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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
>
>
>
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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