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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: [mg19574] Re: Manipulation of equations and inequalities in "high-school style"
  • From: hanson.nospam at physics.auburn.edu (James D Hanson)
  • Date: Wed, 1 Sep 1999 23:07:06 -0400
  • Organization: Auburn University Physics
  • 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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Three extra bits you need, == instead of = for equations; Map to do
something to both sides of the equation; and functions (the things you
actually do).

In[1]:= ? Map

"Map[f, expr] or f /@ expr applies f to each element on the first level in \
expr. Map[f, expr, levelspec] applies f to parts of expr specified by \
levelspec."

In[2]:= eq1 = (2 x + a == x - b)

Out[2]= a+2 x==-b+x

In[3]:= eq2 = Map[#-a &,eq1]

Out[3]= 2 x==-a-b+x

In[4]:= eq3 = Map[#-x &,eq2]

Out[4]= x==-a-b

-- 
James D. Hanson                      ph. (334) 844-5044
Department of Physics                fax (334) 844-4613
206 Allison Laboratory
Auburn University, AL 36849-5311     hanson.nospam at physics.auburn.edu


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