Answers composed entirely mechanically, e.g. by computer algebra systems

Question

Some users post many entirely machine-composed answers, e.g. integrals computed by Maple (e.g one user has over 150 such answers).

Should such "answers" be CW?

Should they be comments?

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Update ($2$ days later) $ $ Based on initial feedback in comments, answers (and downvotes), it seems some readers may have misinterpreted the scope of the question (which I thought would be clear from the many linked examples).

To clarify, this question concerns only answers that consist of a computer algebra system command followed by its output (the "answer", e.g. here or here). In particular this question does not concern answers that additionally include proofs or explanations of the way the answer was derived (be they human or machine generated). There is no intent to discriminate against machine-assisted answers (having been a Macsyma developer I have much respect for such symbiotic collaboration).

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Note that if someone wanted to gain rep quickly for nefarious purposes, then this loophole provides an easy quick method for doing so. Even a user with little knowledge of mathematics can feed these problems into a computer algebra system - even a bot could do so.

Answer 1

I appreciate people taking the time to show how a problem can be solved using a computer (I have done it myself several times) and, honestly, I do not see why they should be deprived of the little symbolic recognition that a few rep points mean; it is often not a trivial task to coerce a computer to do what one wants. Not everyone knows how to do this, quite a few are not even aware that it is possible to do it (specially in more elaborate areas, like commutative algebra and such), and one can learn quite a bit by being exposed to this information.

On the other hand, answers which simply give a number, as in this example, and not even an indication of how they were obtained, should not be CW but, IMO, simply downvoted.

Answer 2

This depends on the question and the precise type of answer. If somebody wishes to simply know the value of some definite integral or some anti-derivative they might be perfectly happy with an answer of the form: Using SomeCASCommamnd you get Result. (Such an answer can also be non-trivial.)

If the intent of the question is beyond any reasonable doubt to do something 'by hand' (typical examples, last digits or generally values modulo $n$ of exponential expressions) and somebody posts a CAS-solution simply brute-forcing it) then this is an unhelpful answer or perhaps even a non-answer and should be treated as such.

If the intent is unclear this is an issue with the question and should not necessarily be held against respondents.

Whether the answer is CW or not is mainly irrelevant in my mind, yet I do not see any reason for it to be CW. In the latter case a comment might still be appropriated, though sometimes even this might not be desirable.

Answer 3

Sometimes it's not fine

If:

• Only raw calculation result are involved. These type of questions are better up as a comment, since they donot help the asker in any ways (actually) but only show what's unnecessary concerning an answer. Example of such an answer:

  Q: What are the last three digits of $3^{297}$?
  A: According to XYZ CAS it's $963$

_{I think this is the only point this question's about, but I think more detail needs to be involved?}

Sometimes it's fine

If:

• If the question or a minor step involved with it can be done both by hand and a CAS and the answer-er explains how to "actually do it" and if it is tedious for the answer-er (not for the OP, the question was meant to teach something to OP), then it may be fine to do it.Example of such an answer(kinda exxagerated):

  A: ... the previous thing can be expanded easily, but it's tedious so I use a CAS and get: $$(x+y)(y+z)^2(z+x)^3=\scriptsize x^4 y^2+2 x^4 y z+x^4 z^2+x^3 y^3+5 x^3 y^2 z+7 x^3 y z^2+3 x^3 z^3+3 x^2 y^3 z+9 x^2 y^2 z^2+9 x^2 y z^3+3 x^2 z^4+3 x y^3 z^2+7 x y^2 z^3+5 x y z^4+x z^5+y^3 z^3+2 y^2 z^4+y z^5$$ So we can...

Sometimes misinterpreted

Sometimes some answer-ers put up answers without explanation. It should not be taken for granted that a CAS has been used (it may be or not be). It's better to judge using your own intelligence when it fits.

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Provide Feedback

I think I tried to add relevant points but some may agree/disagree. I feel this post should be free for everyone to edit (after discussing in comments, preferably) so that additional point can be added and irrelevant removed.

Answer 4

I think @ADG has provided a nice summary of when it is and isn't acceptable to post answers involving CAS. CAS is a lovely tool that I certainly use to check my hand-derived results and sometimes to get around tedious algebra that isn't the entire point of a problem.

However, CAS can be downright misleading, if not thoroughly disconcerting, if used mindlessly, even if technically correct. I'll discuss a real example here on M.SE.

The problem concerns a double integration. Really, the trick to analytical evaluation lies in a change in the order of integration. That is where the thinking is. Maybe a CAS can recognize the thought pattern and produce the correct answer. I don't know of one, however. All I know is what happened when someone (a Maple salesperson?) answered the question with Maple I/O.

So, I reproduce the pure CAS answer:

$$-1/12\,{\frac {2\,{\mbox{$_3$F$_2$}(1/6,1/2,1/2;\,7/6,3/2;\,1)}\Gamma \left( 5/6 \right) \Gamma \left( 2/3 \right) -{\pi }^{3/2}}{\Gamma \left( 5/6 \right) \Gamma \left( 2/3 \right) }}$$

To the inexperienced reader trying to learn something, this is enough to discourage. Seriously, if you were struggling in Calc III and were presented with this answer, wouldn't you be tempted to give up?

The sad part is that the answer is quite correct, numerically. But we have generalized hypergeometric and ugly-looking gammas. That integral must be so very hard!

This is why CAS-only solutions are unacceptable in many cases, even if the OP only asked for the result of evaluating the integral. There is a level of thought - at this time, human thought - that the problem deserves, and that someone posting an answer at M.SE needs to describe. The OP needs to be taught to recognize that a change in order of integration can reduce some of these double integrals to simple single integrals.

In this case, as the accepted solution explains, the double integral evaluates to $\pi/24$. That's it. I don't care if the CAS solution agrees with this somehow, either numerically or through a complicated series of identities; the CAS has failed to present the answer in a useful form. It, and any answer like it that favors mindlessness and I/O over understanding and exposition, should be downvoted thoroughly.

Answer 5

Whether an answer is useful or not depends on much more than whether it was produced by a human or a machine. The one case where a machine-produced answer is not likely to be helpful is that of a student trying to solve a homework problem. But even there, the machine's result might show that the student's approach is wrong. For example, it often happens that the student is looking for an exact solution when what is really needed is an existence proof. If the exact solution turns out not to have a "closed form" expression, or to be expressed in terms of special functions, that would be an important clue.

In "real life", as opposed to homework, when someone asks a mathematical question they are usually interested mainly in what the answer is; the algorithm by which the answer was obtained is of secondary interest. I see no reason to disqualify machine-produced answers there.

Answer 6

I cannot think of a reason why it would ever be helpful to something which could, with trivial effort or thought, be retrieved from computer algebra software as an answer - this is to say, answers which, like those linked to in the question above, provide only the input and output to a computer algebra system, especially when the input is not particularly cleverly composed (i.e. using common functions in obvious ways). Why should our site be a duplicate of this one (or various common softwares), when that one is really much better at taking suitable questions and immediately giving correct results? Correct results (even numerical) are often helpful as comments, especially on problems that seem otherwise intractable, but otherwise, it's sort of like addressing the question somewhere else. Such answers should be downvoted.

One of this site's strength is that it can offer strong explanations of how to resolve questions and can actually, perhaps, help people learn mathematics. In my opinion, the best answers on this site use a lot of words beyond what is strictly necessary for the mathematics - they use extra words to clarify tricky things, offer insight into bizarre twists in proofs, or draw attention to important tricks. Sometimes "You can use CAS to solve this/aid the solution by doing ________" is helpful, but there is a marked danger here: CAS is a black box. It doesn't tell us how it works. Even an answer which primarily relies on CAS should do more than provide the proper input and the output - what else it ought to do varies, but perhaps it should explain exactly what the functions used are doing, gesture to important bits of it, or explain how the problem can be broken into commands amenable to CAS.

We don't need any new criteria to judge that answers which just feed the question directly into CAS with no further explanation are poor quality. Such answers are, as a matter of their empty composition, of lesser quality than what other answers this site has produced and of lesser quality than we should expect of future answers.

Answer 7

I have noted the same user that Bill Dubuque mentions: he now has almost 300 answers, most of them providing Maple code (more than 10 have been removed in the last 24 hours). Unfortunately, Bill Dubuque's question has been misunderstood as "what to do with posters that provide CAS answers", when in reality it is about posters that massively provide them according to what it seems to be an agenda (otherwise, CAS answers may be fine with me, depending on the context).

What I suspect is that the user in discussion is far from innocent and is probably working for Maple, subtly advertising their products. While I admit that this kind of advertising is intelligently done and on the light side of annoyance, there is a risk of slowly turning MSE into a commercial battleground (a thing that Wikipedia moderators know very well).

What I suggest is that moderators check whether this user's IPs are in any way connected to Maple domains (or to some reseller's domain). I also suggest them contacting this user and explicitly ask him whether he works for any software-selling company. I guess that this can't be banned from MSE, but at least it should be made transparent (disclosed as such in the profile page).

Answer 8

It may be a secondary point, but not a minor one I think, but in many cases the attribution of the result to a computer program is given in the Answer. So it's not "composed entirely mechanically", and the attribution to the source of result is a Good Thing(tm) by Community standards.

On the central point, I see no justification for a rule that such Answers should be CW. Could many such Answers be improved by further explanation of how the result was derived? Sure, but that is the case with the majority of Answers (even mine!), at least to an extent that improves content for future Readers.

The proposed rule seems fraught with difficulties of implementation and unintended consequences, to wit:

Who would draw the line as to how much of the content results from a program, and how much from a Human Being(tm)? What if the Answer were prepared by a Human, but checked with assistance of software, and one or more defects corrected? Would anyone know, absent the disclosure of this by the post itself? If it were disclosed, should the preparer be penalized for having done so?