Important: The polytools package has been deprecated. Use the superseding command PolynomialTools[Shorten] instead.

This function applies transformations on f in an effort to make f smaller, more precisely, to make its length smaller. The following transformations are tried: adding or multiplying x by a constant, replacing x by its reciprocal, and combinations of these transformations.

When a field extension is given by an irreducible polynomial f this procedure can be used to search for a simpler polynomial representing the same field extension.

If f contains only one variable then the second argument x is optional.

$\mathrm{with}\left(\mathrm{polytools}\right)$

$\left[\mathrm{minpoly}\,\mathrm{recipoly}\,\mathrm{shorten}\,\mathrm{sort\_poly}\,\mathrm{split}\,\mathrm{splits}\,\mathrm{translate}\right]$

$\mathrm{shorten}\left(x^2+x+1\,x\right)$

$x^2+3$

$\mathrm{shorten}\left(3x^3+18x+14\,x\right)$

$x^3-6$

$\mathrm{shorten}\left(x^4+32\,x\right)$

$x^4+2$