Hello, Marc van Leeuwen, and
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You may want to stop by
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Arcfrk (
talk) 22:13, 29 February 2008 (UTC)
I have some concerns about your recent edits to the polynomial article, so I thought I should raise them here to give you a chance to think about some corrections. My concerns are:
A lot of thought has gone into the polynomial article over a long period of time, and there is a danger that significant changes such as yours could trigger an edit war. To avoid this, I find it is often best to propose major changes on an article's talk page first, to test whether I am about to step into a controversial area. Gandalf61 ( talk) 11:04, 7 March 2008 (UTC)
Let me reply point by point.
Tip. You can undo a sequence of consecutive edits in one go by the following steps.
If you want to do this often, there are "rollback" tools that will make this easier, but probably this will be good enough for now. -- Lambiam 12:37, 8 March 2008 (UTC)
Marc, I redid the first two parts of the article because they were very unorganized, and the definition of a polynomial was very poor. It was not my intent to permanently leave out your edits, but I was a little upset that you did a complete undo and I did not have the time to re-include your edits. I will try to go back and re-include your edits. My apologizes. 24.96.130.30 —Preceding unsigned comment added by 24.96.130.30 ( talk) 20:44, 8 March 2008 (UTC)
I, too, like the word "term" better than "monomial", but the literature uses "monomial", and we have to reflect actual usage, rather than personal preference. (Also, the word "term" can mean an entry in an infinite sequence, and so "monomial" is more specific.) I'll double check to make sure the article uses "term" fairly high up in the discussion.
As a general rule, it is best to discuss edits on the talk page, before spending large amounts of time on a rewrite. Rick Norwood ( talk) 17:32, 10 March 2008 (UTC)
I like your proof of the irrationality of the golden ratio. I think Dicklyon would like to see a specific reference to that proof somewhere in the literature, since presumably someone has thought of it before. (If not, they really should have!) Cheers, silly rabbit ( talk) 13:38, 28 March 2008 (UTC)
Marc, I've completely changed the section (originally mostly due to you, it looks like) in Cayley-Hamilton theorem concerning proofs. I've tried to retain the philosophical points you made, but some of what you said was simply not true, and it was overly opinionated. I'm afraid a lot of the pedagogy of comparing and correcting incorrect proofs has gone by the wayside as a result of the last one. Since you seem to feel strongly about the issue, I thought you would like to know so you could take a look. By the way: do you know of a published source for the proof you wrote (now tidied up a bit and included as the "First proof")? I gave a second proof from Atiyah-MacDonald, a third proof based on one which had appeared on that page some time ago, and a fourth based on some of the comments you made, but these latter two are likewise unreferenced (unreferenceable?). Ryan Reich ( talk) 14:22, 4 July 2008 (UTC)
In the article of polynomials it says "Univariate polynomials have many properties not shared by multivariate polynomials. For instance, the terms of a univariate polynomial are totally ordered by their degree, while a multivariate polynomial can have many terms of the same degree." This, as written is false. Terms in multivariate polynomials, as well as univariate, can be totally ordered by degree (depends on the degree). The main difference is that that order is not natural. franklin 16:19, 7 January 2010 (UTC)
Sorry the removed sentence was intended for another page. franklin
I have to disagree with that formulas are finite expressions by definition. In the article for formula nothing is said about that. Actually the term formula refers to the fact the the formula sould give the solution of arbitrary coefficients. Formulas involving infinite number of additions and multiplications exists as is mensioned a just a paragraph below. franklin 18:40, 9 January 2010 (UTC)
I got confused by the notation about the modules. -- m: drini 17:07, 19 January 2010 (UTC)
I saw in an edit summary at List of poker hands this familiar lament:
To do this, add {{Reflist|group="note"}}
(the same code that appears in the notes section) to the bottom of the section that you're editing. (Similarly, you can add {{
Reflist}}
to preview references, etc.)
It's not perfect, of course; the hard part is remembering to delete this when you're done with the preview!
— Toby Bartels ( talk) 06:54, 3 February 2010 (UTC)
Actually, to be precise one would have to transpose one of the vectors, since dot product is defined for a pair of vectors of the same type. It may be clearer simply to point out the connection to scalar (dot) product. Tkuvho ( talk) 15:08, 21 February 2010 (UTC)
I am disturbed by your edits to Combinadic, which don't make sense to me. Please see remarks at Talk:Combinadic#van_Leeuwen_edits and explain, so I can try to understand what's going on. Thank you. Zaslav ( talk) 20:16, 21 March 2010 (UTC)
As to the link to the Java code you removed, I would like suggestions on how to improve the Java code (since it made your eyes bleed *funniest comment I've seen in months!*). It does work, though I admit that my variable names may be odd *smirk*. I am not a professional when it comes to combinatorics (is it that obvious?), but I am eager to learn. I am open to whatever is necessary to increase the readability of the code and thus be resubmitted as a link to the article. -- Lasloo ( talk) 22:13, 16 July 2010 (UTC)
I am confused by your edits to the Factoradic page. Though what the link said was a proposal, a little more searching said that it isn't just a proposal, it is, in fact, used to represent this number system. Moreover, even you wrote more or less the same thing after editing. Please share your views. And, I am working on the mathematical operations on this system. If you have an insight in this field, I will be highly obliged to know. One Harsh ( talk • contribs)
an*n! + an-1*(n-1)! +.. + a2*1! + a1*0! + b1/2! + b2/3! +.. + + bn-1/n! +..
Thanks for the insight. One Harsh talk —Preceding undated comment added 16:38, 31 March 2010 (UTC).
Please read my comments on the definition of a reflection. I believe you are mistaken in how you wrote the definition. I restrained myself from reverting your recent change because we can't have a fight; we need a discussion. We need to settle this before revising the article once more. (By the way, I think you've done some nice work in other articles.) Zaslav ( talk) 11:11, 11 April 2010 (UTC)
Inorder is perfectly well defined on infinite binary trees. However, what it is well defined as is not a sequence of nodes (obviously) but a total ordering on them. The ordering between any two nodes is the same as it is in the finite subtree formed by the paths from the two nodes to the tree root. — David Eppstein ( talk) 15:35, 13 April 2010 (UTC)
For the recursion
what do you think of initializing it with the Laurent series for the (1+X)0 case? That is, for any integer k, the initialization would be
The use of the recursion would thus derive that the constant term for (1+X)n is 1 for any positive integer n. However, as the page currently is, we instead assume that the constant term is always 1, via the initial condition
Thanks -- Quantling ( talk) 15:23, 21 April 2010 (UTC)
I agree that there are some infelicities in my proof that should be cleared up, but the proof has the attractive property of being simple and self-contained. Many readers of the Wikipedia math contributions are not professionals looking for cutting edge stuff, but relative novices. There should be proofs for them too.
I should add that it's nice to give an example. This clears up lots of confusions.
I have added the "reviewers" property to your user account. This property is related to the Pending changes system that is currently being tried. This system loosens page protection by allowing anonymous users to make "pending" changes which don't become "live" until they're "reviewed". However, logged-in users always see the very latest version of each page with no delay. A good explanation of the system is given in this image. The system is only being used for pages that would otherwise be protected from editing.
If there are "pending" (unreviewed) edits for a page, they will be apparent in a page's history screen; you do not have to go looking for them. There is, however, a list of all articles with changes awaiting review at Special:OldReviewedPages. Because there are so few pages in the trial so far, the latter list is almost always empty. The list of all pages in the pending review system is at Special:StablePages.
To use the system, you can simply edit the page as you normally would, but you should also mark the latest revision as "reviewed" if you have looked at it to ensure it isn't problematic. Edits should generally be accepted if you wouldn't undo them in normal editing: they don't have obvious vandalism, personal attacks, etc. If an edit is problematic, you can fix it by editing or undoing it, just like normal. You are permitted to mark your own changes as reviewed.
The "reviewers" property does not obligate you to do any additional work, and if you like you can simply ignore it. The expectation is that many users will have this property, so that they can review pending revisions in the course of normal editing. However, if you explicitly want to decline the "reviewer" property, you may ask any administrator to remove it for you at any time. — Carl ( CBM · talk) 12:33, 18 June 2010 (UTC) — Carl ( CBM · talk) 12:52, 18 June 2010 (UTC)
Hi, I made a question on the talk page of that article and I have the impression you might know the answer. Can you please help me with that? -- Sandrobt ( talk) 16:09, 6 September 2010 (UTC)
You may be interested in Talk:Symbolic computation#Merger with computer algebra system. Yaris678 ( talk) 17:21, 25 November 2010 (UTC)
I'd appreciate your input in this discussion of the current lead in of the continued fraction article. — Quantling ( talk | contribs) 19:53, 30 November 2010 (UTC)
Nice job with the lead of compact space. I think that this is probably what was needed there. I'd like to solicit some input about how to approach the "Introduction" section. I have posted at Talk:Compact space. Sławomir Biały ( talk) 13:30, 9 January 2011 (UTC)
Hi Marc van Leeuwen, I'm the user whose changes to Permutation you've reversed. The current version is clearly better than what was there originally. Consensus on the talk page seemed to be that the historical notes and quotation are out-of-place in the introduction; perhaps they could be placed in a new "History" section? -- 18.87.1.234 ( talk) 16:10, 20 January 2011 (UTC)
In the recursion article, it's not particularly "ridiculous" to define the natural numbers as a subset of the reals. On the one hand, the reals can be defined as the unique complete ordered field, which does not make any mention of the natural numbers. On the other hand, without an "ambient" set of numbers, the notation "n+1" is meaningless, because the "+" operation isn't defined. — Carl ( CBM · talk) 13:34, 14 February 2011 (UTC)
By the way, I noticed your clean-up work on several articles, and it is much appreciated; don't take my comments here as a criticism of your editing. I just felt you might have overstated the claim about this particular issue. — Carl ( CBM · talk) 14:40, 14 February 2011 (UTC)
I'm not sure what you mean. Specifically, raising a number to the power of an underlined integer.
This is in regards to your last edit at combinations. AAS 16:37, 27 March 2011 (UTC) — Preceding unsigned comment added by Ann arbor street ( talk • contribs)
Yes, this is a bad habit of mine. I'll try to avoid it in the future. There was an editing conflict. TR replied while I was still editing. I should have probably added my new text after TR's reply, but TR perfectly understood what I meant, even though my text was not complete yet, and his reply provided additional information, so his reply will still make sense to future readers. Paolo.dL ( talk) 12:18, 29 April 2011 (UTC)
I don't understand the reason why you don't like my sentence describing a rotation matrix as a matrix representing a rotation "about the origin of a CS". This is perfectly correct. It would not be correct, however, to write that it represents a rotation "about an axis", as this is true only in 3-D (not in 2-D, not in 4-D, etc.), and only if you choose to interpret the rotation as a rotation about a single axis by a given angle ( Axis angle), rather than a sequence of rotations about three axes, by three different Euler angles. Whatever option you choose, the rotation (or rotations) occurs about the origin, and this is the key point. The origin is the center of a circle (in circular motion) or a sphere (in 3-D) or n-sphere (in n-D). We are not giving a complete geometrical interpretation of the rotation matrix, and we don't need to. For instance, we both feel it's not necessary to add "by a given angle".
Expressions such as yours "in terms of a CS" or "w.r. to a CS" are not clear enough in my opinion.
Let me explain. If you say that the matrix rotates a vector, then you don't need to specify about what point it rotates, as by definition the tail of a vector is the origin of the CS. If you see a vector simply as an arrow with no fixed position for its tail (an oriented distance between two points in space), then the concept of rotation becomes even simpler, as you don't need to care about the origin of the CS. This arrow has an orientation in space, that does not change when you translate both its tail and tip. So, a rotation in this case is independent of the point about which it is performed. On the other hand, the concept of "rotation of a point" (see circular motion) is much more tricky, as a point has no orientation in space. Only the correspoinding vector has an orientation. The point can only rotate about another point which does not pass through it, and the final (linear and angular) position of this point (as well as its initial position!) depends on the point about which you choose to perform the rotation.
Paolo.dL ( talk) 15:30, 29 April 2011 (UTC)
I don't think it is necessary to say that the rotation is represented in a coordinate system. The problem is that "rotation of a point" does not make perfectly sense, while "rotation of a vector" perfectly does. However, we can't write that the matrix rotates the vector, because we are using the word vector to indicate a 3x1 matrix. In this case, "rotates" might be interpreted as "transposes" (to 1x3). Isn't this the reason why you did not like the expression "rotated vector", which I used when I wrote that phrase?
I understand your point, but we are dealing with a single point here, not a rigid body. I would not say that the earth rotates about a point, but I can safely say that a point rotates about another, meaning that the point moves along a spherical surface. Isn't that simple enough? Moreover, the motion along that spherical surface may occur along an arc of a circle or, (as in the representation with Euler angles), along three "orthogonal" arcs. You can think of a rotation of a point on the earth as a rotation about the "center of the earth". It's just a matter of representation.
The reason why I don't like "rotation of a point" is that a "rotation" is a "change in orientation", and a point cannot change its orientation, as it has no orientation in space. Only a set of points fixed with respect to each other, such as a line segment, a vector, a plane, or a rigid body can change its orientation. So, the expression "rotation of a point P" can be accepted (and is accepted, as in circular motion) only when you specify at least another point about which P rotates.
Two points are enough to define the concept of rotation, one point is not. I am just suggesting to give the minimum amount of information, because I cannot find a simple way to generalize the concept of "axis of rotation" to N-D. (Again, we are not saying that the rotation is "by a given angle").
You might not like it, and I can see why you don't like it, but the concept of rotation of a point about the origin, contrary to what you say, is perfectly correct in N-D. Think about the rotation of a spinning top "about its tip". Any given "particle" of the top moves along a spherical surphace about the top, while the top not only spins, but also "precesses" and "nutates". Also, a diver performing a twisting somersault can be described as a body rotating about its center of mass. A ship sailing on the ocean rotates (approximately) about the center of the earth. People can understand this easily enough.
Paolo.dL ( talk) 10:30, 30 April 2011 (UTC)
Hello Marc van Leeuwen,
I appreciate your diligence in this matter. When I had requested a citation the equations appeared incorrect (in the range of the summation); however, that issue appears to have been corrected. Now that examples are clearly in congruence with the provided definition, I agree that no citation is necessary. Keep up the good work and collaborative mindset. KlappCK ( talk) 14:19, 13 May 2011 (UTC)
Hi Marc!
I've just read your reply on my question in the discussion of Proofs of Fermat's theorem on sums of two squares. Thank you for your attention, but unfortunately I didn't find any hint for the answer of my question in the page you suggested. If you think you understood my question, could you reply there and be more specific as where to find? I questioned the claim on the title of this section there, because it was used as tool in Euler's proof (in the fifth step) as though it was quite commonplace (but for me, who understood every other step in the proof, was totally unknown).
Best regards, Wisapi ( talk) 00:21, 15 May 2011 (UTC)
I'm trying to let you indeed have the last word at
talk:Determinant, so I am replying here instead. I have to ask: why do you feel the need to use such normative language? "Adjoint" is not "wrong", it is an older term for the adjutant adjugate. Yes it would be nice to have a uniform vocabulary, but mathematics grows and changes -- and older terms are often preserved in applied fields. Anyone refusing to acknowledge older terminology will just end up being confused -- and not letting our students know this does them a disservice. (My take, obviously.) --
Elphion (
talk) 21:24, 4 June 2011 (UTC)
FYI, no opinion on notability, but this article is new. Best, Sławomir Biały ( talk) 20:30, 21 July 2011 (UTC)
Hi Marc,
Thank you for helping me editing the Lehmer Code article, but you see, I working on it right now at this very moment so your last move proved more ennoying than helpfull, sorry. — Preceding unsigned comment added by Herix ( talk • contribs) 13:24, 8 October 2011 (UTC)
I tried to find a cite for the proof you added to Menelaus' theorem. Could you add your source so I can remove the 'unreferenced' tag on the section?-- RDBury ( talk) 21:23, 1 November 2011 (UTC)
I don't agree in following statement: a search tree is a binary tree data structure.
First, I think that a search tree can be any tree which performs searching operation effectively. For example, B-tree, Ternary search tree, and van Emde Boas tree are not binary search trees, but they are search trees.
Second, I see your reason in changing tree to binary tree. You describe that inorder only works for binary tree. However, from inorder, it states that tree traversal (included inorder) may be generalized to other trees as well.
Therefore, search tree definition should not be limited to only binary tree.
(Sorry for my bad English.) Nullzero ( talk) 14:35, 27 October 2012 (UTC)
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Since in the article [1] it is said that the formulas give "ever longer expressions that do not seem to follow any simple pattern", I would like to draw your attention to the "Waring formula", which gives a fairly easy way of computing the coefficients in this expansion: Namely the coefficient of the monomial M=\Pi_{i=1}^l e_i^{m_i} in the expansion of p_k (for 1*e_1+2*e_2+...+l*e_l=k) is given by (-1)^{m_2+m_4+...}*k*(e_1+e_2+...+e_l-1)!/(e_1!e_2!*...e_l!).
For instance in the example in the text we have l=3, m_1=5, m_2=0, m_3=1, m_4=3, k=5+3*1+4*3=20 and the coefficient is (-1)^{0+3}*20*8!/(5!*1!*3!)=-20*8*7=-1120
Maybe you can extend the article on Newton identities or maybe even write a separat article about the "Waring formula".
For proofs of this formula see the literature: [2] [3] [4] 213.47.239.29 ( talk) 22:29, 16 February 2014 (UTC)
References
An article that you have been involved in editing, Polynomial expression, has been proposed for a merge with another article. If you are interested in the merge discussion, please participate by going here, and adding your comments on the discussion page. Thank you. Toby Bartels ( talk) 16:18, 13 April 2014 (UTC)
You've clearly done a lot of great work on Wikipedia, so I hope that you agree that this is a better place to put what you wrote. —Toby
As a frequent contributor to Wikipedia in the area of mathematics, I kindly request you to examine, and perhaps, to contribute to the discussion regarding the notability of the article on Program for Research In Mathematics, Engineering and Science (PRIMES). It has been marked for deletion, and your opinion is welcomed. Dodecahedronic ( talk) 13:11, 29 September 2015 (UTC)
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Hi, you have added a reference to the Hadamard's book in Homothetic transformation in 2011 (this edit: Special:Diff/416538586). You provided a page number there, but without a year of publication.
Was that a year 2008 publication, translated by Mark E Saul as described here and here in AMS? -- CiaPan ( talk) 12:00, 8 July 2019 (UTC)
Dear Marc,
Thanks for looking at the change I made to the redirect "combinations and permutations". It was pretty hard work for me to get this much done, and now you just reverted it without giving me a chance to improve on it. I know, you wrote "better use a template", but I did put a template in, and have no idea how to go on from here. The help section is a maze to me, with tons of text to read before you realize that it’s not applicable and/or incomplete and you need to read 3 more of those pages.
In short: if you value contributions, please give less experienced users like me a hand. The learning curve for editing Wikipedia is horrendously steep anyway.-- Geke ( talk) 18:53, 5 January 2020 (UTC)
Hello, Marc van Leeuwen, and
welcome to Wikipedia! Thank you for
your contributions. I hope you like the place and decide to stay. Our
intro page provides helpful information for new users - please check it out! If you need help, visit
Wikipedia:Questions, ask me on my talk page, or place {{helpme}}
on this page and someone will show up shortly to answer your questions. Happy editing!
Arcfrk (
talk) 22:13, 29 February 2008 (UTC)
You may want to stop by
Wiki Project Mathematics main page and the associated
talk page and also to add yourself to the
list of participants. By creating an article on Littlewood–Richardson rule you have filled a serious gap in Wikipedia coverage, I hope that you'll expand it further. Again, welcome!
Arcfrk (
talk) 22:13, 29 February 2008 (UTC)
I have some concerns about your recent edits to the polynomial article, so I thought I should raise them here to give you a chance to think about some corrections. My concerns are:
A lot of thought has gone into the polynomial article over a long period of time, and there is a danger that significant changes such as yours could trigger an edit war. To avoid this, I find it is often best to propose major changes on an article's talk page first, to test whether I am about to step into a controversial area. Gandalf61 ( talk) 11:04, 7 March 2008 (UTC)
Let me reply point by point.
Tip. You can undo a sequence of consecutive edits in one go by the following steps.
If you want to do this often, there are "rollback" tools that will make this easier, but probably this will be good enough for now. -- Lambiam 12:37, 8 March 2008 (UTC)
Marc, I redid the first two parts of the article because they were very unorganized, and the definition of a polynomial was very poor. It was not my intent to permanently leave out your edits, but I was a little upset that you did a complete undo and I did not have the time to re-include your edits. I will try to go back and re-include your edits. My apologizes. 24.96.130.30 —Preceding unsigned comment added by 24.96.130.30 ( talk) 20:44, 8 March 2008 (UTC)
I, too, like the word "term" better than "monomial", but the literature uses "monomial", and we have to reflect actual usage, rather than personal preference. (Also, the word "term" can mean an entry in an infinite sequence, and so "monomial" is more specific.) I'll double check to make sure the article uses "term" fairly high up in the discussion.
As a general rule, it is best to discuss edits on the talk page, before spending large amounts of time on a rewrite. Rick Norwood ( talk) 17:32, 10 March 2008 (UTC)
I like your proof of the irrationality of the golden ratio. I think Dicklyon would like to see a specific reference to that proof somewhere in the literature, since presumably someone has thought of it before. (If not, they really should have!) Cheers, silly rabbit ( talk) 13:38, 28 March 2008 (UTC)
Marc, I've completely changed the section (originally mostly due to you, it looks like) in Cayley-Hamilton theorem concerning proofs. I've tried to retain the philosophical points you made, but some of what you said was simply not true, and it was overly opinionated. I'm afraid a lot of the pedagogy of comparing and correcting incorrect proofs has gone by the wayside as a result of the last one. Since you seem to feel strongly about the issue, I thought you would like to know so you could take a look. By the way: do you know of a published source for the proof you wrote (now tidied up a bit and included as the "First proof")? I gave a second proof from Atiyah-MacDonald, a third proof based on one which had appeared on that page some time ago, and a fourth based on some of the comments you made, but these latter two are likewise unreferenced (unreferenceable?). Ryan Reich ( talk) 14:22, 4 July 2008 (UTC)
In the article of polynomials it says "Univariate polynomials have many properties not shared by multivariate polynomials. For instance, the terms of a univariate polynomial are totally ordered by their degree, while a multivariate polynomial can have many terms of the same degree." This, as written is false. Terms in multivariate polynomials, as well as univariate, can be totally ordered by degree (depends on the degree). The main difference is that that order is not natural. franklin 16:19, 7 January 2010 (UTC)
Sorry the removed sentence was intended for another page. franklin
I have to disagree with that formulas are finite expressions by definition. In the article for formula nothing is said about that. Actually the term formula refers to the fact the the formula sould give the solution of arbitrary coefficients. Formulas involving infinite number of additions and multiplications exists as is mensioned a just a paragraph below. franklin 18:40, 9 January 2010 (UTC)
I got confused by the notation about the modules. -- m: drini 17:07, 19 January 2010 (UTC)
I saw in an edit summary at List of poker hands this familiar lament:
To do this, add {{Reflist|group="note"}}
(the same code that appears in the notes section) to the bottom of the section that you're editing. (Similarly, you can add {{
Reflist}}
to preview references, etc.)
It's not perfect, of course; the hard part is remembering to delete this when you're done with the preview!
— Toby Bartels ( talk) 06:54, 3 February 2010 (UTC)
Actually, to be precise one would have to transpose one of the vectors, since dot product is defined for a pair of vectors of the same type. It may be clearer simply to point out the connection to scalar (dot) product. Tkuvho ( talk) 15:08, 21 February 2010 (UTC)
I am disturbed by your edits to Combinadic, which don't make sense to me. Please see remarks at Talk:Combinadic#van_Leeuwen_edits and explain, so I can try to understand what's going on. Thank you. Zaslav ( talk) 20:16, 21 March 2010 (UTC)
As to the link to the Java code you removed, I would like suggestions on how to improve the Java code (since it made your eyes bleed *funniest comment I've seen in months!*). It does work, though I admit that my variable names may be odd *smirk*. I am not a professional when it comes to combinatorics (is it that obvious?), but I am eager to learn. I am open to whatever is necessary to increase the readability of the code and thus be resubmitted as a link to the article. -- Lasloo ( talk) 22:13, 16 July 2010 (UTC)
I am confused by your edits to the Factoradic page. Though what the link said was a proposal, a little more searching said that it isn't just a proposal, it is, in fact, used to represent this number system. Moreover, even you wrote more or less the same thing after editing. Please share your views. And, I am working on the mathematical operations on this system. If you have an insight in this field, I will be highly obliged to know. One Harsh ( talk • contribs)
an*n! + an-1*(n-1)! +.. + a2*1! + a1*0! + b1/2! + b2/3! +.. + + bn-1/n! +..
Thanks for the insight. One Harsh talk —Preceding undated comment added 16:38, 31 March 2010 (UTC).
Please read my comments on the definition of a reflection. I believe you are mistaken in how you wrote the definition. I restrained myself from reverting your recent change because we can't have a fight; we need a discussion. We need to settle this before revising the article once more. (By the way, I think you've done some nice work in other articles.) Zaslav ( talk) 11:11, 11 April 2010 (UTC)
Inorder is perfectly well defined on infinite binary trees. However, what it is well defined as is not a sequence of nodes (obviously) but a total ordering on them. The ordering between any two nodes is the same as it is in the finite subtree formed by the paths from the two nodes to the tree root. — David Eppstein ( talk) 15:35, 13 April 2010 (UTC)
For the recursion
what do you think of initializing it with the Laurent series for the (1+X)0 case? That is, for any integer k, the initialization would be
The use of the recursion would thus derive that the constant term for (1+X)n is 1 for any positive integer n. However, as the page currently is, we instead assume that the constant term is always 1, via the initial condition
Thanks -- Quantling ( talk) 15:23, 21 April 2010 (UTC)
I agree that there are some infelicities in my proof that should be cleared up, but the proof has the attractive property of being simple and self-contained. Many readers of the Wikipedia math contributions are not professionals looking for cutting edge stuff, but relative novices. There should be proofs for them too.
I should add that it's nice to give an example. This clears up lots of confusions.
I have added the "reviewers" property to your user account. This property is related to the Pending changes system that is currently being tried. This system loosens page protection by allowing anonymous users to make "pending" changes which don't become "live" until they're "reviewed". However, logged-in users always see the very latest version of each page with no delay. A good explanation of the system is given in this image. The system is only being used for pages that would otherwise be protected from editing.
If there are "pending" (unreviewed) edits for a page, they will be apparent in a page's history screen; you do not have to go looking for them. There is, however, a list of all articles with changes awaiting review at Special:OldReviewedPages. Because there are so few pages in the trial so far, the latter list is almost always empty. The list of all pages in the pending review system is at Special:StablePages.
To use the system, you can simply edit the page as you normally would, but you should also mark the latest revision as "reviewed" if you have looked at it to ensure it isn't problematic. Edits should generally be accepted if you wouldn't undo them in normal editing: they don't have obvious vandalism, personal attacks, etc. If an edit is problematic, you can fix it by editing or undoing it, just like normal. You are permitted to mark your own changes as reviewed.
The "reviewers" property does not obligate you to do any additional work, and if you like you can simply ignore it. The expectation is that many users will have this property, so that they can review pending revisions in the course of normal editing. However, if you explicitly want to decline the "reviewer" property, you may ask any administrator to remove it for you at any time. — Carl ( CBM · talk) 12:33, 18 June 2010 (UTC) — Carl ( CBM · talk) 12:52, 18 June 2010 (UTC)
Hi, I made a question on the talk page of that article and I have the impression you might know the answer. Can you please help me with that? -- Sandrobt ( talk) 16:09, 6 September 2010 (UTC)
You may be interested in Talk:Symbolic computation#Merger with computer algebra system. Yaris678 ( talk) 17:21, 25 November 2010 (UTC)
I'd appreciate your input in this discussion of the current lead in of the continued fraction article. — Quantling ( talk | contribs) 19:53, 30 November 2010 (UTC)
Nice job with the lead of compact space. I think that this is probably what was needed there. I'd like to solicit some input about how to approach the "Introduction" section. I have posted at Talk:Compact space. Sławomir Biały ( talk) 13:30, 9 January 2011 (UTC)
Hi Marc van Leeuwen, I'm the user whose changes to Permutation you've reversed. The current version is clearly better than what was there originally. Consensus on the talk page seemed to be that the historical notes and quotation are out-of-place in the introduction; perhaps they could be placed in a new "History" section? -- 18.87.1.234 ( talk) 16:10, 20 January 2011 (UTC)
In the recursion article, it's not particularly "ridiculous" to define the natural numbers as a subset of the reals. On the one hand, the reals can be defined as the unique complete ordered field, which does not make any mention of the natural numbers. On the other hand, without an "ambient" set of numbers, the notation "n+1" is meaningless, because the "+" operation isn't defined. — Carl ( CBM · talk) 13:34, 14 February 2011 (UTC)
By the way, I noticed your clean-up work on several articles, and it is much appreciated; don't take my comments here as a criticism of your editing. I just felt you might have overstated the claim about this particular issue. — Carl ( CBM · talk) 14:40, 14 February 2011 (UTC)
I'm not sure what you mean. Specifically, raising a number to the power of an underlined integer.
This is in regards to your last edit at combinations. AAS 16:37, 27 March 2011 (UTC) — Preceding unsigned comment added by Ann arbor street ( talk • contribs)
Yes, this is a bad habit of mine. I'll try to avoid it in the future. There was an editing conflict. TR replied while I was still editing. I should have probably added my new text after TR's reply, but TR perfectly understood what I meant, even though my text was not complete yet, and his reply provided additional information, so his reply will still make sense to future readers. Paolo.dL ( talk) 12:18, 29 April 2011 (UTC)
I don't understand the reason why you don't like my sentence describing a rotation matrix as a matrix representing a rotation "about the origin of a CS". This is perfectly correct. It would not be correct, however, to write that it represents a rotation "about an axis", as this is true only in 3-D (not in 2-D, not in 4-D, etc.), and only if you choose to interpret the rotation as a rotation about a single axis by a given angle ( Axis angle), rather than a sequence of rotations about three axes, by three different Euler angles. Whatever option you choose, the rotation (or rotations) occurs about the origin, and this is the key point. The origin is the center of a circle (in circular motion) or a sphere (in 3-D) or n-sphere (in n-D). We are not giving a complete geometrical interpretation of the rotation matrix, and we don't need to. For instance, we both feel it's not necessary to add "by a given angle".
Expressions such as yours "in terms of a CS" or "w.r. to a CS" are not clear enough in my opinion.
Let me explain. If you say that the matrix rotates a vector, then you don't need to specify about what point it rotates, as by definition the tail of a vector is the origin of the CS. If you see a vector simply as an arrow with no fixed position for its tail (an oriented distance between two points in space), then the concept of rotation becomes even simpler, as you don't need to care about the origin of the CS. This arrow has an orientation in space, that does not change when you translate both its tail and tip. So, a rotation in this case is independent of the point about which it is performed. On the other hand, the concept of "rotation of a point" (see circular motion) is much more tricky, as a point has no orientation in space. Only the correspoinding vector has an orientation. The point can only rotate about another point which does not pass through it, and the final (linear and angular) position of this point (as well as its initial position!) depends on the point about which you choose to perform the rotation.
Paolo.dL ( talk) 15:30, 29 April 2011 (UTC)
I don't think it is necessary to say that the rotation is represented in a coordinate system. The problem is that "rotation of a point" does not make perfectly sense, while "rotation of a vector" perfectly does. However, we can't write that the matrix rotates the vector, because we are using the word vector to indicate a 3x1 matrix. In this case, "rotates" might be interpreted as "transposes" (to 1x3). Isn't this the reason why you did not like the expression "rotated vector", which I used when I wrote that phrase?
I understand your point, but we are dealing with a single point here, not a rigid body. I would not say that the earth rotates about a point, but I can safely say that a point rotates about another, meaning that the point moves along a spherical surface. Isn't that simple enough? Moreover, the motion along that spherical surface may occur along an arc of a circle or, (as in the representation with Euler angles), along three "orthogonal" arcs. You can think of a rotation of a point on the earth as a rotation about the "center of the earth". It's just a matter of representation.
The reason why I don't like "rotation of a point" is that a "rotation" is a "change in orientation", and a point cannot change its orientation, as it has no orientation in space. Only a set of points fixed with respect to each other, such as a line segment, a vector, a plane, or a rigid body can change its orientation. So, the expression "rotation of a point P" can be accepted (and is accepted, as in circular motion) only when you specify at least another point about which P rotates.
Two points are enough to define the concept of rotation, one point is not. I am just suggesting to give the minimum amount of information, because I cannot find a simple way to generalize the concept of "axis of rotation" to N-D. (Again, we are not saying that the rotation is "by a given angle").
You might not like it, and I can see why you don't like it, but the concept of rotation of a point about the origin, contrary to what you say, is perfectly correct in N-D. Think about the rotation of a spinning top "about its tip". Any given "particle" of the top moves along a spherical surphace about the top, while the top not only spins, but also "precesses" and "nutates". Also, a diver performing a twisting somersault can be described as a body rotating about its center of mass. A ship sailing on the ocean rotates (approximately) about the center of the earth. People can understand this easily enough.
Paolo.dL ( talk) 10:30, 30 April 2011 (UTC)
Hello Marc van Leeuwen,
I appreciate your diligence in this matter. When I had requested a citation the equations appeared incorrect (in the range of the summation); however, that issue appears to have been corrected. Now that examples are clearly in congruence with the provided definition, I agree that no citation is necessary. Keep up the good work and collaborative mindset. KlappCK ( talk) 14:19, 13 May 2011 (UTC)
Hi Marc!
I've just read your reply on my question in the discussion of Proofs of Fermat's theorem on sums of two squares. Thank you for your attention, but unfortunately I didn't find any hint for the answer of my question in the page you suggested. If you think you understood my question, could you reply there and be more specific as where to find? I questioned the claim on the title of this section there, because it was used as tool in Euler's proof (in the fifth step) as though it was quite commonplace (but for me, who understood every other step in the proof, was totally unknown).
Best regards, Wisapi ( talk) 00:21, 15 May 2011 (UTC)
I'm trying to let you indeed have the last word at
talk:Determinant, so I am replying here instead. I have to ask: why do you feel the need to use such normative language? "Adjoint" is not "wrong", it is an older term for the adjutant adjugate. Yes it would be nice to have a uniform vocabulary, but mathematics grows and changes -- and older terms are often preserved in applied fields. Anyone refusing to acknowledge older terminology will just end up being confused -- and not letting our students know this does them a disservice. (My take, obviously.) --
Elphion (
talk) 21:24, 4 June 2011 (UTC)
FYI, no opinion on notability, but this article is new. Best, Sławomir Biały ( talk) 20:30, 21 July 2011 (UTC)
Hi Marc,
Thank you for helping me editing the Lehmer Code article, but you see, I working on it right now at this very moment so your last move proved more ennoying than helpfull, sorry. — Preceding unsigned comment added by Herix ( talk • contribs) 13:24, 8 October 2011 (UTC)
I tried to find a cite for the proof you added to Menelaus' theorem. Could you add your source so I can remove the 'unreferenced' tag on the section?-- RDBury ( talk) 21:23, 1 November 2011 (UTC)
I don't agree in following statement: a search tree is a binary tree data structure.
First, I think that a search tree can be any tree which performs searching operation effectively. For example, B-tree, Ternary search tree, and van Emde Boas tree are not binary search trees, but they are search trees.
Second, I see your reason in changing tree to binary tree. You describe that inorder only works for binary tree. However, from inorder, it states that tree traversal (included inorder) may be generalized to other trees as well.
Therefore, search tree definition should not be limited to only binary tree.
(Sorry for my bad English.) Nullzero ( talk) 14:35, 27 October 2012 (UTC)
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Since in the article [1] it is said that the formulas give "ever longer expressions that do not seem to follow any simple pattern", I would like to draw your attention to the "Waring formula", which gives a fairly easy way of computing the coefficients in this expansion: Namely the coefficient of the monomial M=\Pi_{i=1}^l e_i^{m_i} in the expansion of p_k (for 1*e_1+2*e_2+...+l*e_l=k) is given by (-1)^{m_2+m_4+...}*k*(e_1+e_2+...+e_l-1)!/(e_1!e_2!*...e_l!).
For instance in the example in the text we have l=3, m_1=5, m_2=0, m_3=1, m_4=3, k=5+3*1+4*3=20 and the coefficient is (-1)^{0+3}*20*8!/(5!*1!*3!)=-20*8*7=-1120
Maybe you can extend the article on Newton identities or maybe even write a separat article about the "Waring formula".
For proofs of this formula see the literature: [2] [3] [4] 213.47.239.29 ( talk) 22:29, 16 February 2014 (UTC)
References
An article that you have been involved in editing, Polynomial expression, has been proposed for a merge with another article. If you are interested in the merge discussion, please participate by going here, and adding your comments on the discussion page. Thank you. Toby Bartels ( talk) 16:18, 13 April 2014 (UTC)
You've clearly done a lot of great work on Wikipedia, so I hope that you agree that this is a better place to put what you wrote. —Toby
As a frequent contributor to Wikipedia in the area of mathematics, I kindly request you to examine, and perhaps, to contribute to the discussion regarding the notability of the article on Program for Research In Mathematics, Engineering and Science (PRIMES). It has been marked for deletion, and your opinion is welcomed. Dodecahedronic ( talk) 13:11, 29 September 2015 (UTC)
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Hi, you have added a reference to the Hadamard's book in Homothetic transformation in 2011 (this edit: Special:Diff/416538586). You provided a page number there, but without a year of publication.
Was that a year 2008 publication, translated by Mark E Saul as described here and here in AMS? -- CiaPan ( talk) 12:00, 8 July 2019 (UTC)
Dear Marc,
Thanks for looking at the change I made to the redirect "combinations and permutations". It was pretty hard work for me to get this much done, and now you just reverted it without giving me a chance to improve on it. I know, you wrote "better use a template", but I did put a template in, and have no idea how to go on from here. The help section is a maze to me, with tons of text to read before you realize that it’s not applicable and/or incomplete and you need to read 3 more of those pages.
In short: if you value contributions, please give less experienced users like me a hand. The learning curve for editing Wikipedia is horrendously steep anyway.-- Geke ( talk) 18:53, 5 January 2020 (UTC)