User talk:Marc van Leeuwen

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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)

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[edit] Your recent edits to Polynomial

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:

  1. By replacing "monomial" with "term" and using a definiton of "term" that allows terms with coefficients of 0, you introduce complexity and the possibility of confusion. The number of "terms" in a polynomial is no longer well defined - as is apparent in your discussion of the zero polynomial. And you have to qualify "term" when defining the degree of a polynomial - the degree of a polynomial now becomes the highest degree of its non-zero terms.
  2. You have defined the degree of a variable in a polynomial, but you have lost the definition of the degree of a polynomial itself.
  3. By replacing "equivalent" with "equal" you have obscured the fact that equivalence of polynomials as formal expressions is (and should be) independent of any field in which they are evaluated as polynomial functions. For example, the polynomials x2+1 and x+1 are not equivalent, but in the field Z2 they are equal as functions, because they take the same value at each of the points in that field. In your terminology, you would have to say that x2+1 and x+1 are equal as functions over Z2 but not equal when considered as formal polynomials, which I think is confusing.

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.

  1. I did intentionally allow zero terms, because I think it is not common use to forbid them. Think of such uses as "to add two polynomials, one adds the coefficients of similar terms (terms involving the same monomial)". Note that to be able to pronounce such a fairly simple sentence, one must allow introduction of terms with zero coefficient, just to have something at hand to add. Also the explanation of "similar terms" needs some notion of the term stripped of its coefficient; if one does not allow "monomial" to refer to that, life gets rather hard. (I do plead guilty to trying to educate the general public by pushing the terminology "mononomial" for an isolated term viewed as a polynomial.) The fact that the number of terms of a polynomial is no longer well defined does not seem so much of a problem to me, since operations like gathering similar terms or cancelling terms do change the number of terms in an expression. What is well defined (even if not very frequently used) is the number of nonzero terms in the standardized form of a polynomial. If you want to allow dropping "nonzero" from that phrase by forbidding zero terms altogether, I do not object, although I don't think it really makes life easier. In fact I was, somewhat against my habits, trying to not be pedantic here.
Now that I think about this again, I see you may have a point that the initial description gives the standardized form of the polynomial, which need not contain zero terms; those terms will then be allowed further on per equivalence by the usual rules. For the zero polynomial one would have an expression that is a sum of no terms at all; while there is no doubt that the value of an empty sum is 0, it might schock people to manipulate expressions that could be completely void (but after all this is a bit like the empty string). The real difficulty is striking a balance between precision and language that could scare people. It is not hard to be exact: a polynomial is a linear combination of monomials (defined to exclude coefficients of course). But that is hardly informative to someone new to the subject.
  1. I added the precision that what was being defined in the given place was in fact the degree in a variable (the corresponding paragraph failed to mention that it was supposing the single variable case, which I added as well). Feel free to add a corresponding sentence about the total degree, or about unqualified degrees in the presence of only a single variable; I just did not want to change too much at once.
  2. As the lead states, a polynomial is an expression, not a function. This means one does not use evaluation (which is only introduced much later by the way) to decide equality (or equivalence) of polynomials, and I think most people agree about that (besides giving wrong results in specific cases, it would be a rather cumbersome test). The issue here has nothing to do with polynomial function, but whether one considers for instance (X+1)2 to be equal or only equivalent to X2+2X+1. I think if you ask, most mathematicians will vote for "equal". They are certainly equal in a polynomial ring, but one can maintain that they are only equivalent as polynomials. People using computer algebra would probably favor that point of view. (I see that the point you are advancing is actually that some polynomials could be considered equal without being equivalent; this to me would seem a very curious situation, and not just for polynomials.) But for the article it might be best to simply not raise the question, and use "equivalent". Go ahead and revert that part of my edit and remove the somewhat pedantic remark following it if you feel this is more appropriate. I was only being bold. Marc van Leeuwen (talk) 11:59, 7 March 2008 (UTC)
To the extent that you actually agree with the criticism, it is more appropriate that you make the requisite changes. I prefer the approach in which the coefficient of a term cannot be 0, as should be clear from the following edits I made earlier to clear up the confusion raised by the ambiguity of the issue: [1] & [2].  --Lambiam 12:17, 8 March 2008 (UTC)

[edit] Undoing multiple edits

Tip. You can undo a sequence of consecutive edits in one go by the following steps.

  • Go to the revision history of the page in question. You will see a radio button in front of each revision. These radio buttons are arranged in two columns, in each of which one is selected; initially the right column has one button only, for the latest revision.
  • Select the radio button in the left column for the revision that is one older than the one resulting from the earliest edit you want to undo.
  • Select the radio button in the right column for the revision resulting from the last (most recent) edit in the sequence to be undone.
  • Click the button titled "Compare selected versions".
  • You will get a diff page, in which the caption of the right column has an undo button. Click it.
  • If you get a message that the edit could not be undone due to conflicting intermediate edits, you're out of luck.
  • Otherwise, fill in the edit summary appropriately (usually I make sure I have the user name or IP address of the offending editor already in the copy buffer), and save the page.

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)

[edit] Polynomial Undo

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)

[edit] coming to terms

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)

[edit] Nice proof

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)