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Re: Manipulating square roots
*To*: mathgroup at smc.vnet.net
*Subject*: [mg112377] Re: Manipulating square roots
*From*: "David Park" <djmpark at comcast.net>
*Date*: Sat, 11 Sep 2010 05:45:39 -0400 (EDT)
The Presentations package has a routine FactorOut that is useful here. The
trick is to pull a "factor" out of an expression and then protect the result
so that Mathematica won't simplify it back.
FactorOut[factor, quotientfunction : Indentity, factorfunction :
Identity][expr] will pull factor out of expression and write the result as
factorfunction[factor] quotentfunction[Expand[expr/factor]].Factor would not
even have to be in expr. The functions, if not Identity, would most commonly
be HoldForm.
Here we go back and forth between the two forms.
Needs["Presentations`Master`"]
expr = Sqrt[a^2 - b^2];
step1 = MapAt[FactorOut[a^2, HoldForm], expr, 1]
step2 = Simplify[step1, a > 0] // ReleaseHold
Giving...
Sqrt[a^2 (1-b^2/a^2)]
a Sqrt[1 - b^2/a^2]
step3 = MapAt[FactorOut[1/a^2, HoldForm], step2, {2, 1}]
step4 = Simplify[step3, a > 0] // ReleaseHold
Giving...
a Sqrt[(a^2-b^2)/a^2]
Sqrt[a^2 - b^2]
This has the advantage of doing it by calculation, but a simple rule as you
wrote might be simpler. It depends on the context in which you are doing the
transformation.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
From: alan [mailto:alansbarnett at verizon.net]
How can I get mathematica to bring a factor inside a square root? For
instance
a Sqrt(1-(b/a)^2) -> Sqrt(a^2-b^2) (if a is real and a > 0).
Also, how do I get Mathematica to perform the operation in reverse?
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