Declaring a positive variable [duplicate]

Question

This question already has an answer here:

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].
@LeonidShifrin: No way to say that R is positive once for all?
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].

covopsdaf2 · Answer 1 · 2013-03-16 15:14:26Z

up vote 2 down vote

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 at 15:14

covopsdaf2
1505

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

marked as duplicate by Leonid Shifrin, Jens, rm -rf♦ Mar 16 at 17:19