I could not find anything on any legal requirements to use trademark symbols if you are not the trademark holder (or are required to use them by a contract). Here, several attorneys state that you do not have to use them even in the “stronger” case that you are reselling the product. Briefly, it’s the trademark owner who is responsible for using it and there is nothing that requires you to use these symbols, unless you have signed a contract to do so:
It is the trademark registrant/manufacturer who is responsible for putting the indication on the product, not you.
Since you are merely resoling [sic] the product, you have no obligation to put any symbol (R or TM) anywhere.
This leaves the question of style, on which I share the opinion of But FUNKY!!!web!!!DUDES.com is their trademark! (written by a professional copy editor), which is mainly on capitalisation and punctuation, but can also be applied to trademark symbols to some extent:
One should rather adhere to general spelling and language rules and to what benefits the reader than to what a company wants its product to be called:
The companies and their trademark lawyers want you to duplicate their capitalization. They also want you to use the trademark symbol. They also want you to use the word "brand" and a generic identifier to guard against the loss of their trademarks (journalists eat Big Macs; McDonald's lawyers might want us to eat BIG MAC® brand sandwich products). Are you going to give in to all of those demands? Do you want your stories to look like press releases?
Following this, I would call Mathematica just “Mathematica”, maybe in italics or small-caps in accordance with the journal’s or your own style and accompanied by an appropriate citation.
I would not use a copyright symbol as it does not benefit the reader or anybody else¹ – it just diverts from the content of the text and slightly looks like you are paid by the software company to advertise their product. (I also would not use “Wolfram Mathematica“ unless I have to expect that some reader confuses it with something else which is also called “Mathematica”.)
There may be some situations specific to Mathematica, where one has to expect some readers to be confused, as, e.g., they do not directly identify it as a software due to its name being not obviously a name. However, in those cases you can refer to it as “the Mathematica computer algebra system” or provide a citation.
¹ except, perhaps, the marketing people of the software company – who are not going to read your publication