TITLE: How do we explain the use of a software on a math paper?
QUESTION [24 upvotes]: Suppose one has written a math/computer science paper that is more focused in the math part of it. I had a very complicated function and needed to find its maximum, so I used Mathematica (Wolfram) to do it. How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...".
It looks very sloppy.

REPLY [5 votes]: How do I explain that? "Using wolfram we find the maximum of $f$ to be $1.0328...$ therefore...". It looks very sloppy.

Well, it looks sloppy because it kind of is sloppy by your description. Maybe the right framework for thinking about your question is to imagine that the maximization you are claiming is a component in a claimed proof of, say, the Riemann hypothesis. Would you pay serious attention to a paper containing such a claimed proof that purported to rely on an opaque software-based maximization without providing any code, let alone any guarantees that the code and the underlying software platform it runs on do what they say they do? I wouldn’t, nor do I expect any serious person to allow such a paper to be published.
Now, I‘m guessing the problem your paper claims to solve isn’t as important as the Riemann hypothesis. The question of what authors of math papers can get away with and still get their paper published is distinct from the question of what authors should do as an ideal to aspire to that would make their paper’s claims truly convincing and watertight. People do get away with all kinds of minor (or even major) sloppiness, of the kinds you mention and of other kinds having nothing to do with the use of computers, all the time. I know I have. Nonetheless, since you seem to be asking about what is the “right” way to explain your result, the answer (assuming you are publishing what is meant to be a rigorous theorem with a proof that’s up to the standards of a good pure math journal) is: provide as many details about your claimed maximization as are needed to convince almost everyone in the research community of the validity of your claims. 
For myself, seeing your Mathematica code would be an absolute minimum to satisfy this condition. Depending on the precise nature of your calculations, I may also want to see that they satisfy some combination of the following conditions:

They are based on algorithms that have been around for a long time and everyone is sure are correct.
They are based on algorithms that have themselves been published in peer-reviewed journals.
They can be replicated with relative ease in software packages other than Mathematica.

Hope this helps.