Re: Algebraic Symbol Manipulation

*To*: mathgroup at smc.vnet.net*Subject*: [mg54160] Re: [mg54125] Algebraic Symbol Manipulation*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 12 Feb 2005 01:57:10 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

The Mathematica syntax and commands for solving this problem would be as follows. First, let's define the equation. eqn = V == 1/3 Pi r^2h; Notice that eqn is a symbol that stands for the entire equation. It is Set with =. But in the equation itself we use == for the equal symbol. Then to solve the equation we write... hsol = Solve[eqn, h][[1,1]] h -> (3*V)/(Pi*r^2) The '[[1,1]]' was added to the Solve statement because there was only a single solution and it was returned as a List within a List. Generally there are multiple solutions and multiple variables and that is why Mathematica returns Lists of solutions. In this case we just picked off the inner solution. The solution was returned as a rule with an arrow. It is stored under the name hsol. You can use hsol to substitute into any expression that contains h. The substitution is done using '/.'. For example... 3h + h^2 /. hsol (9*V)/(Pi*r^2) + (9*V^2)/(Pi^2*r^4) But you might want to define h as a function of V and r. You can do this with the following... h[V_, r_] = h /. hsol (3*V)/(Pi*r^2) Then for example, if you wanted an expression for the height of right circular cones with a radius of 2, you could write... h[V, 2] (3*V)/(4*Pi) If you are a beginner at Mathematica it is worthwhile to work through most of Part I of The Mathematica Book, actually typing in expressions and making certain they work. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: mattisbusy at gmail.com [mailto:mattisbusy at gmail.com] To: mathgroup at smc.vnet.net Hello, I was wondering how to manipulate Mathematica into solving a problem such as this: Solve for h: V = 1/3(pie)r^2h I would think you would do: Solve[{1/3(pie)r^2h},{h}] - although it does not compute the expected answer. Am I doing this right? Thanks!