Important: The types TermOrder and ShortTermOrder have been deprecated.  Use the superseding type/MonomialOrder and type/ShortMonomialOrder instead.

The type TermOrder checks if T is a term order, as declared by Groebner[termorder].  This representation is used to denote general term orders over general skew algebras.

The type ShortTermOrder checks if ST is a short term order description.  Such a structure is used as a shortcut for term order structures in particular commutative cases.  The available forms are the function calls built on tdeg, wdeg, plex, lexdeg, matrix and their min forms that are described in Groebner[termorder].  The variables declared by those simplified forms are only those that are involved in the term order.  Thus, the same short term order description may be used in different contexts with or without parameters.

$\mathrm{type}\left(1\,\mathrm{TermOrder}\right),\mathrm{type}\left(1\,\mathrm{ShortTermOrder}\right)$

Warning, type TermOrder is deprecated. Please, use type MonomialOrder.
Warning, Type ShortTermOrder is deprecated. Please, use type ShortMonomialOrder.

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

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

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

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

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

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

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{plex}\left(x\,y\,z\right)\,\mathrm{TermOrder}\right),\mathrm{type}\left(\mathrm{plex}\left(x\,y\,z\right)\,\mathrm{ShortTermOrder}\right)$

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

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

$x^2$

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

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

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

$x^2$