In general, based on my non-lawyer reading of patents, most software patents cover doing the described algorithm on a computer. Are there any legal issues at all in doing an algorithm by hand, on pencil and paper?
What if, instead of pencil and paper, you used a general purpose computer mathematical environment (e.g. Wolfram Alpha) to interactively perform each step? This doesn't seem very different in character to me than performing the algorithm manually. Is there any precedent for this?
Of course, there are all sorts of other gray areas - for example, what if you designed a custom interactive program that used ideas from the patented algorithm to "give hints" to the user as to what to do next, without actually performing those steps? Have any of these boundaries of what it means to "perform" algorithms come up in real cases?
This question is asked purely in the spirit of intellectual curiosity - I am not asking for legal advice on a particular situation.