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MathGroup Archive 1998

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Re: new user help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13363] Re: new user help
  • From: "Allan Hayes" <hay at haystack.demon.cc.uk>
  • Date: Mon, 20 Jul 1998 02:50:16 -0400
  • References: <6okkvj$1md@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

John M. Dlugosz wrote in message <6okkvj$1md at smc.vnet.net>...
>I'm lost.  I just don't know how to get started...
>
>The excersize I've chosen for myself is to start with
>
> x^2+y^2+4x-6y+4==0
>
>and manipulate it into the form (x-h)^2+(y-k)^2==r^2
>
>So... how do I "manipulate" the equasion?  The functions like Expand,
>Factor, etc. don't help much.  I my calculator (an HP48) I can point to
>specific subexpressions and apply operations to them, like factor,
>distribute, changing forms, etc.
>
>How do I collect the x's together in parens, the y's in parens, and
>complete the squares?  Doing it on paper defeats the point!  I want to
>learn how to "do math" using this tool.  That's more than just asking
>"OK, what's X?".  It means manipulating things and arranging them,
>getting to know how the symbols all fit together.
>
>--John

>

John,
You  have a good point, but sometimes we have to explain or show how to
do things in text, and Mathematica has good typsetting facilities for
doing this. Nevertheless, Mathematica does allow manipulation of input
and output by ordinary evaluation, direct typing, evaluating in place
(select the expression and press Control+Shift+Reurn on a PC or Command
+ Return on a Mac) and by using a palette like Algebraic Manipulation
(found in the menu File > Palettes,

Here is sequence of evaluations and editings (I have had to convert all
the cells to OutputForm (see Cell menu) after the calculation to show
them in th email)

In[1]:=
         2    2
Collect[x  + y  + 4 x - 6 y + 4, {x, y}] == 0

Out[1]=
           2          2
4 + 4 x + x  - 6 y + y  == 0

In[2]:=
                  2                      2 Factor[4 + 4 x + x ] +
Factor[9 - 6 y + y ] - 9 == 0 Out[2]=
            2           2
-9 + (2 + x)  + (-3 + y)  == 0
I
n[3]:=
            2           2
-9 + (2 + x)  + (-3 + y)  + 9 == 0 + 9

Out[3]=
       2           2
(2 + x)  + (-3 + y)  == 9


A convenient way to get Mathematica to give the answer is

In[4]:=
             2    2
SolveAlways[x  + y  + 4 x - 6 y + 4 ==

          2          2
   (x - a)  + (y - b)  + r, {x, y}]

Out[4]=
{{r -> -9, a -> -2, b -> 3}}


Of course one can write ones own code for manipulating equations and
completing squares etc but you need to wiegh up the usefulness of this.


------------------------------------------------------------- Allan
Hayes
Training and Consulting
Leicester UK
http://www.haystack.demon.co.uk
hay at haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44(0)116 271 8642



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