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MathGroup Archive 1999

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19629] Re: Manipulation of equations and inequalities in "high-school style"
  • From: phbrf at t-online.de (Peter Breitfeld)
  • Date: Mon, 6 Sep 1999 04:20:43 -0400
  • Organization: das ist ein breites Feld ...
  • References: <7q9hdf$o62@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Silvano D'Orazio <silvano at iprolink.ch> schrieb:
> 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
> 
I use the following function to do this:

GleichungsVerkn[verkn_]:=
Module[{ver},   
        ver=verkn /.Equal->List/.List->Equal;
        ver[[1]]=Simplify[ver[[1]]];
        ver[[2]]=Simplify[ver[[2]]];
        Return[ver]
]

your second example is now done like this:

In[1]:=eq = (2^(x - 1))^(1/2) == 5b
Out[1]= ...

In[2]:=eq=GleichungsVerkn[Log[eq]]//PowerExpand
Out[2]=1/2(-1 + x) Log[2] == Log[5] + Log[b]

In[3]:=GleichungsVerkn[2/Log[2]eq+1]
Out[3]=x == 1 + (2 Log[5b])/Log[2]

With this function you can compose equations too, so e.g.
GleichungsVerkn[(a==b)+(c==d)] returns a+c==b+d

 Peter
-- 
=--=--=--=--=--=--=--=--=--=--=--=--=  http://home.t-online.de/home/phbrf  
Peter Breitfeld, Saulgau, Germany        PGP public key: 08548045  =--=--=



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