RE: Simple questions about Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg31892] RE: [mg31888] Simple questions about Mathematica*From*: "David Park" <djmp at earthlink.net>*Date*: Mon, 10 Dec 2001 06:14:31 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Stephen, Trying to match square roots with replacement rules is always a bit of a problem because Mathematica represents them by Power[expr,1/2] in the numerator and Power[expr,-1/2] in the denominator. So it is better to use Power to begin with. So this works... expr = 2/(3*Sqrt[a^2 + b^2]) + (1 - Sqrt[a^2 + b^2])^2 + E^(-a + Sqrt[a^2 + b^2]); expr /. Power[a^2 + b^2, n : (-1/2 | 1/2)] -> Power[x, n] E^(-a + Sqrt[x]) + (1 - Sqrt[x])^2 + 2/(3*Sqrt[x]) where I have used the Alternatives pattern matching construction for n. The replacement rule could also be written as: expr /. (a^2 + b^2)^n:(1/2 | -(1/2)) -> x^n As for running Mathematica in a "batch" mode, I always use Mathematica interactively, and I think that is the best way to use it. But I never have occasion to run really time consuming problems. Perhaps someone else will give you advice on that. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > -----Original Message----- > From: Stephen Gray [mailto:stevebg at adelphia.net] To: mathgroup at smc.vnet.net > Sent: Sunday, December 09, 2001 6:07 AM > To: mathgroup at smc.vnet.net > Subject: [mg31892] [mg31888] Simple questions about Mathematica > > > 1. Suppose I solve some equations and get a complicated > expression containing multiple identical elements such as > sqrt(a^2+b^2). To make the expression smaller, clearer, and > easier to deal with, I want to substitute say R=sqrt(a^2+b^2) > everywhere in the main expression and have R available as > a symbol from then on. I see nothing in Help or anywhere > else about how to do this. But it's such a standard thing to > do that there must be an easy answer. > > 2. I'm not sure how a "batch" file is suppposed to be > prepared and fed to Mathematica. That is, I want to > prepare a bunch of operations and variables in advance > and feed it in, preferably having mathematica give me > line-by-line output as it would if I were typing each line > in one by one. > > As a new user I really need answers to these questions. > Thanks in advance for any information. >