Notes on Polynomial Teacher                   July, 1995

     pt is a small symbolic and numerical algebra program,
intended for use by students and their teachers from about
eighth grade to college. It should run on any Macintosh 
computer, but has been tried only on the Classic, Quadra 610 
and 950, Centris 650, and PowerPC 5200 and 7100. It is strictly text-based with
no graphics at all.

     Here is an example of a pt session, where "pt>>" is
the prompt, followed on that line by what the user typed,
and on succeeding lines by the output:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
pt>> 2x+x+5

 ansr =
           
    3 x + 5

pt>> solve 3x+5=11

    2.000 
pt>> f=3x^2 + x

 f =
        2
    3 x   + x

    =3(x+0.333)(x)


pt>> f(4)

 ansr =
      
    52

pt>> g=xx+1

 g =
       2    
     x   + 1

    =(x+i)(x-i)


pt>> g/f
            = quotient   +   remainder/f    

 quotient =
         
    0.333

 remainder =
     
    -0.333 x + 1

pt>> 2g-3f

 ansr =
         2    
    -7 x   -3 x + 2

    =-7(x+0.790)(x-0.362)


pt>> 1/3-2/5

 ansr =
          
    -0.067
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
     There is no choice about the number of decimal places;
it is three, and numerical accuracy is not guaranteed but 
tends to be more or less acceptable for elementary purposes.
One certainly needs to be aware, for example that -1/15 is not quite the same
thing as -0.067, and so forth. Polynomials of degree 4 or less are factored
automatically, and you can force the program to find roots of things up to degree
9 by using the word "solve" as above, but numerical errors will occur, and this 
is a good teaching opportunity. For example:

pt>> (x-3)^3

 ansr =
       3       2            
     x   - 9 x   + 27 x - 27

    =(x-3.000)(x-3.000)(x-3) <--/* here the roots weren't exactly 3 as they
should have been */


pt>> (x-3)^4

 ansr =
       4        3        2             
     x   - 12 x   + 54 x   - 108 x + 81

    =(x-2.998)(x-2.998)(x-3-0.003i)(x-3.003)<--/* ouch! to avoid this
embarassment, spend money on a professional program- this one is free:)*/

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
     More documentation is included in the program. pt was written by Bob
Terrell, and comments may be sent to him at bterrell@math.cornell.edu