That’s a great question, and in the US I really don’t think there’s a definitive answer, even if you ask a patent attorney. Supposedly you can patent a “practical application” of a mathematical formula, but what does that even mean? “A = pi * r^2” has the practical application of calculating the area of a circle. Does that mean that this application can be patented? What exactly is the threshold of “practical?” Does it mean “can make money?” This is why many, myself included, are of the opinion that software patents are a huge can of worms that never should have been opened in the first place.
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