The Content(Poly, 'p') calling sequence returns the content of the Ore polynomial Poly. If the second (optional) argument p is present, the primitive part of Poly is assigned to p.

The Primitive(Poly, 'c') calling sequence returns the primitive part of the Ore poly Poly. If the second (optional) argument c is present, the content of Poly is assigned to c.

If the coefficients of Poly are integral (commutative) polynomials, then its content $c$ is the gcd of its coefficients and its primitive part is equal to (1/c) Poly.

If the coefficients of Poly are rational functions, then its content $c$ and primitive part pp satisfy:

The primitive part pp is an Ore polynomial with integral (commutative) polynomial coefficients whose content is 1. Poly = c pp

The MonicAssociate['left'](Poly, 's') or MonicAssociate(Poly, 's')  calling sequence returns (1/l) Poly where l is the leading coefficient of Poly. If the second (optional) argument s is present, (1/l) is assigned to l.

The MonicAssociate['right'](Poly, A, 's') calling sequence returns Poly a,  where a belongs to the coefficient field such that the product (Poly a) is monic. If the third (optional) argument s, is present, a is assigned to s.

The Normalize(Poly) calling sequence returns Poly with nonzero leading coefficient when Poly is nonzero; returns 'OrePoly'(0), otherwise.

$\mathrm{with}\left(\mathrm{OreTools}\right)\:$

$\mathrm{Ore1}≔\mathrm{OrePoly}\left(n\,n^2\,n^3\right)$

$\mathrm{Ore1}≔\mathrm{OrePoly}\left(n\,n^2\,n^3\right)$

$\mathrm{Content}\left(\mathrm{Ore1}\,'\mathrm{pp}'\right)$

$n$

$\mathrm{pp}$

$\mathrm{OrePoly}\left(1\,n\,n^2\right)$

$\mathrm{Primitive}\left(\mathrm{Ore1}\,'c'\right)$

$\mathrm{OrePoly}\left(1\,n\,n^2\right)$

$c$

$n$

$\mathrm{MonicAssociate}\left['\mathrm{left}'\right]\left(\mathrm{Ore1}\,'s'\right)$

$\mathrm{OrePoly}\left(\frac{1}{n^2}\,\frac{1}{n}\,1\right)$

$s$

$n^3$

$\mathrm{MonicAssociate}\left('\mathrm{OrePoly}'\left(0\right)\right)$

$\mathrm{OrePoly}\left(0\right)$

$A≔\mathrm{SetOreRing}\left(n\,'\mathrm{shift}'\right)$

$A≔\mathrm{UnivariateOreRing}\left(n\,\mathrm{shift}\right)$

$\mathrm{MonicAssociate}\left['\mathrm{right}'\right]\left(\mathrm{Ore1}\,A\,'s'\right)$

$\mathrm{OrePoly}\left(\frac{n}{{\left(n-2\right)}^3}\,\frac{n^2}{{\left(n-1\right)}^3}\,1\right)$

$s$

${\left(n-2\right)}^3$

$\mathrm{Normalize}\left('\mathrm{OrePoly}'\left(0\,n\,n-1\,0\,0\right)\right)$

$\mathrm{OrePoly}\left(0\,n\,n-1\right)$

$\mathrm{Primitive}\left(\mathrm{Ore1}\,'c'\right)$

$\mathrm{OrePoly}\left(1\,n\,n^2\right)$

$c$

$n$