check for monomial order data structures - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : Numbers : Type Checking : type/MonomialOrder

type/MonomialOrder - check for monomial order data structures

type/ShortMonomialOrder - check for short monomial order descriptions

Calling Sequence

type(T, MonomialOrder)

type(ST, ShortMonomialOrder)

Parameters

T

-

table that denotes a monomial ordering on an algebra

SP

-

short monomial order description

Description

• 

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.

Examples

A short monomial order description.

withGroebner:

typeplexx,y,z,MonomialOrder,typeplexx,y,z,ShortMonomialOrder

false,true

(1)

LeadingMonomialax2+bxy+cxz,plexx,y,z

x2

(2)

The previous order can equivalently be declared as a (general) monomial order:

withOre_algebra:

A:=poly_algebrax,y,z,rational=a,b,c:

T:=MonomialOrderA,plexx,y,z:

LeadingMonomialax2+bxy+cxz,T

x2

(3)

typeT,MonomialOrder,typeT,ShortMonomialOrder

true,false

(4)

A monomial order for a skew polynomial ring.

A:=diff_algebraDx,x,comm=μ,s,polynom=s:

T:=MonomialOrderA,tdegDx,s:

typeT,MonomialOrder,typeT,ShortMonomialOrder

true,false

(5)

Neither a monomial order nor a short monomial order description.

type1,MonomialOrder,type1,ShortMonomialOrder

false,false

(6)

See Also

Groebner, Groebner[MonomialOrder], MonomialOrders, type


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam