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 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