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Evaluate In Place

• To: mathgroup@smc.vnet.net
• Subject: [mg11931] Evaluate In Place
• From: Des Penny <penny@suu.edu>
• Date: Thu, 9 Apr 1998 00:33:32 -0400
• Organization: Southern Utah University

Hi Groupers:

I find the new feature (at least I think it's new with V3.0) of
Evaluating In Place to be extremely useful for debugging purposes.
Since I haven't seen it discussed in this forum I thought a note might
be appropriate.

The command is executed by selecting part of the input line and
executing the pull down command Kernel>Evaluation>Evaluate In Place.

A simple example is:

In[15]:=
x=3;

Now consider the following cell:

x^2+2x

Select x^2 and evaluate in place.  Now repeat with 2x. You will get in
turn:

9+2x
9+6

A more interesting example is the following expression:

In[19]:=
x=.;
expr=(1-x)/(3(x^2+2x y))

Out[19]=
(1 - x)/(3*(x^2 + 2*y*x))

My students have some trouble understanding the internal form of
expressions like this.  If we look at:

In[20]:=
FullForm[expr]

Out[20]//FullForm=
Times[Rational[1,3],Plus[1,Times[-1,x]],
Power[Plus[Power[x,2],Times[2,x,y]],-1]]

By selecting and evaluating in place
  Times[-1,x]
we get:

Times[Rational[1,3], Plus[1,-x],Power[Plus[Power[x,2],Times[2,x,y]],-1]]

We can now select and evaluate in place parts of the expression to get
in turn:

Times[Rational[1,3],1-x,Power[Plus[Power[x,2],Times[2,x,y]],-1]]

Times[Rational[1,3],1-x,Power[Plus[x^2,2 x y],-1]]

Times[Rational[1,3],1-x,Power[x^2 + 2*x*y,-1]]

Times[Rational[1,3],1-x,1/(x^2 + 2*x*y)]

And finally:

In[30]:=
Times[1/3,1-x,1/(x^2 + 2*x*y)]

Out[30]=
(1 - x)/(3*(x^2 + 2*x*y))

What a great debugging tool!  When faced with a deeply nested
Mathematica expression, it is now no longer necessary to physically
break it apart and execute each part in a separate cell.  You can now
execute each portion in place and understand its effect.

Cheers,

--
Des Penny
Physical Science Dept.
Southern Utah University
Cedar City, UT 84720

Office: (435) 586-7708
FAX:  (435) 865-8051
email: penny@suu.edu

Home: (435) 586-2286
email: dpenny@iname.com