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My algorithm uses the modified version of existing algorithm (architectural modification) and I have combined it with existing mathematical law. so can a patent restrict others form using such combination of modified algorithm with a Mathematical law?

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I agree with George White. I have several algorithm based patents. In all cases, they patent the application of a novel algorithm to solving a very specific problem (analysis of real time PCR results). I've been told (I'm not a lawyer myself) that an algorithm, by itself, would be considered "abstract" and thus unpatentable.

Even if you decide on a specific application of your algorithm for the patent, it still needs to be novel and non-obvious to someone skilled in the art. Since you are modifying an existing algorithm and combining it with another existing mathematical law, the question the examiner might pose is whether the modification and combination is something someone skilled in the art might think of and is thus obvious. It might take a skilled patent attorney to draft and prosecute a patent against such a challenge.

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It is possible but it would need to be applied to some useful end. Using the terms algorithm and mathematical law in the text of a patent application would liking get it rejected out of hand unless phrased very carefully.

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