I tend to think of these things as an engineer, rather than a mathematician. A mathematician will say that all algorithms are abstract ideas. I tend to think that "alias analysis" is the abstract idea, while Steensgaard's algorithm is a specific, concrete way of implementing the idea with desirable properties and trade-offs.
Then, are mergesort and quicksort both patentable as specific, concrete ways of implementing the idea of sorting with desirable properties and trade-offs?
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I tend to think of these things as an engineer, rather than a mathematician. A mathematician will say that all algorithms are abstract ideas. I tend to think that "alias analysis" is the abstract idea, while Steensgaard's algorithm is a specific, concrete way of implementing the idea with desirable properties and trade-offs.
Then, are mergesort and quicksort both patentable as specific, concrete ways of implementing the idea of sorting with desirable properties and trade-offs?