Declaring a positive variable

Question

Why I have this behaviour?

R /: Greater[R, 0] = True
R > 0
  => True
Simplify[Sqrt[R^2]]
  => Sqrt[R^2]

I expect R as last result.

You have to use assumptions: Simplify[Sqrt[R^2], Assumptions :> R > 0]. — Leonid Shifrin, Mar 16 '13 at 15:14
@LeonidShifrin: No way to say that R is positive once for all? — enzotib, Mar 16 '13 at 15:26
It's definitely best to work with $Assumptions, but if for some reason you don't want that, and want to avoid Simplify, then you could also just define R = Abs[r]. — Jens, Mar 16 '13 at 15:42

score 2 · Answer 1 · answered Mar 16 '13 at 15:14

2

One way to do this would be to keep a list of assumptions for your system, i.e.

assumptions = {R >= 0};
Simplify[Sqrt[R^2], Assumptions -> assumptions]

which returns R as expected.

answered Mar 16 '13 at 15:14

joshsilverman

There is no way to attach that information to R, so to avoid to recall the Assumptions option each time? – enzotib Mar 16 '13 at 15:19

1 Answers1