Talk:Computer algebra

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Article could use a reference to the same concept beyond CS. Can't find a wiki yet. VoidLurker (talk) 20:43, 30 March 2009 (UTC)

I still don't really have a good understanding of what symbolic computation is, versus numerical computation. Some examples would help. Coldhawaiian (talk) 23:19, 29 October 2010 (UTC)

Merger with computer algebra system

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

Not to merge pretty clear consensus against.--Salix (talk): 10:16, 2 December 2010 (UTC)

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I propose that Computer algebra system be merged into Symbolic computation. The second is what the first does. I can see that the CAS article is more developped, but I think taking the name of the activity is better than taking the name of the tool. The start of the merged article would be something like:

“ Symbolic computation or algebraic computation is the use of computers, to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols. A computer algebra system (CAS) is a software program that facilitates symbolic computation. ”

I guess the alterntive is to start with

“ A computer algebra system (CAS) is a software program that facilitates symbolic computation - the manipulation of mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols. Symbolic computation is also known as algebraic computation. ”

Yaris678 (talk) 13:35, 19 November 2010 (UTC)

Oppose. The two topics are distinct enough to deserve separate articles. By analogy, we have separate entries for automobiles and internal combustion engines. Although the internal combustion engine is necessary for the operation of an automobile, there are other aspects of automobiles worthy of note, e.g., different models, look/feel, etc. Likewise, an article on computer algebra systems should cover the popular CASs, their differences, general design principles (eg interactive vs noninteractive, functional vs procedural ). Symbolic computation should focus more on the algorithms and principles of symbolic computation rather than the specific implementations. Sławomir Biały (talk) 17:10, 19 November 2010 (UTC)

I think covering design principles and algorithms in one article would make sense. Your automobile analogy illustrates this quite well. And automobile can have a power source that is not an internal combustion engine. An internal combustion engine can power things other than an automobile. In contrast, a computer algebra system must perform symbolic computation and anything that performs symbolic computation is a computer algebra system. Yaris678 (talk) 17:20, 20 November 2010 (UTC)

I'm not really involved with any of these articles, so feel free to disregard my opinion... but given the short size of Symbolic computation and the seeming lack of prospect of fleshing it out to something else than a link collection without a lot of content duplication, the proposal seems to have a lot of merit to me. I feel the automobile analogy is false; compare hypothetical articles on Car manufacturing and Car factory. — Pietrow ☏ 21:59, 25 November 2010 (UTC)

Strongly oppose: I specifically disagree that "anything that performs symbolic computation is a computer algebra system". You can do this with pencil and paper, certainly -- and there are developments in the field that have little or nothing to do with CAS. CRGreathouse (t | c) 00:57, 28 November 2010 (UTC)

Do you have a source that says that algebraic manipulation with pencil and paper is symbolic computation? The article currently says "Symbolic computation or algebraic computation, relates to the use of machines, such as computers, to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols." Yaris678 (talk) 17:23, 28 November 2010 (UTC)

Please. Most of the field was developed before computing machines. For example, Laplace developed the first version of what became the Risch algorithm. If you need a citation on that, it's in A Short Account of the History of Mathematics. CRGreathouse (t | c) 17:32, 28 November 2010 (UTC)

Do you mean this book? Google gives no mention of symbolic computation or Risch algorithm. Or am I to assume that you are being facetious since you started by saying "please"?

I am not saying that what you are saying is not true. I am saying that if it is true then we should change the article. It would be nice to be able to cite something for the new text since the definition has been basically unchanged since the article was created in November 2005.

Yaris678 (talk) 18:32, 28 November 2010 (UTC)

Of course the book isn't going to mention the Risch algorithm because the book predates the algorithm! CRGreathouse (t | c) 21:54, 28 November 2010 (UTC)

So that's a "yes" to being facetious. Yaris678 (talk) 12:38, 29 November 2010 (UTC)

Symbolic calculations may be done by hand, but so can numerical calculations. When I saw this proposed merger, at first I thought no, no, no, but then I thought we don't have separate articles for Numerical computation and Computer numerical system although we do have List of numerical analysis software, but then I thought, well actually we do have calculator but then calculators aren't as sophisticated as numerical software like Matlab, and we don't actually have an article on Numerical software per se, and why should we since we have Numerical analysis#Software so we could merge Computer algebra system with symbolic computation to match the situation with the Numerical analysis article, or we could create a Numerical software article to match computer algebra system, or we could say there is no reason to be consistent so forget about the numerical stuff. Also numbers are symbols so what is the distinction anyway ? Since we don't merge calculator into arithmetic, then on balance I'm thinking of opposing the merger since CASs can do other things than symbolic computation: CASs can do numerical computation, CASs can produce graphs and charts and all sorts of mathematical visualization, CASs include programming languages, CASs can output mathematically typeset documents in a variety of formats. So CASs are systems that include symbolic algebra but they do other stuff as well, so definitely oppose. 2.97.17.13 (talk) 22:54, 28 November 2010 (UTC)

Thank you for your considered opinion. It makes a nice change.

I agree with pretty much everything you say but I would like to quibble with the last two sentences. Software does exist that does more than just symbolic computation, but isn't such software also more than just a computer algebra system?

By the way, I'm not massively bothered either way. My main aim here is to improve Wikipedia. If we decide not to merge but the merge discussion leads to some new content for the articles then that is still a productive outcome from the discussion, in my view.

Yaris678 (talk) 12:38, 29 November 2010 (UTC)

I oppose -- some of what's in Computer algebra system might belong here instead and both articles that could use some work, but these are different, though related, topics. In general, I think Wikipedia is better off not merging related articles -- when this happens, both topics suffer. There is a case elsewhere on Wikipedia where (years ago) I gave up arguing with someone who thought they were the only person who knew anything and the result is that one of the two merged topics is now, essentially, gone, edited into non-existence. RoyLeban (talk) 10:03, 2 December 2010 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

To answer Yaris678, since the section is now archived: no, not being facetious. The work predating the Risch algorithm predates the algorithm, tautologically, and so it's not surprising that the book fails to mention the Risch algorithm. CRGreathouse (t | c) 14:41, 16 December 2010 (UTC)

A benefit of keeping symbolic computation = symbolic calculation separate from computer algebra is that some authors use computer algebra to include algebraic methods that relate to manipulation of large numbers (see Modern Computer Algebra by von zur Gathen and Gerhard), other authors are unhappy with the inclusion of mechanization of mathematical topics categorized as analysis (e.g. differentiation, integration) under algebra, and some authors use symbolic calculation to include the mechanized manipulation of expressions that are symbolic but not mathematical (e.g. chemical formulas). These usages need stronger mention in the respective articles. Michael P. Barnett (talk) 20:05, 15 March 2011 (UTC)

Comment about previous merge proposal

I am just reading the closed discussion. I am highly surprised that nobody gave the main argument against the merge: Symbolic computation, also called computer algebra, is a well established and active scientific area, with several annual conferences (ISSAC is the main one) and journals (Journal of symbolic computation is the main one). The design and implementation of computer algebra software is only a part of this scientific activity. Thus, such a merge would be exactly as meaningful as merging computer science and software. D.Lazard (talk) 11:01, 14 November 2012 (UTC)

Empty sections

It is bad practice to create an empty section as a placeholder. Better to work on a draft in your user space and then copy it over. RockMagnetist (talk) 16:35, 16 November 2012 (UTC)

Another good alternative is to add a {{todo}} template to this talk page with a list of the sections you want to create. RockMagnetist (talk) 16:37, 16 November 2012 (UTC)

I'd like to answer a comment in the computer algebra systems talk page here. I think the reasoning behind speedy deletion of articles with no content also applies to sections. Placeholders for future content don't help readers, most of whom probably don't visit the page a second time. However, it's o.k. to have a section with one or two sentences to summarize the topic. RockMagnetist (talk) 15:55, 19 November 2012 (UTC)

The article is looking much better. Don't forget to add citations, though. RockMagnetist (talk) 16:46, 21 November 2012 (UTC)

Structure of the article

As everybody may see, I have started to expand the article by inserting the basic common knowledge of this area. For the moment, I have structured it in "computer science aspects" and "mathematical aspects". I am not satisfied with that: these two kinds of aspects are not always well separated (see section "Equality"). Moreover, I'll soon introduce a section "other representations" to consider the other (than as expressions) methods to represent mathematical objects. As most sections already written deal with the general representation of expressions, it is not clear where "other representations" should be placed. Thus the structure of the organization in sections may not be considered as stable. On the other hand the material in each existing section should be rather stable. D.Lazard (talk) 18:24, 23 November 2012 (UTC)

"Simplification" section -- two issues

First post so excuse my formatting if I got it wrong. The first issue is simple. The first sentence uses the word "derivation" when it should be "differentiation."

Also, I'm pretty sure that the line $x\cdot a^{x-1}\cdot 0+a^{x}\cdot (1\cdot \log a+x\cdot {\frac {0}{a}}).$ is incorrect. The section implies that this is how ${\frac {d}{dx}}a^{x}$ would be computed using the rules of differentiation; however in the first term, $x\cdot a^{x-1}\cdot 0$ they are misguidedly using the pattern for the derivative of a power function. Luckily for the author, the mistake is averted by multiplying by 0 as a result of the (again improperly used) chain rule. (The zero probably came from ${\frac {d}{dx}}a$ via the chain rule).

The derivative of a general exponential function $a^{x}$ can be correctly figured out using implicit differentiation, and this first cancelling term is never seen. Note that the derivative of lnx must be proved first but that can be done easily with the limit definition. For an general exponential function, first define y as an exponential function of x:

$y=a^{x}$

Now take log of both sides:

$\log _{a}y=x$

Use a log property to convert to base e:

${\frac {lny}{lna}}\cdot y=x$

Now differentiate both sides with respect to x. Note that a is constant, x is the variable of differentiation and y is a function of x.

${\frac {1}{lna}}\cdot {\frac {1}{y}}\cdot dy/{dx}=1$

Multiply both sides by lna\cdoty

${\frac {dy}{dx}}=(lna)y$

Now substitute the original equation.

${\frac {dy}{dx}}=(lna)a^{x}$

Anyway, maybe I'm missing something here but I don't see how this could possibly be computed using the method cited in the article, and I think that it is incorrect reasoning.

Samwinnick (talk) 20:11, 7 June 2013 (UTC)

Problems with lead

A user has expressed concerns with the lead - too long, includes information that is not in the body, does not summarize the body properly. I think the first two concerns can be answered with one edit. For remaining concerns, it would be helpful to provide specifics here. RockMagnetist(talk) 15:26, 25 May 2017 (UTC)

One sentence from present lead:

Software applications that perform symbolic calculations are called computer algebra systems, with the term system alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the language used for the implementation), a dedicated memory manager, a user interface for the input/output of mathematical expressions, a large set of routines to perform usual operations, like simplification of expressions, differentiation using chain rule, polynomial factorization, indefinite integration, etc.

And then it ends with "etc." because more could be listed in the mammoth 'with' appendix. — MaxEnt 21:55, 17 January 2018 (UTC)

History of computer algebra

I have reverted the recent edits of the history section because there are WP:OR that contain several historical errors. Firstly, it is an error of asserting that Hermann paper is the first paper on computerized algebra: Macaulay's work on multivariate resultant is an earlier work, which has been much more influential on computer algebra. Secondly, Buchberger thesis was not published in 1965 (date of the defense of the thesis) but only in 1972. Thirdly, although very important, Buchberger's theory became fundamental for symbolic computation only at the end of the seventies, after the development of the symbolic computation softwares (Macsyma and Reduce) and the basic algebraic algorithms (gcd and factorization of polynomials, ...). For the history of the subject, before 1970, citing Buchberger, but not Moses (leader of Macsyma team), Tony Hearn (author of Reduce), Collins (many efficient algebraic algorithms) is a blatant break of WP:NPOV policy. D.Lazard (talk) 09:51, 24 August 2017 (UTC)

My apologies for unintentionally introducing incorrect information - I am not a specialist in this area but I do believe that the "History" section warrants more in-depth coverage than a couple of lines about computational efficiency. I was aware of Tony Hearn's Reduce but not the others, nor had I realized that it predated Buchberger's theory. I used the talk that I cited as the main source of information for my edits although it does now appear that was a bad idea. Do you have a pointer for a more comprehensive source? --Blueclaw (talk) 15:57, 24 August 2017 (UTC)

I agree that it would be great to have a more detailed history section. The problem is that this needs sources, and there is no general source. The few sources that I knows are texts of searchers in computer algebra, generally talking of there preferred subfield. I think of

• Moses about Macsyma and the beginning of computer algebra software.
• Kaltofeln: several papers on polynomial factorization (the remark on the work needed for passing from mathematical abstract algorithms to algorithms that are sufficiently efficient for being implemented comes from one of his articles)
• Some talks of Buchberger about the history of Gröbner bases
• My paper on Thirty years of polynomial system solving, and now?
• Possibly some sections of Cox, Little, O'Shea books.

Because of the lack of sources about the general history of the subject, it is very difficult to expand the history section without introducing original research (in Wikipedia sense, see WP:NOR), and keeping a neutral point of view (see WP:NPOV). IMO, this is for this reason that this section is so sketchy. D.Lazard (talk) 21:25, 24 August 2017 (UTC)

Requested move 25 October 2017

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: moved per nominator, and per common sense. —usernamekiran(talk) 18:40, 1 November 2017 (UTC)

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Symbolic computation → Computer algebra – Computer algebra redirects here. "Computer algebra" is another common name for "symbolic computation", that is less ambiguous. Moreover, we have also Computer algebra system and List of computer algebra systems, that are strongly connected. Thus the move would be a clarification. D.Lazard (talk) 13:52, 25 October 2017 (UTC)

• Comment I'm not sure about this. While there is a lot of overlap between symbolic computation and computer algebra, I don't think they are synonymous. There are topics like computer-assisted proofs and automated theorem proving, i.e., topics in computational logic, that are considered part of symbolic computation,[1] but are not necessarily identified with computer algebra. --Mark viking (talk) 18:52, 25 October 2017 (UTC)

I agree. However the content of this article is only about the computer algebra part of symbolic computation. The other kinds of symbolic computation could be the object of another article or of a dab page. This is what I meant when saying that "computer algebra" is less ambiguous, D.Lazard (talk) 20:25, 25 October 2017 (UTC)

Thanks for the clarification. I understand and, allowing for a DAB at some point, I agree with your points. — Preceding unsigned comment added by Mark viking (talk • contribs) 21:30, 25 October 2017 (UTC)

• Support given the discussion above. --Mark viking (talk) 21:30, 25 October 2017 (UTC)

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The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Distinction between "normal form" and "canonical form"

@D.Lazard: In this revision of this article, you mentioned a distinction between "normal form" and "canonical form" in computer algebra systems. Does this article include any references that explain this distinction? Jarble (talk) 00:18, 2 March 2018 (UTC)

This distinction is explained (without reference) in Canonical form. It appears in most textbooks of computer algebra. In particular Davenport and al. has a section on this (section 2.3.1, Représentations canoniques et normales in the French version; I have not the English translation under hands). It would be useful to add this reference here and in Canonical form. D.Lazard (talk) 09:06, 2 March 2018 (UTC)

References

Requested move 11 May 2020

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Not moved (non-admin closure) Sceptre (talk) 10:26, 26 May 2020 (UTC)

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Computer algebra → Symbolic computation – Please place your rationale for the proposed move here. 58.236.219.64 (talk) 09:10, 11 May 2020 (UTC) —Relisting. buidhe 07:13, 19 May 2020 (UTC)

See also § Requested move 25 October 2017. — D.Lazard (talk) 10:31, 11 May 2020 (UTC)

• Strongly oppose. "Computer algebra" is a well defined scientific area, whose name is standardly used by people knowing it, whichever they work in this area or not. At the beginning of its history, computer algebra was also called "symbolic computation", probably because computer algebra systems were the first software that do not work with numbers (or character strings) but with symbols representing other kinds of entities (possibly themselve). Presently, "symbolic computation" is a much wider area. Above sketched definitions of computer algebra and symbolic computation are not original research, as being discussed in the opening editorial of Journal of Symbolic Computation. Presently, Symbolic computation redirects here. The only reasonable question is whether it should remain a redirect, or must be transformed into a dab page or a broad-concept article (in both case, it should keep a link to Computer algebra). D.Lazard (talk) 10:03, 11 May 2020 (UTC)

References

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The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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