What is the algorithm for the "Shorten" command in Maple?

Question

There is a package in Maple called "PolynomialTools". That has a command "Shorten". Does anybody know on what algorithm this is based. The maple manual does not explain much.

Example:

with(PolynomialTools): Shorten(x^2+x+1,x);

Answer 1

That PolynomialTools:-Shorten Maple Library command is a renamed version of the shorten command written by Mark van Hoeij.

That PolynomialTools:-Shorten command is based on the (now deprecated) Maple Library command polytools[shorten].

See here, for van Hoeij's Maple page. I did not see a reference to it on his publications page. It may be that shorten was first implemented before 2001.

Perhaps you could ask him.

Answer 2

Here is what the "shorten" command does to a polynomial $f(x)

$\bullet$ make a substitution to remove the $x^(n-1)$ term

$\bullet$ scale $x$ by some rational number,

$\bullet$ if $\mbox{deg } (f,x)=2$ then square-free factor the discriminant

I was hoping that through some substitutions in $x$ it would find a polynomial with a minimum height, but it doesn't do that.