I want to let
Simplify know the exact value of a symbol, to resolve logical statements, but don't want it to actually replace it. For instance, I would like something like
assumptions = x==4; Simplify[Sqrt[x^2], assumptions]
to output x and not 4 (or
How can this, or something analogous, be done?
Edit: It wasn't clear enough that I understand that in this case an assumption like
x>0 would output what I want -- however, this is not what I'm looking for. This is what I have been doing so far, but it is messy and needs focused attention. That is, I need to be sure that the
eps that I set to define a range as
assumptions = (x > xValue - eps) && (x < xValue + eps)
is small enough for every independent simplification to be equivalent to that of
assumptions = x == xValue
Even if I could generaly chose a value exaggeratedly small such that this would be the case for all my problems, I'd still like to find a better alternative -- if there is one.