I am busy writing a report for university.
For this, I did some programming in MATLAB and simulations in Aspen Plus and HYSYS.
When referring to these software in the report, should I symbols such as ® /© next to their names?
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There is nothing that says it is bad to include them. It's not really required for more common writing. If you aren't following a specific journal format it's acceptable to use the symbol the first time you introduce the brand then you can drop it off the next time to use it or you can use it every time you mention the brand. It's really your preference.