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 IBM compatible
computer, but has been tried only on a 386.
It is strictly text-based with no graphics at all. There is
also a Macintosh version.
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
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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:-) */
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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