The type ShortMonomialOrder checks if ST is a short monomial order description.

The type MonomialOrder checks if T is a monomial order, as declared by the command Groebner[MonomialOrder]. This representation is used to denote general monomial orders over general skew algebras, possibly with parameters, and possibly in positive characteristic.

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

$\mathrm{type}\left(\mathrm{plex}\left(x\,y\,z\right)\,\mathrm{MonomialOrder}\right),\mathrm{type}\left(\mathrm{plex}\left(x\,y\,z\right)\,\mathrm{ShortMonomialOrder}\right)$

$\mathrm{false},\mathrm{true}$

$\mathrm{LeadingMonomial}\left(a{x}^2+bxy+cxz\,\mathrm{plex}\left(x\,y\,z\right)\right)$

$x^2$

$\mathrm{with}\left(\mathrm{Ore\_algebra}\right)\:$

$A≔\mathrm{poly\_algebra}\left(x\,y\,z\,\mathrm{rational}=\left\{a\,b\,c\right\}\right)\:$

$T≔\mathrm{MonomialOrder}\left(A\,\mathrm{plex}\left(x\,y\,z\right)\right)\:$

$\mathrm{LeadingMonomial}\left(a{x}^2+bxy+cxz\,T\right)$

$x^2$

$\mathrm{type}\left(T\,\mathrm{MonomialOrder}\right),\mathrm{type}\left(T\,\mathrm{ShortMonomialOrder}\right)$

$\mathrm{true},\mathrm{false}$

$A≔\mathrm{diff\_algebra}\left(\left[\mathrm{Dx}\,x\right]\,\mathrm{comm}=\left\{\mathrm{\mu }\,s\right\}\,\mathrm{polynom}=s\right)\:$

$T≔\mathrm{MonomialOrder}\left(A\,\mathrm{tdeg}\left(\mathrm{Dx}\,s\right)\right)\:$

$\mathrm{type}\left(T\,\mathrm{MonomialOrder}\right),\mathrm{type}\left(T\,\mathrm{ShortMonomialOrder}\right)$

$\mathrm{true},\mathrm{false}$

$\mathrm{type}\left(1\,\mathrm{MonomialOrder}\right),\mathrm{type}\left(1\,\mathrm{ShortMonomialOrder}\right)$

$\mathrm{false},\mathrm{false}$