Re: Manipulation of equations and inequalities in "high-school style"

*To*: mathgroup at smc.vnet.net*Subject*: [mg19664] Re: Manipulation of equations and inequalities in "high-school style"*From*: "William M. MacDonald" <wm2 at umail.umd.edu>*Date*: Wed, 8 Sep 1999 02:24:13 -0400*Organization*: University of Maryland*References*: <7q9hdf$o62@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <7q9hdf$o62 at smc.vnet.net> , silvano at iprolink.ch (Silvano D'Orazio) wrote: > Does anybody know a Mathematica (3 or 4) package which allows > manipulaton of equations and inequalities like high-school students > are supposed to do? > > For example > > 2x+a = x-b subtract a > 2x = x-b-a divide by 2, subtract x > x = -b-a > > or > > (2^x-1)^(1/2) = 5b log both sides > (1/2)(x-1)log2 = log5 + logb multiply by 2, divide by log2 > > > 2(log5 + logb) add 1 > x-1 = -------------- > log2 > > and so on. > > I think I saw such a notebook or package some years ago, but I am not > able to find it any more. > I think I am not the only teacher who would find this very useful. > Thanks for all hints. > > Silvano D'Orazio > > > > -----------== Posted via Newsfeeds.Com, Uncensored Usenet News ==---------- > http://www.newsfeeds.com The Largest Usenet Servers in the World! > ------== Over 73,000 Newsgroups - Including Dedicated Binaries Servers ==----- > Note that a List can be handled just the way that you would handle an equation. This means that you can do the following to take the log of both sides: Log[(eq/.Equal->List)]/.List->Equation or to multiply by 2 ( 2 (eq/.Equal->List))/.List->Equation You can write a procedure to allow you to manipulate an equation, add two different equations to cancel terms, etc. The other solution is to write an equation that is to be manipulated as a two-element List. Then you can operate on it just the way that scientists and engineers do, i.e. eq={2 x + a, x-b} 2 eq {4 x + 2 a, 2 x - 2 b} ArcSin[eq] {ArcSin[2 x + a], ArcSin[x-b]} etc. I have repeatedly suggested to Wolfram technical staff, and to Stephen Wolfram, that Equal be given the same properties for a single equation as List, that Listable symbols operate on Equal[exp1,exp2] just as they do on List[exp1,exp2] -- William M. MacDonald Professor of Physics University of Maryland Internet: wm2 at umail.umd.edu