Talk:Sylvester matrix

Recent edits by
I will revert the recent edits by, because they break Wikipedia policies and guidelines on many points, as I will show below. Please do not reinsert them without a consensus in this talk page (see WP:BRD).

The added content is unsourced. As far as I know, if some part of this content appears in some reliable source, this may be only in papers by Akritas. Therefore this content is original research (see WP:OR) and thus forbidden in Wikipedia. As it is natural to guess that user Akritas2 is the same person as the searcher named Akritas, adding this content results in a conflict of interest (see WP:COI).

This added content introduces some terminology as it would be standard, when it is used only by Akritas and nobody else. This is confusing and possibly misleading for readers.

In this added content there is the assertion that some well known book (Basu, Pollack, Roy) gives a wrong definition. This is not sourced and appears to be a personal opinion of the editor. This also breaks Wikipedia policy of neutrality (see WP:NPOV). Such an assertion of erroneous content must be not only sourced, but explicitly attributed to its author, not to Wikipedia, as does Akritas2 edits.

This added content contains very technical (see WP:TECHNICAL) assertions on PRS sequences, which are misplaced in this article. It contains also links to software written by the editor (or his students). This is again a conflict of interest, and also breaks Wikipedia policy of external links (see WP:EL).

D.Lazard (talk) 16:25, 3 April 2016 (UTC)


 * RESPONSE 1: Lazard, your guess is right; Akritas2 = Akritas.  HOWEVER, your are totally WRONG in saying that the content is unsourced.  These things were known to Sylvester back in the 19-th century. The references are in my paper that you kept, OR you can ask me to explicitly state them. Apparently you did NOT read our paper.
 * RESPONSE 2: The readers are uniformly confused by the state of affairs, NOT by me. See for example http://planetmath.org/sturmstheorem, where they warn the readers "Be aware that some computer algebra systems may normalize remainders from the Euclidean Algorithm which messes up the sign." Confusion reigns and all I am trying to do is clear things up.
 * RESPONSE 3: Here you are right. I should merely had mentioned that there exists a different terminology. BUT the point you are missing is that there DOES exist another sequence different from subresultant prs. We call it modified subresultant prs, they call it signed subresultant prs. We and they AVOID the use of prem (your favorite function).
 * RESPONSE 4: I do not see any conflict of interest. The software is distributed with sympy 1.0 and I do not see why we cannot reference it to make the readers understand the true nature of things. You are excellent at making things readable. So why don't you work on my text?
 * — Preceding unsigned comment added by Akritas2 (talk • contribs) 17:06, 3 April 2016‎

To sum things up:

Please send me your e-mail address at akritas@uth.gr so that I can send you some papers to peruse. Then you can rewrite what I said in your own words. And it will be better if you wrote it instead of me, because nobody will accuse me of promoting our papers and software.

I can see that you have a great desire to straighten things up. But citing the Bassu, Pollack, Roy book in your subresultant prs article is completely inappropriate for the simple reason they never mention subresultant prs's in their book. For them subresultant prs's are "non-signed" sequences and they only deal with "signed" ones. This is absurd to say the least since we have proved that ALL prs's are "signed", that is the sign matters for ALL prs's.Akritas2 (talk) 06:14, 4 April 2016 (UTC)


 * But citing the Bassu, Pollack, Roy book in your subresultant prs article is completely inappropriate: There is no Subresultant prs article in Wikipedia. Even if this article would exists, it would not be owned by anybody. Moreover, here, we are in the talk page of Sylvester matrix, in which Basu, Pollack, Roy is not cited (except by yourself in your edit). Thus this is not the place for discussing about this book and subresultant prs. Also, if I would write about subresultant prs, I certainly would not use this book as main reference. Finally, it is contradictory to write in the same paragraph that they never mention subresultant prs's in their book and For them subresultant prs's are "non-signed". D.Lazard (talk) 08:29, 4 April 2016 (UTC)


 * I thought it was you who cited BPR in Polynomial_greatest_common_divisor.


 * Talking about BPR in the Sylvester page is VERY appropriate since it is related to Sylvester's matrix of 1853. Akritas2 (talk) 09:13, 4 April 2016 (UTC)
 * Effectively, this is probably me who has cited the BPR book there (I have not checked in the history). I have cited it as being the most accessible book among several, which give the same definition of the subresultant polynomials. However, I have not cited it about the section about subresultant prs algorithm. Unfortunately this section is not sourced (probably because I have not checked which is the best reference). Again, this discussion is misplaced in this article.
 * This article could be expanded by a section about subresultants, as they may be extracted from Sylvester matrix. Nevertheless, such a section must use the standard definition of Sylvester matrix and subresultants, as they appear in all textbooks dealing with the subject. And the definition of the signs of the subresultants must not be changed, even if it is not the most suited one for applying Sturm theorem. D.Lazard (talk) 09:52, 4 April 2016 (UTC)


 * I guess we are both right. I checked your reference again and you are using their first edition. I have the second edition where they define ONLY signed subresultant prs's and signed prs(!!) YES, that is what they call Sturm's sequence.


 * Anyway, in this article I think it is worth noting that for COMPLETE prs's the Sylvester matrix of 1840 is associated with the Euclidean algorithm and the subresultant prs whereas the Sylvester matrix of 1853 is associated with the Sturmian algorithm and the modified subresultant prs.  You can source Sylvester's papers of 1840 and 1853 as found in the paper cited below.


 * Actually, Sylvester's matrix of 1853 is more important than the other one. It was used by Anna Johnson in the 1917 paper to connect the matrix with Sturm's sequence. She was the first person in the literature to actually develop the modified subresultant prs algorithm, which was dormant for about a century. For a nice historical account read "ON A THEOREM BY VAN VLECK REGARDING STURM SEQUENCES", Serdica J. Computing 7 (2013), No 4, 101–134.


 * I hope I have persuaded you to include additional material in the Sylvester matrices article. Akritas2 (talk) 12:16, 4 April 2016 (UTC)