# Talk:Symbolic computation

To-do list for Symbolic computation:
 Here are some tasks awaiting attention: Expand : add sections on: History Computer science aspects Expressions Simplification Mathematical aspects

## Untitled

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)

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:

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 above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

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 ${\displaystyle x\cdot a^{x-1}\cdot 0+a^{x}\cdot (1\cdot \log a+x\cdot {\frac {0}{a}}).}$ is incorrect. The section implies that this is how ${\displaystyle {\frac {d}{dx}}a^{x}}$ would be computed using the rules of differentiation; however in the first term, ${\displaystyle x\cdot a^{x-1}\cdot 0}$ 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 ${\displaystyle {\frac {d}{dx}}a}$ via the chain rule).

The derivative of a general exponential function ${\displaystyle a^{x}}$ 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:

${\displaystyle y=a^{x}}$

Now take log of both sides:

${\displaystyle \log _{a}y=x}$

Use a log property to convert to base e:

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

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.

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

Multiply both sides by lna\cdoty

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

Now substitute the original equation.

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

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)