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I am trying to define a new Domain for variables to use with functions like FindInstance or Solve. For example, If I wanted to solve x+y+z=1 over the Reals, I'd get a large solution space. But If I solved it over the Rationals, I'd get a smaller solution space. If I wanted to solve it over the reciprocal of the Integers, then I'd get the solutions {1/2, 1/3, 1/6}, {1/2, 1/4, 1/4}, {1/3, 1/3, 1/3}, and their permutations. If I solved it over the reciprocals of the powers of 2, then I'd only get {1/2, 1/4, 1/4} and its permutations.

I wanted to define new Domains A, B, and C, where:

  • A is the Ring of Dyadic Rationals (All Integers divided by all powers of 2),
  • B is the set of Unit Dyadic Rationals (1 divided by all powers of 2, and 0),
  • C is the set of all Unit Fractions (1 divided by all integers(except 0), and 0).

If there is a smarter way to do what I'm trying to do, I'd also love to know that.

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