type/TermOrder(deprecated) - Maple Help

type/TermOrder

type for term order data structures

type/ShortTermOrder

type for short term order descriptions

 Calling Sequence type(T, TermOrder) type(ST, ShortTermOrder)

Parameters

 T - table that denotes a term ordering on an algebra SP - short term order description

Description

 • 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.

Examples

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

Neither a term order nor a short term order description!

 > $\mathrm{type}\left(1,\mathrm{TermOrder}\right),\mathrm{type}\left(1,\mathrm{ShortTermOrder}\right)$
 Warning, type TermOrder is deprecated. Please, use type MonomialOrder. Warning, Type ShortTermOrder is deprecated. Please, use type ShortMonomialOrder.
 ${\mathrm{false}}{,}{\mathrm{false}}$ (1)

A term order.

 > $\mathrm{with}\left(\mathrm{Ore_algebra}\right):$
 > $\mathrm{with}\left(\mathrm{Groebner}\right):$
 > $A≔\mathrm{diff_algebra}\left(\left[\mathrm{Dx},x\right],\mathrm{comm}=\left\{\mathrm{\mu },s\right\},\mathrm{polynom}=s\right):$
 > $T≔\mathrm{termorder}\left(A,\mathrm{tdeg}\left(\mathrm{Dx},s\right)\right):$
 > $\mathrm{type}\left(T,\mathrm{TermOrder}\right)$
 ${\mathrm{true}}$ (2)

A short term order description.

 > $\mathrm{type}\left(\mathrm{plex}\left(x,y,z\right),\mathrm{TermOrder}\right),\mathrm{type}\left(\mathrm{plex}\left(x,y,z\right),\mathrm{ShortTermOrder}\right)$
 ${\mathrm{false}}{,}{\mathrm{true}}$ (3)
 > $\mathrm{leadterm}\left(a{x}^{2}+bxy+cxz,\mathrm{plex}\left(x,y,z\right)\right)$
 ${{x}}^{{2}}$ (4)

The previous term order can equivalently be declared by:

 > $A≔\mathrm{poly_algebra}\left(x,y,z,\mathrm{rational}=\left\{a,b,c\right\}\right):$
 > $T≔\mathrm{termorder}\left(A,\mathrm{plex}\left(x,y,z\right)\right):$
 > $\mathrm{leadterm}\left(a{x}^{2}+bxy+cxz,T\right)$
 ${{x}}^{{2}}$ (5)