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type/ClosedIdeal

type for finite-dimensional ideals

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

type(G, ClosedIdeal(T))

Parameters

G

-

set or list of polynomials

T

-

table that denotes a monomial ordering on an algebra

Description

• 

The type ClosedIdeal checks if the leading monomials of G with respect to T generate a zero-dimensional ideal.

• 

When G is a Groebner basis with respect to T, the call type(G, T) is equivalent to the call Groebner[IsZeroDimensional](G, T), and checks if the ideal generated by G is finite-dimensional. type/ClosedIdeal is therefore less general but does not compute any Groebner basis (as opposed to IsZeroDimensional).

Examples

withOre_algebra:

withGroebner:

Apoly_algebrax,y,z:

TMonomialOrderA,tdegx,y,z:

Fx22xz+5,xy2+yz3,3y28z3:

typeF,ClosedIdealT

false

(1)

Thus far, no Groebner basis has been computed.

GBasisF,T:

typeG,ClosedIdealT

true

(2)

IsZeroDimensionalF

true

(3)

IsZeroDimensionalG

true

(4)

See Also

Groebner

Groebner[IsZeroDimensional]

Groebner[MonomialOrder]

type

 


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