to be understood. In our case, exponentiation occurs in essentially two contexts: in algebra and discrete mathematics, the exponents are (often implicitly) restricted to integers, and it is easy to define the exponentiation as binary operation with a first argument belonging to any ring and the second argument being a natural integer. In this context, it is natural to define 0⁰ as 1, as this follows immediately from the recursive definition of the exponentiation.

On the other hand, in calculus and engineering applications, exponents are often continuous functions. In such a context, as functions are generally continuous, it is common, for computing limits, to substitute the variables by their limit values. This works almost always, and the cases where this does not works are easily detected as indeterminate forms (here "indeterminate" does not means "undefined", but rather "unspecified"), such as 0/0, 0⁰, 0·∞, ... As this method for computing limits is fundamental, given a specific value to 0⁰ in case of continuous exponents is error prone.

By the way, in some of your posts you wrote that the norm IEEE754 defines 0⁰ as 1. This is true only if the exponent has the data type "integer" (function "pown"). On the other hand , if the exponent is of type float (real), this is the function "powr" that is applied, which results in NaN (Not a Number). In other words, the authors of the norm (which are good mathematicians) say essentially the same as above. D.Lazard (talk) 14:31, 30 April 2015 (UTC)

You mentioned the difficulties in the use of transformations in regards to computer algebra systems, which may also indicate a problem of ambiguous notation. For some in the 0^0 debate, the 0 is an exact zero, whereas for others, it may also represent an approximate 0. Then a problem arises that we don't have a widely used symbol to distinguish the two. Maple distinguishes them as follows 0 = exact zero, while 0.0 = approximate zero. It evaluates 0^0 as 1, and evaluates 0.0^0.0 as Float(undefined). Both of these are excellent choices, and both are IEEE compliant (Maple goes wrong when you type 0^x though, which is unfortunate because it makes it impossible to implement certain formulas from combinatorics without first implementing a my_pow program). Lacking different symbols for exact and approximate zeros, like Maple has, is bound to cause conflicts when some insist that 0 can denote only an exact zero, and others insist it can denote both.

In other math conflicts (e.g. 0.9999 or Russell's paradox), the problem doesn't go away until the foundations are defined with more rigor. The way I check if an argument is rigorous is by seeing if it can be reduced (at least in principle, in practice it'd be a long path!) to the axioms of set theory. Natural numbers can be constructed from sets (or by some other means), then construct the integers/rationals/reals as sets mod an equivalence relation, etc. There are computer algebra systems that have attempted this type of rigor. But there are also drawbacks, sometimes you just want to type something without going through the effort of defining everything. This convenience comes at a price, we may want the computer to simplify ln(x^5) to 5ln(x) but what if the user hasn't specified the context? (to be precise: the domain of the function denoted by ln). Functions with different domains are really different functions, confusingly denoted by the same name: ln. How then is Maple to know if ln(x^5) to 5ln(x) is a valid step? The 0^0 question appears to be intractable now, but it might be less controversial when there is more clarity about the meaning of the expressions. MvH (talk) 16:41, 30 April 2015 (UTC)MvH

PS. [not so important for the discussion:] Your line: "This works almost always, and the cases where this does not works are easily detected as indeterminate forms". Instead of "indeterminate forms", I would instead say: "discontinuous functions". The list of indeterminate forms is not the full list of problematic limits. That list is simply "discontinuous functions. It is a defining characteristic of continuous functions that the function commutes with limits. I think the usefulness of the phrase "indeterminate form" is only temporary; before continuous functions are defined/understood. MvH (talk) 16:52, 30 April 2015 (UTC)MvH

To editor D.Lazard: When you write this "the most interesting results being those that can be applied/used in various areas of mathematics". In your view, the different areas of math are not part of one large unified framework? (e.g if someone attempts to put everything together under one framework, say under set theory or category theory, this wouldn't really represent how you view math?). To look at it in another way, when a theorem is proved in one area of math, this doesn't necessarily make it a theorem that's valid to all areas of math? (at least, those where it can be interpreted). This way, you are able accept the binomial theorem as fact, even accept 0^0=1 as fact, without accepting it as a universal fact. (In contrast, my view is: r^0 = 1 for any r in any commutative ring with 1 is a corollary of the binomial theorem, but also follows directly from the definition written in its simplest form. The reals form a commutative ring with 1, so it holds there too, and context-arguments are rejected since they appear ambiguous if you view all of math under one foundation. But if there is not one foundation of all of math, things can look different). MvH (talk) 17:45, 30 April 2015 (UTC)MvH

The fact that there exist a common foundation for all mathematics (for example Zermelo–Fraenkel set theory) does not implies that methods and point of views (that is framework) may differ depending on areas of mathematics (consider, for example algebraic number theory and analytic number theory). A theorem proved in an area of mathematics is true in all mathematics. However an important theorem may hardly reduced to its formal statement (computer scientists would say its syntax). Its meaning (computer scientists would say its semantic) is also important, and this may often be expressed in various points of view. My favorite example is Riemann–Roch theorem which is stated and proved in completely different ways in algebraic theory and in topology. However, the two statements become equivalent if one consider an algebraic curve that is also a Riemann surface. This is the reason for which the two seemingly different theorems share the same name. Please do not forget that foundations have been developed to insure the correctness of the practice of mathematicians, and there there several possible foundations that on most mathematics may be build. For example most formal proofs, such as that of Feit–Thompson theorem, are not based on Zermelo—Fraenkel, but on an intuitionist logic.

Does such a proof automatically imply that the same result is also provable in ZF(C)? (although I haven't checked this, I thought it is true that if a result can be stated in ZFC, and can be proven using category theory, then it can also be proven in ZFC) (In other words: if a proof is nicer in category theory, then use that, if it is nicer in ZFC, then use that, either way, it can be accepted as proven in ZFC).

PS. Your Riemann-Roch example put a smile on my face, it reminds me how beautiful math can be. Say you want to know the genus of X, and decide to ask an algebraist and a topologist. The algebraist did a completely different computation than the topologist, and yet they come up with the same number. Even though we should expect this when we wear our "professional mathematicians hat", deep down it's really quite astonishing if you think about it. The only difference we might expect in their e-mails is that one of them is likely write "algebraic curve" and the other one is more likely to say "Riemann surface". Such is the beauty of math that some statements can still be surprising even after we checked the proof! MvH (talk) 20:59, 30 April 2015 (UTC)MvH

For the problem of 0⁰, you are wrong is asserting "Instead of "indeterminate forms", I would instead say: "discontinuous functions"". Because of the theorem: "Let f be a function that is built up from the usual elementary functions. The limit at a of f is f(a) if the computation of f(a) does not involves any indeterminate form. If an indeterminate form is involved, other methods are required to decide if the limit exists, and to compute it." That is indeterminate forms are the basic tool for finding discontinuities. D.Lazard (talk) 19:32, 30 April 2015 (UTC)

Ker T

You reverted my change from double quotes to italics, writing "... italics cannot be used here..." -- but why not?

The current version looks terrible, just as it did before. The "T" looks like a "7".

If italics cannot be used, it would be better to write ker T in a different font, or even without any quoting mechanism at all. No one -- and I mean no one -- will be confused by that. Dratman (talk) 00:11, 21 May 2015 (UTC)

To editor Dratman: I have replaced the quotes by the template {{math}}, which uses a serif font. D.Lazard (talk) 02:53, 21 May 2015 (UTC)

Much better Dratman (talk) 12:54, 21 May 2015 (UTC)

Fix to Extended E. Algorithm.

Hi, You reverted me on that one. I think the current formulation is wrong--the example is pretty clearly using the q from the same line as it is updating (i+1). Could you take a look again? If I'm missing something, that's fine, but I don't see what I could be missing there. Thanks. 141.212.111.127 (talk) 21:28, 26 May 2015 (UTC)

To editor 141.212.111.127: In the example, the index of q, in the row i is not i, it is i – 1, as noted in the top row. Thus, except for a shift of one in the indexes, the notation in the description is the same as in the example. However, the description is somewhat ambiguous, and I have edited it for clarification. D.Lazard (talk) 07:56, 27 May 2015 (UTC)

Ah, missed the fact that the column is labelled as q_i-1 not q_i. Certainly less than clear, but got it now. Thanks. 141.212.111.127 (talk) 19:06, 27 May 2015 (UTC)

Fix to Gaussian integer

I wish there was an quicker way to say thanks for catching that! 71.41.210.146 (talk) 23:49, 29 May 2015 (UTC)

Iterative algorithm in Exponentiation by squaring is wrong

Your change to the algorithm I'd added seems to be wrong. Try n=2 for example, it seem to produce x*x*x as answer instead of x*x. I also believe, my original version is much more readable for a novice while being similarly performant. Unless you have any objection to my original version, could you please revert it back to that one? — Preceding unsigned comment added by Sytelus (talk • contribs) 01:28, 10 June 2015 (UTC)

To editor Sytelus: I have fixed (I hope) the iterative algorithm. I have not reverted to your version for two reasons. Firstly, for having the same variable names in all the algorithms; this allows to see easily that the tail recursive version and the iterative version do the same computation, in the same order. Secondly, it is unhelpful to test the parity of n – 1 when n is odd. Finally, I do not agree that your original version is more readable for a novice: it contains two nested while loops, which makes it difficult to understand for a novice. D.Lazard (talk) 08:29, 10 June 2015 (UTC)

There is still problem with this line if n = 0 then return x. For x^0 = 1. For full correctness, 0^0 should be thrown as error. — Preceding unsigned comment added by Sytelus (talk • contribs) 11:34, 10 June 2015 (UTC)

Thanks, I have fixed it. "For full correctness": For integer exponents, the correct value of 0^0 is 1. See Exponentiation § Zero to the power of zero and the specification of "pown" in the norm IEEE754. D.Lazard (talk) 14:16, 10 June 2015 (UTC)

Turing thesis

I don't edit so much anymore, and I don't plan to undo your edit, but on the Turing thesis article, the key to Turing's conception of computability was indeed the idea of a human working algorithmically with pencil and paper. Indeed, the key point of Turing's 1936 paper [6] was section 9, where he analyzed the work of a human computer (at the time, "computer" referred to a human doing computing), and argued that any algorithm that could be computed by a human could be computed by a Turing machine. The key reason that Turing machines are of interest, compared to other models such as Church's λ calculus, is that Turing machines allowed Turing to make this philosophical argument (referring to "states of mind", etc.) that his formal notion of computable functions captured all the functions that a human could algorithmically compute. Without that argument, Turing would not have been able to claim a solution to the Entscheidungsproblem, which is about human, rather than mechanical, computation. — Carl (CBM · talk) 01:34, 20 June 2015 (UTC)

To editor CBM:: I think that we are both right (or both wrong). In fact, as it is frequently the case for mathematical breakthroughs, one has to distinguish between the (philosophical ?) interpretation of the result by the original authors, and the present scientific status of the same result. What I have tried to explain is what is called "Church–Turing thesis" in modern textbooks on computability, a subarea of computer science. It is clear that the modern point of view on the thesis is not the same as that of Turing, which, itself may differ from that of Church. Nevertheless, the use of the word "machine" by Turing shows that the mechanical aspect of computability was present in his though. I'll look on Turing paper to try to find a formulation that is compatible with both original Turing thought and the modern concept of Church–Turing thesis. D.Lazard (talk) 04:44, 20 June 2015 (UTC)

What I was stating is the modern interpretation of the result; I work in computability theory myself. The Stanford Encyclopedia article [7] treats "mechanical" and "effective" as synonyms, and defines them in terms of a human with pencil and paper. That article spends significant space on the difference between Turing's thesis that Turing machines capture all algorithmic human computation, and the stronger thesis that Turing machines capture all machine computation. I would also recommend section 3 of Soare's well known paper Computability and Recursion [8]. — Carl (CBM · talk) 12:35, 20 June 2015 (UTC)

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Send on behalf of The Wikipedia Library using MediaWiki message delivery (talk) 04:31, 7 July 2015 (UTC)

Opened a dispute resolution request for the Oder of a polynomial article

I've opened a dispute resolution request for the Order of a polynomial edit dispute you're trying to start. Please contribute to the discussion in Wikipedia:Dispute resolution noticeboard#Talk:Order of a polynomial.23Disambiguating -- Mecanismo | Talk 15:20, 21 August 2015 (UTC)

Addition (Code)

Hey there. The point of the code is to show how addition is implemented in C code in a manner that is representitive of what is going on in hardware (i.e. using AND and XOR bitwise manipulations). In my original edit, I had an "as shown below" comment on this in the text, but it looks like it was deleted by another user which put the code example out of context. I have added this so it reads:

"In practice, comutational addition may achieved via XOR and AND bitwise logical operations in conjunction with bitshift operations as outlined in the C code below. "

I think it is perhaps interesting for people to see how addition is actually implemented both in software and in hardware (i.e. unrevelling the + operator). This is really basic computer science which I feel gives value to the article as it shows a critial link between software and hardware (without going into assembly). — Preceding unsigned comment added by Mwchalmers (talk • contribs) 14:59, 16 September 2015 (UTC) --Mwchalmers (talk) 15:07, 16 September 2015 (UTC)

To editor Mwchalmers: Please put new sections in talk page at bottom (or use "New section" button at the top of the page. Also, please your posts with four tilde (~~~~).

I have answered in advance on Talk: Addition#addition on computers

Bitwise addition in never implemented in software (except, may be, as exercise for beginners), as hardware addition is dramatically faster.

The algorithm, not the C code, may be interesting here. The Wikipedia guidelines (see MOS:CODE and MOS:ALGO) ask to write algorithms in pseudo-code, not in any specific programming language. This is specially worth here, as bitwise addition is never programmed in any programming language (except by software for designing hardware, that may be viewed as programming languages compiled into hardware). So, please, rewrite the algorithm in pseudo-code, instead of reverting. D.Lazard (talk) 15:59, 16 September 2015 (UTC)

I see your point in going with pseudocode, as the algorithm, not the C, is what is interesting here. I have written some pseudocode with comments which works well with the full-adder circuit shown in the section. I think it really adds to the section to have a pseudocode as people often associate code with computing. It is nice to provide some intuitive link between how an algorithm in code and an algoritm in hardware. I have also labeled the carry specifically as well as where the XOR and AND operations appear in the code. I have included both the iterative and recursive versions, which is interesting in itself as it implies a connection between iteration and recursion. Feel free to make changes to the pseudocode if you think it is still too C-like or the comments are too sparse. Somehow it should be clear that integer addition is implied. Mwchalmers (talk) 10:31, 17 September 2015 (UTC)

Integers, mentioning positive integers

Hi, how are you? Hope everything is great. I think that more people should edit about this subject so let's check if someone else agrees with you. I think that expanding information may be helpful for the reader. Some reader have no other access to knowledge then wikipedia. So I think it is better to provide too much information than a missing information Cheers for your involvement! — Preceding unsigned comment added by 37.142.195.135 (talk) 14:24, 11 October 2015 (UTC)

To editor 37.142.195.135: Please, sign your posts in talk page with four tildes ([[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard#top|talk]]) 14:59, 11 October 2015 (UTC)), and put them at bottom (for this it is easier by using the button "New section" at top of the page)

I agree that too much information is better than too few, but missing information is better than wrong information. Your edit was wrong in two aspects: Firstly, the natural numbers and the positive integers integers are not groups. Secondly, you assume that zero is not a natural number, which is a rather common convention but is not more common than the convention that zero is a natural number. This is discussed in the article Natural number. As Natural number is linked in the second paragraph of the lead, it is not useful to repeat this discussion here. Finally, the assertion that the positive integers and the natural numbers are included in the integers is already in the second paragraph of the lead. It is not useful to repeat it at the end of the lead.

Finally, you must be aware that when someone's edit has been reverted, Wikipedia rule is to discuss in the talk page and to keep the older version until a consensus is obtained (see WP:BRD). Starting an edit war, as you do, may cause that you may be blocked for editing. D.Lazard (talk) 14:59, 11 October 2015 (UTC)

October 2015

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Sorry about that

Appreciate you picking up my misunderstanding on the wikilink change I made to point to the wrong lattice article! - Letsbefiends (talk) 18:48, 29 October 2015 (UTC) Letsbefiends (talk) 18:48, 29 October 2015 (UTC)

Self-contradicting sentences.

Comments and reverted edits to Extended Euclidean algorithm

I don't understand the auto-reply from TW:

"This does improve the article. In particular, this is not a good idea to mix the description and the proof of an algorithm."

- seems to be contradictive. If it DOES improve  ... - why is it (the proposals - edits) deleted by reverting?  

--

For hardcore mathematicians, you may get away with implicit notation. In descriptions and proofs based on mixed mathematical formulas and English wordings, a few additional words may enhance the readability for less experienced people, that actually want to learn more on the subjects in question. That was the reason ("to learn") for my visit on this Wiki topic. The edits should serve to broaden the understanding.

Examples of reverted edits in the description section: Differences [9]

... of decreasing remainders such .... 

- what is wrong with the descriptive word decreasing? If we implicitly assume that Euclid only knew $\mathbb {N} _{0}$ then $r_{i}$ is strictly decreasing for each iteration.

WikiBC (talk) 22:34, 7 November 2015 (UTC)

To editor WikiBC: OK, I have written too quickly the edit summary, and I have omitted "not" after "does". About the reverted edits, I have to say that, when several edits are done in a row, it is much less time consuming to revert them all than editing in detail. Here, I would probably not have reverted "decreasing" if added alone. However, although correct, I find it slightly confusing, as emphasizing on the proof of Euclidean algorithm, which is out of scope here. The second reverted edit amounts also to explain why standard Euclidean algorithm works, which is out of scope in an article about the extended Euclidean algorithm. It also introduces the notation "gcd(.,.)", which is unnecessary and may be confusing. Your third edit does not improve the article either, as introducing the greatest common divisor of r_k, which is not standardly defined. Thus none of your three edits improve the article. D.Lazard (talk) 10:31, 8 November 2015 (UTC)

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Locus (mathematics)

Hi. You have reverted my edit in Locus (mathematics) in section Commonly studied loci because :

"Mandelbrot set is not commomly called a locus. "connectedness locus" seems a neologism. " 

but my edit was :

the most famous connectedness locus is the Mandelbrot set

I didn't said that it is commonly called. I do not agree with you. See google results : 3 510

so I have reverted your edit. --Adam majewski (talk) 20:58, 23 December 2015 (UTC)

I'll reply in the talk page of Locus_(mathematics). D.Lazard (talk) 21:29, 23 December 2015 (UTC)

Rather, I have edited the article for wikifying the reverted edit. I have also expanded the lead. D.Lazard (talk) 12:15, 24 December 2015 (UTC)

OK. Thx.. Regards--Adam majewski (talk) 16:28, 28 December 2015 (UTC)

unicritical polynomial

Hi. You have reverted my edit about unicritical polynomial because :

• uncommon terminology. Can you check google. Second link  : http://arxiv.org/abs/1203.5447 by Milnor. Is it uncommon ? I do not agree with you.
• Unsourced. Ok, but you can add source or ask me to do it but not revert.

--Adam majewski (talk) 20:31, 23 December 2015 (UTC)

To editor Adam majewski: The source that you provide shows

1. it is not the polynomial that is qualified as unicritical, but the map.
2. this terminology is used in the study of dynamical systems, but this does not show that it is used elsewhere.

Moreover this is a primary source. Wikipedia policy asserts that, in such a case, secondary sources must be provided for establishing that the terminology is notable enough to be mentioned in WP. Also, Wikipedia policy of WP:BRD says that if your edit is reverted, it is to you to open a discussion in the talk page for trying to search a consensus.

For the moment, as far as I know

1. the terminology seems to not be notable enough for Wikipedia
2. if it will be shown to be notable, it seems that is does not deserve to appear in the article Polynomial, but rather in Dynamical system, or in a section of Polynomial devoted to polynomials in dynamical systems.
3. In any case, this terminology has nothing to do in the general definition of a polynomial

D.Lazard (talk) 21:26, 23 December 2015 (UTC)

Your explanatin sounds clear and logical. Maybe a beter place for unicritical polynomial would be :

• a new section : polynomial as a map in dynamical systems
• see also section with to the link unicritical polynomial

What do you think ? --Adam majewski (talk) 16:33, 28 December 2015 (UTC)

nonlinear systems

http://www.cns.gatech.edu/courses/index.html now, this institute is about nonlinear science. and yet it offers courses on nonlinear physics. what is nonlinear physics concerned with? right: nonlinear systems. the abovementioned article has a foreword that says: This article is about "nonlinearity" in mathematics, physics and other sciences. nonlinear science redirects there. would you like to rethink your statement about the ulam quote not belonging here? oh, and i ref-d it. -- Kku 22:31, 10 February 2016 (UTC)

Edit warring at Fundamental theorem of calculus

Your recent editing history at Fundamental theorem of calculus shows that you are currently engaged in an edit war. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the article's talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See BRD for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

Being involved in an edit war can result in your being blocked from editing—especially if you violate the three-revert rule, which states that an editor must not perform more than three reverts on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring—even if you don't violate the three-revert rule—should your behavior indicate that you intend to continue reverting repeatedly. You've now hit three reverts, please stop and discuss further. Thank you -- samtar ^{talk or stalk} 19:21, 24 February 2016 (UTC)

// LOL. This is what happens when admins act like bots. OverLordGoldDragon (talk) 19:25, 24 February 2016 (UTC)OverLordGoldDragon

"Edit-blocked"

And why is that? I've been advised to "proceed boldly" by user "samtar" (https://en.wikipedia.org/wiki/User:Samtar) if no response is made within 3 days. A week has passed - no response has been made. What "consensus" can be reached if the other party does not respond? None. I thereby re-insert my edit.

OverLordGoldDragon (talk) 18:57, 24 February 2016 (UTC)OverLordGoldDragon

To editor OverLordGoldDragon:: You have been advised on your talk page and in revert summaries that before reinserting your change, you must wait a consensus on the talk page of the article. I see on Talk:Fundamental theorem of calculus that you have not participated to the discussion there, and that there is a consensus against your edits. Thus you are wrong by writing that there are no response: there are several posts showing that your edits are wrong. You may not invoke the WP:BRD process for being bold, as several different editors have reverted your edits. D.Lazard (talk) 19:13, 24 February 2016 (UTC)

(edit conflict) To clarify OverLordGoldDragon, I stated you may boldly re-add the content if you received no replies or objections. However, this isn't the case, and once you've boldly done an action, and someone reverts it you need to discuss any further changes and not edit war. You have both now reverted three times, so I suggest taking this to the article's talk page and try to reach some sort of consensus. Thank you -- samtar ^{talk or stalk} 19:27, 24 February 2016 (UTC)

To editor D.Lazard:: You are correct. I have not received a notification of the Talk page being updated, thereby missing the response. I will stop editing the page at this time. OverLordGoldDragon (talk)

Order of approximation

Thank you. Now better. I also thought of adding a short section at the end where some "real life" historic examples would be just mentioned. This might include: (1) How Boltzmann wrote a beautiful equation of any vessel, from small to as big as the whole Universe, and to do sth with it used the first order Taylor's approximation; (2) a link to mass-energy equivalence that would show why Einstein insisted that E= mc2 was an approximation; (3) how Planck used what he called first order Stirling's formula which greatly helped him to kick off the idea of energy elements. I think some examples would match here. What do you think?C. Trifle (talk) 21:15, 19 March 2016 (UTC)

To editor C. Trifle: These examples could be useful, if not too technical for this article. However, this article is almost a stub (and as multiple issues) and deserves to be expanded in various directions. Firstly it is at the interface of physics and mathematics, although this is not clear from its categories nor from its content that appears as statistics oriented. More precisely, "computing at order n" is an informal way that is commonly used in physics for describing operations that may be formalized at the cost of some boring work. This needs to be explained here, although it is not easy to do this in a way that is convenient for both physicists and mathematicians. Secondly, the arithmetic of orders of approximation is lacking (that is properties such as "the nth approximation of the product of the nth approximations of two functions is an nth approximation of their product). These are two directions in which the article could be improved, but there are many others. D.Lazard (talk) 10:02, 20 March 2016 (UTC)

Polynomial

I'm not a mathemician, but to me that is a superb article. Only "B" quality classification? Tony (talk) 12:05, 6 June 2016 (UTC)

Thanks, although I am not the main editor of this article. About the rating, usually, I don't care of it. So I am not a good juge for it. D.Lazard (talk) 12:46, 6 June 2016 (UTC)

high dimensional space anchor

What I'm trying to achieve is encoding more precisely where the information is. Consider the effect for tools like 'word2vec' extended to work on wikipedia pages & links. and whatever other possibilities appear in future with tooling. automatic translation hints .. Surely the more precisely definitions and concepts are linked, the better? — Preceding unsigned comment added by Fmadd (talk • contribs) 14:47, 14 June 2016‎

To editor Fmadd: Please, sign your posts in talk page with four tildes (~~~~)

I don't understand what you mean with 'word2vec'. If it is a specific navigation tool, that you want to extend to wikipedia, that is the word2vec developer to adapt the tool to WP structure, and not the converse. The reason is evident: there are too many navigation tools. In Wikipedia, the standard use of anchors is for linking to a part of a section (see Help:Link#Linking to part of a section). For making clear where is the linked term, the common usage is to write it in boldface (see WP:R#PLA). As WP:wikipedia is not a dictionary, and is devised for human readers (rather than machine tools), there is no tool for delimiting the linked information. This is often meaningless, as in many cases, the linked information covers a large part of the article. D.Lazard (talk) 15:36, 14 June 2016 (UTC)

machine tools can improve rapidly IF given labelled data. I'm extremely surprised that so people in the wikipedia community seem opposed to increasing it's value to machine tools in this obvious way. Currently machine translation is highly erroneous, right? but the more accurately terms are defined (the more hints we give machines), the quicker we're going to move to a world where (i) language barriers don't matter, and (ii) where machines can answer plain text queries, and so on. Machine tools rely on labelling. wikipedia is large body of text available to researchers with this excellent labelling mechanism, which could deliver more. "build and they will come". word2vec generates 'word embeddings' that give surprising useful results, which increase the ability of machines to process text with neural nets. The tool could be adapted to use wiki links as single 'words' (i.e. generating an embedding for each page) - the more accurate a location defines a concept the better. Fmadd (talk) 15:53, 14 June 2016 (UTC)

"I'm extremely surprised that so people in the wikipedia community seem opposed to increasing it's value to machine tools in this obvious way." I do not think that the wikipedia community is opposed to anything which is useful. However the work of building an encyclopedia is huge, and there is hardly a sufficient number of editors for maintaining the good articles and improving the numerous bad articles. You cannot ask them to spent their time for a task that is not the primary objective of Wikipedia. I suggest you writing a template {{definition|anchor name|text of definition}}, and trying to convince the community of creating it and using it (that is placing it around the text of the target definition). You will probably better to ask the question, and/or to start a discussion about this at WP:Village pump. D.Lazard (talk) 16:56, 14 June 2016 (UTC)

Ctg

Hi! Ctg does redirect to Trigonometric functions but CTG does not WhisperToMe (talk) 15:46, 2 July 2016 (UTC)

BTW I got "Ctg" from "Luxury train hits Dhaka-Ctg route" WhisperToMe (talk) 15:48, 2 July 2016 (UTC)

To editor WhisperToMe: Ok, I'll reinsert the template in the target section. D.Lazard (talk) 17:14, 2 July 2016 (UTC)

Chinese Remainder Theorem

Hello Mr Lazard -- thank you for you message on my talk page. I'm not sure how editors proceed when they need to discuss something like my draft of a new section for the CRT: On my talk page? on yours? by e-mail? on the CRT talk page? I was hoping more than one party might be interested to comment on my draft -- but maybe they're waiting for your comments first? I take it the CRT page was originally your idea? RobLandau (talk) 12:24, 13 July 2016 (UTC)

To editor RobLandau: Normally, discussions on the ways for improving an article should appear in the talk page of this article. This is the case of the discussion on your draft. Other discussions, such as this one, or my warning that I have moved your post may appear either in your talk page or in mine. However, it is better to answer on the same page as the page where a question has been asked. This allows the other users to easily follow the discussions. Normally, when you edit a page, it is added to your watchlist, which you may reach with the button at the top of your screen. This allows you to follow the modifications of the pages you are interested in. To be sure that an editor will be informed of your posts, you may use the templates {{tl:to}} (used above in this paragraph), {{ping}} (which produces @RobLandau:) or {{u}} (which produces RobLandau). All produce a notification on the top of your screen.

About the CRT page, it was created 8 years before my first edit of Wikipedia (see history pages). So the article was not originally my idea. On the opposite, I found it difficult to read because it used complicate technicalities for describing rather simple things. Many mathematical articles share this issue, and your post was an occasion for me for improving this particular article. D.Lazard (talk) 12:59, 13 July 2016 (UTC)

Also, I suggest you to make small edits for learning Wikipedia standard style. Adding a whole section, which is not conform to Wikipedia guidelines will probably lead to be reverted. When you will be more experimented, you will have more chances to not been reverted when adding large pieces of text. D.Lazard (talk) 12:59, 13 July 2016 (UTC)

Set builder notation

You commented recently on the article Set-builder notation. I have done some editing there recently, and left some talk page comments, which you may want to review. — Carl (CBM · talk) 13:18, 24 July 2016 (UTC)

Chinese remainder theorem

Your recent wholesale deletion of my edit to Chinese remainder theorem using the semi-automated Twinkle was unfair. Your comment was "Unsourced, and the general description of the method is lacking." Let me address these individually: A lack of references - except in biographies of living people - is not cause for deletion. You should have placed a {{citation needed}} tag instead of deleting. The "lack of method" is a personal opinion and should have been raised on the talk page. I am sure that if you load the page outside of the semi-automated Twinkle programme (which I used to use before I moved on to Huggle) you will find that the argument is very clear. I have reinstated the content and added the reference Chapter 1, Section 5 of Humphries, J. F.; Prest, M. Y. (2004), Numbers, Groups & Codes, Cambridge University Press, pp. 55 & 56. — Fly by Night (talk) 01:10, 29 August 2016 (UTC)

Maths Wiki Project talk page

I've left a request for comment at Maths Wiki Project talk page regarding your second revert. I've also commented on the Chinese remainder theorem's talk page. — Fly by Night (talk) 20:03, 1 September 2016 (UTC)

Numbers

Hi I try to add a few lines to the article numbers, talking about polygonal numbers but you said that there are no reason for emphasizing in them. I think the polygonal numbers are important and need to be explained. Could you give me the reasons? Thanks — Preceding unsigned comment added by Elkintoilustrado (talk • contribs) 21:22, 4 September 2016 (UTC)

To editor Elkintoilustrado: I agree that polygonal numbers are important and deserve to have an article (which exists already for a long time). However there are tenths of subclasses of integers that have a similar importance or are more important, and it would be boring to cite them all in this article. If there will be a WP:consensus among Wikipedia editors to mention polynomial numbers in this section, this mention should be similar to that of Fibonacci numbers and perfect numbers. You are welcome to start a discussion in Talk:Number for searching for such a consensus. D.Lazard (talk) 07:37, 5 September 2016 (UTC)

Graph of a function

My addition of the plot of a function with discontinuities was done in good faith, and maybe the article should be expanded with such a section. Without a doubt your use of Wikipedia:Twinkle is on the abusive side: Wikipedia:Twinkle#Abuse (Simiprof (talk) 15:40, 26 September 2016 (UTC))

To editor Simiprof: I agree that a section about plotting discontinuities could be useful, but presently it is lacking. Therefore, your file is confusing as illustrating things that are not in the article. That is the reason of my revert, which has been explained in the edit summary (verbatim:Confusing, as graphs of discontinuous functions are not considered here.). The software that I have used for the revert does not matter here, and my revert is conform to Wikipedia guidelines and policies. See WP:BRD for details. Also your use of "abuse" is a personal attack, which is forbidden in Wikipedia, see WP:No personal attacks D.Lazard (talk) 16:24, 26 September 2016 (UTC)