When a current policy of claiming machines are "in" and software is "out", then computing devices are defined as machines. Therefore, it is a Machine that receives, adds, calculates, and compares. See a previous post discussing the policy of software-machine equivalence.
An algorithm is a computer executable code for adding, analyzing, comparing, processing, etc.
A proficient, professional patent writer can define a single invention in multiple ways, such as a method (method for...), apparatus (apparatus that …), a system (system comprising of...), and a computer program (that …).
US PTO allows three independent claims with 17 dependent claims for a basic filing fee, extra claims incure a per item charge. See more on claims language in the category of Patent Writing: Claims.
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