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Inventions, systems, methods and algorithms -- such as compression algorithms, innovative machines for removing foot-hair, or even new ways of implementing old machines -- may be patented.
Creative works -- such as books (including manuals and technical documents), computer programs, other art, and even the arrangement of collections of other creative works -- can be, and are by default, copyrighted.
Words and phrases -- such as "Coca Cola" or "The future's bright, the future's Orange" -- may be trademarked for a certain context only. It's important to note that trademarks are unique in that they must be aggressively maintained in order to retain their trademark status. This means that if a company suddenly goes after you for displaying their trademark, it's not because they're evil, it's because if they let you, then it's not their trademark any more.
The d20 system is not patented. "d20", with reference to the d20 gaming system, is trademarked. A manual or document explaining the d20 system is copyrighted.
Upside: Since it is not patented, you may use the d20 system.
Downside #1: Since it is trademarked, you may not advertise your system as a "d20" system.
Downside #2: Since they are copyrighted, you may not copy material from documents explaining the d20 system into your code. Instead, you must find your own words.
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