Typically, use of a trademark symbol by the owner (in your example, Wolfram) is an assertion of their rights - "Hey, we own this name! It refers to our product and you cannot use it to mislead folks into thinking it is your product, or your use of our product, or that we endorse your product's integration with our product..." and so on. So, it is critical for the owner of the trademark to use it often and consistently.

You, on the other hand, do not need to use it to protect their rights, but need to use it in order to not to infringe on their rights. For example, use the mark it if you are talking about your product or service in relation to their trademarked product.

The more formal the mode of publication, the more you should consider using their mark. Book=yes, email=probably not. Like an abbreviation, use it once at the first occurrence only. Nobody wants to read something littered with circle-R. First use signifies you recognize their rights.

Typically, use of a trademark symbol by the owner (in your example, Wolfram) is an assertion of their rights – “Hey, we own this name! It refers to our product and you cannot use it to mislead folks into thinking it is your product, or your use of our product, or that we endorse your product’s integration with our product...” and so on. So, it is critical for the owner of the trademark to use it often and consistently.

You, on the other hand, do not need to use it to protect their rights, but need to use it in order to not to infringe on their rights. For example, use the mark it if you are talking about your product or service in relation to their trademarked product.

The more formal the mode of publication, the more you should consider using their mark, e.g., you should use it in a book, but probably not in an email. Like an abbreviation, use it once at the first occurrence only. Nobody wants to read something littered with ®s. The first use signifies that you recognize their rights.