Is it mandatory to include the registered trademark symbol ® next to the name of a computer program? Suppose you write a paper and you use Wolfram Mathematica to do calculations. In the article, should the program be mentioned with the registered-trademark symbol immediately following the name and in superscript style, i.e., as follows?


  Wolfram Mathematica®
APA, MLA and Chicago style manuals all recommend not to use trademark symbols.
Chicago

In publications that are not advertising or sales materials, all that is necessary is to use the proper spelling and capitalization of the name of the product. A trademark attorney can tell you when the use of the symbol is required.

from The Chicago Manual of Style Online
MLA

Although owners of trademarked names may suggest otherwise, publishers are not obligated to denote the trademark status of a name when that name is mentioned in text. Authors representing trademark owners frequently feel obligated to use the trademark or registered-trademark symbol (™ or ®) after the first mention of their product names but often do not use these symbols consistently to indicate the trademark status of other names not owned by their particular sponsor or employer.
Because the fair and consistent use of these symbols (or of footnotes denoting the trademark owners) requires exhaustive verification and vigilance on the part of the editor and because the use of these symbols (or footnotes) is not required by law, do not add trademark symbols, registered-trademark symbols, or trademark-denoting footnotes to trade names in MLA publications. In the interest of consistency, editors should also delete such references when inserted by authors.
At the same time, MLA recognizes that authors are often supported and encouraged by their institutions or other funders and that this support may be what enables an author to produce any written work at all. MLA editors are therefore advised to consider carefully an author’s express request that trademark status of particular names be denoted (merely including symbols or footnotes in the submitted manuscript does not constitute an “express request”).
If trademark status is denoted in a particular case, these guidelines should be used:

Use the trademark or registered-trademark symbol, not a footnote.
-The author must specify which words should be denoted and with which symbol (™ and ® are not interchangeable). Trade names not specified by the author should not be cited with these symbols.
Use the symbol no more than four times in one article for each trade name: the first mention in the article’s title, the first mention in the running head, the first mention in the abstract, and the first mention in the article’s text.
If the article is part of a JMLA symposium, add symbols to the trade names in question in all other articles in the symposium for consistency.

In all cases, whether trademarks are denoted or not, the proper spelling and capitalization of trade names should always be verified and consistent. See Appendix C for a list of trade names common to MLA publications and their proper spelling.

from the MLA Style Manual
APA

No, it's not necessary to include the trademark symbol for a trademarked term in academic writing. The trademark symbol is generally necessary to include only in commercial writing, meaning writing that pertains to commerce or the buying and selling of goods (e.g., advertisements). The word Twitter (and other names of companies) can be written in regular, nonitalic font as well.

from the APA Style blog (answer by the author to a comment)

In certain jurisdictions the trademark owner may be required to use a trademark symbol or may benefit from the use of such symbols in a law suit (see the International Trademark Association fact sheet on Marking Requirements).