Talk:Polynomial

message: I have reverted the new section "Other bases" because;
*As the term "polynomial" is not used, the relationship with the subject of the article may be unclear for a non-mathematician.
*The heading and the  article should be Positional notation
Nevertheless a section on positional notation, could be useful for saying that this notation represents a polynomial in the basis with some constraints on the coefficients. It would also be useful to explain that the arithmetic operations in positional notations are the polynomial operations, except for the carries. Please, try a better version. D.Lazard (talk) 20:32, 4 May 2019 (UTC)
replies: text: I have rewritten the section somewhat, per your recommendations.  Feel free to modify.  I did not insert material about the arithmetic operations.  Feel free to add that as you like.—Anita5192 (talk) 21:06, 4 May 2019 (UTC)
thread_title:  Revert of the new section  

message: I've long felt that our mathematics articles need some improvements to make them more accessible to the layperson without giving up any mathematical rigor. While I felt this I haven't done anything about it until now. I'm going to try with the very baby step. I think this article generally starts out great, but when I get to one section I thought it could be improved. I won't write out my entire rationale here, but it may be worth glancing at User:Sphilbrick/Mathematics articles if you don't think my proposal is an improvement.  —Preceding undated comment added 20:59, 17 July 2020 (UTC)
replies: text: While I appreciate your intentions, I don't think it's very helpful to elaborate on such a trivial topic as polynomial addition. Seeing as you have a degree in mathematics, perhaps you could focus more on the more intricate passages of the text itself rather than simple formulas which are quite easy to follow. A bit further in the Arithmetic section, the discussion of division could use some improvement, e.g. there is no explanation of the last formula for complex numbers: 5(x - 1)\left(x + \frac{1 + i\sqrt{3}}{2}\right)\left(x + \frac{1 - i\sqrt{3}}{2}\right). This is arguably much less accessible to the layperson than the addition example as it was before. --147.229.196.135 (talk) 01:01, 18 July 2020 (UTC)
replies: text:  Sphilbrick and I have been chatting about this a little at my talk page.  To the IP user, I think the key questions elided by your comment are "trivial to whom?" and "helpful to whom?"  Some part of the audience of this article should be students in what I would call "middle school" (say, ages 11--13); for the article to be helpful/usable to such a reader, I agree with Sphilbrick that, at least in the first section where basic arithmetic of polynomials is introduced, it would be good if the examples were spelled out in sufficient detail to illustrate the behaviors being described (e.g., that regrouping and reordering and simplifying all happen).    You are really right about the discussion of division and factoring; but there are plenty of things wrong with the section before one even gets to that part.  You are invited to pitch in as well :).  --JBL (talk) 01:27, 18 July 2020 (UTC)

text: As JBL mentioned, we've been chatting about mathematics articles. I don't disagree that the specific formula for complex numbers is less accessible to the layperson than polynomial addition, but I'm in a let's walk before we run mode. We also have to think about our audience. what's the over under for the percentage of adults who could and two polynomials. if someone says 50%, I want the under. I also want to distinguish between the proportion of adults who could answer the test question without studying (in my opinion south of 50%) and the proportion of adults who could follow a well-written example, and reproduce it on their own shortly thereafter (north of 80%). I see value in adding intermediate steps to help the reader. I am aware of WP:NOTTEXTBOOK, and will take care, but I don't think I've crossed that line. S Philbrick(Talk) 14:49, 18 July 2020 (UTC)
thread_title:  Edit to Arithmetic section 

message: I added two steps to the polynomial multiplication to show the intermediate steps.
I fully understand that people conversant with the subject will find the intermediate steps unnecessary, but many in our audience will find it helpful, and the more advanced we do can skip to the last step easily. 
The rest of the section has some issues. It isn't that anything seems wrong, so it's hard to put my finger on it but it doesn't feel very organized. I'm in discussion with another editor about how it can be improved.--S Philbrick(Talk) 14:27, 19 July 2020 (UTC)
thread_title:  Arithmetic – polynomial multiplication 

message: I had made some edits which were reverted twice. It was about changing the Summation Notation in Definition Section from:
:\sum_{k=0}^n a_k x^k
to
:a_0 + \sum_{k=1}^n a_k x^k
The first one has a domain of all real numbers but 0 (with an indeterminate form 0^0 when x = 0), the second one has domain of all real numbers as is the case with polynomials. I understand that the former is simpler notation but since this is an important fundamental mathematical topic, I would argue that precision should be favoured over simplistic approach.  --Niteshb in (talk) 01:17, 18 March 2021 (UTC)
replies: text: I would have reverted it too. x^0=1 when the exponent is the integer 0. Without this meaning, rules like x^{i+1}=x\times x^i don't work and zillions of other things break as well. Besides that, we follow reliable sources and they start the summation at 0 overwhelmingly. McKay (talk) 05:21, 18 March 2021 (UTC)
thread_title:  Summation Notation in Definition Section