Re: Rearrangement of expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg91744] Re: Rearrangement of expression*From*: "David Park" <djmpark at comcast.net>*Date*: Sun, 7 Sep 2008 05:34:34 -0400 (EDT)*References*: <g9t6np$j9n$1@smc.vnet.net>

Manipulating expressions is either fun or a pain in the neck. Let's hope you'll get enough suggestions to make it fun. expr = a/Sqrt[a^2 + b^2]; The major difficulty that you throw in is the desired form (b/a)^2. Mathematica always automatically expands that to b^2/a^2 so we will need a rule to put it into a HoldForm powerformat = Power[x_, n_] Power[y_, m_] /; m == -n \[And] n > 0 -> HoldForm[(x/y)^n] Then the easiest solution is: (expr /. a -> 1 /. b -> b/a) /. powerformat Sometimes we might consider that substitutions are a bit risky because we might make a mistake in keeping all the substitutions coordinated. Here is a more formal calculation approach using a routine, MultiplyByOne, from the Presentations package. MultiplyByOne[factor, simplify entire expression, simplify numerator, simplify denominator] multiplies the numberator and denominator by the same factor and applies simplification functions, first to the numerator and denominator, and then to the entire expression. Needs["Presentations`Master`"] expr // MultiplyByOne[1/a, Identity, Identity, Sqrt[Apart[#^2] /. powerformat] &] Of course, this manipulation is only correct if a > 0. {a/Sqrt[a^2 + b^2], 1/Sqrt[1 + b^2/a^2]} /. {{a -> 2}, {a -> -2}} -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ <Gehricht at googlemail.com> wrote in message news:g9t6np$j9n$1 at smc.vnet.net... > Hi! > > Suppose I have the fraction a/Sqrt[a^2+b^2]. How can I rearrange it to > 1/Sqrt[1+(b/a)^2]? > With thanks > Yours Wolfgang >