# I would like to ask about how do certain calculations for example Wolfram Alpha, are there general guidelines?

I would like to ask in a next future how a CAS (I mean a symbolic calculator in mathematics, but I don't understand/know basics in symbolic calculus) does to calculate some operations in mathematics.

Example 1. I do not want to ask about how finds, for example Wolfram Alpha, a root of a non-linear equation. Since the users that provide me answers should said that is only an implementation of, for example, Newton method. Or for example how calculated the LU factorization, a limit or a definite integral. I accept also that there are methods to solve certain problems as plot graphics.

But from my ignorance there is a kind of questions that I don't want to discard because are curious. My problem is that I don't know noting about how symbolic calculators work.

Example 2. I would like to know for example for an identity yet solved in Mathematics Stack Exchange, how a CAS (for example the cited) can obtain such solution. Since it seems magic, and is curious how knows that a series converges or what it is sum, how calculates double integrals or define the convergence or functions.

My

Question. How one can ask (in my situation since I ignore how works such calculator) about how did such calculations (I say for a fixed example) a symbolic calculator? Are rights any of cited questions in Example 2? Since I don't know nothing about how are working with my questions, for example Wolfram Alpha, and I don't know nothing about its engineering, if my example is tagged with (wolfram-alpha) are there more interesting cases, different of those that I cited in Example 2? Thanks in advance.

• If there are examples, near to my purpose, in Mathematics Stack Exchange you can add as a comment or in your answer. Thanks. Also if you want add more tags to this current question in this META.
– user243301
Aug 12 '16 at 13:09
• You might want to consider Mathematica for this purpose instead, by the way.
– Asaf Karagila Mod
Aug 12 '16 at 15:43
• Note that as a rule the Mathematica.SE Community excludes as off-topic questions pertaining to Wolfram Alpha. Aug 12 '16 at 18:28
• I undersand then that the best way is continue studying mathematics and using different CAS, and search information in internet or books. Thanks, thus I discard in a next future asks about this kind or questions.
– user243301
Aug 12 '16 at 19:11

If it were literally a Question about how Wolfram Alpha does a symbolic calculation, this would probably be off-topic. After all Wolfram Alpha is a proprietary software system, containing the facility of proprietary software package Mathematica. Math.SE users would not be in a position to give definitive evidence of how the calculations are done.

On the other hand questions about algorithms that are known to perform symbolic calculations efficiently are welcome at Math.SE (and perhaps at some related SE Communities).

• Very thanks much to clarify my question. Yours is a good answer. I understand your words about the property of Wolfram Alpha, that is welcome because this online calculator is very good. My purpose/goal was say something as: this online calculator did this calculation, do you known how this kind of calculator works to, for example, deduce this convergence or this identity. My thoughts were ask from a general viewpoint, and when I refers the engineering, is because I don't know nothing about symbolic calculator, it was a way of speaking. Very thanks much for your answer, references.
– user243301
Aug 12 '16 at 19:09
• There are open source CAS packages for which the details of how computations are done would be available to public inspection. Provided there is a strong connection to solving a mathematical problem, algorithm questions might be high quality posts. Aug 12 '16 at 19:22
• You are very gentle/kind (in spanish: eres muy amable). I was asking because it a very curious theme. Very thanks much.
– user243301
Aug 12 '16 at 19:30
• @user243301 Wolfram Alpha uses Wolfram Mathematica for lots of its calculations. If you can work out what command it is using then you can read the documentation to find out the method it is likely to use. Also you can explore Wolfram Mathematica commands (and help documentation) in Wolfram Programming Lab. Jan 9 '17 at 12:08
• Thanks a lot @IanMiller and the best year 2017
– user243301
Jan 9 '17 at 21:25