Can I write a computer program based on a theory in a borrowed book?
<p>Suppose I borrow a book from a library and then use the theory described in this book to write a commercial computer program. In this situation, am I infringing any copyright laws?</p>

<p>In the US, Copyright does not extend to theories:</p>

<blockquote>
  <p>Section 102 of the Copyright Act (title 17 of the U.S. Code) clearly
  expresses this principle: “In no case does copyright protection for an
  original work of authorship extend to any idea, procedure, process,
  system, method of operation, concept, principle, or discovery,
  regardless of the form in which it is described, explained,
  illustrated, or embodied in such work.” <a href="https://www.copyright.gov/circs/circ31.pdf" rel="nofollow noreferrer">Copyright of Ideas, Methods, or Systems - govcirc31.pdf</a></p>
</blockquote>

<p>Copyright does protects the <em>expression</em> of a theory. In your case, </p>

<blockquote>
  <p>A computer program is a set of statements or instructions to be used
  directly or indirectly in a computer to bring about a certain result.
  Copyright protection for a computer program extends to all of the
  copyrightable expression embodied in the program. The copyright law
  does not protect the functional aspects of a computer program, such as
  the program’s algorithms, formatting, functions, logic, or system
  design. <a href="https://www.copyright.gov/circs/circ61.pdf" rel="nofollow noreferrer">Copyright
  Registration of Computer Programs - circ61.pdf</a></p>
</blockquote>

<p>So you can develop a commercial computer program that does what the theory postulates, and that program itself will be under your copyright.</p>

<p>The idea that you borrow the book from the library isn't relevant; nor would be reading the book in a bookstore.</p>

united-states copyright software