Higher-level mathematical concepts, such as entirely new methods of calculation, may be patented. For example, this is the abstract of a patent application being reviewed at the moment:
A method for obtaining an estimate of a solution to a first system of linear equations. The method comprises obtaining a second system of linear equations, obtaining an estimate of a solution to said second system of linear equations, determining differences between said first and second systems of linear equations, and determining an estimate of a solution to said first system of linear equations based upon said differences and said estimate of said solution to said second system of linear equations.
In the language of the various laws, this would be called a "process," which the statute degines as "a process, act, or method." Also according to the law, the process must be useful and novel.
It's worth noting, though, that case law has defined that "laws of nature, physical phenomena, and abstract ideas are not patentable subject matter."
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