I would like to write an expression of the form $a/\sqrt{b c}$ as $a/d$ where $d = \sqrt{bc}$. My hope was to use a similar strategy as when the square root is omitted:
Simplify[a/(b c), d == b c]
which yields a/d
.
However,
Simplify[a/Sqrt[(b c)], d == Sqrt[b c], Assumptions -> {b > 0, c > 0}]
yields a/Sqrt[b c]
. As shown, I tried specifying that b, c are positive, but this makes no difference. I have also tried FullSimplify
.
I find the same behavior with Simplify[a/(b c), d == 1/(b c)]
and Simplify[Exp[a]/(b c), d == Exp[a]]
, so there is clearly something going wrong when there is a composition, or when the right hand side of "==" is something other than Plus[blark, blah]
or Times[blark, blah]
.
Does anyone see what I am missing here?
EDIT:
I should clarify, the use-cases I have are more complicated than the simple example above. As pointed out, the simple cases can be handled by TransformationFunctions
. It is not clear this approach works for more complex expressions, such as
Simplify[Exp[a] (g + h)/Sqrt[(b c)], d == Exp[a] (g + h)/Sqrt[(b c)]]
which is more of interest.