type/ClosedIdeal
type for finite-dimensional ideals
Calling Sequence
Parameters
Description
Examples
type(G, ClosedIdeal(T))
G
-
set or list of polynomials
T
table that denotes a monomial ordering on an algebra
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).
withOre_algebra:
withGroebner:
A≔poly_algebrax,y,z:
T≔MonomialOrderA,tdegx,y,z:
F≔x2−2xz+5,xy2+yz3,3y2−8z3:
typeF,ClosedIdealT
false
Thus far, no Groebner basis has been computed.
G≔BasisF,T:
typeG,ClosedIdealT
true
IsZeroDimensionalF
IsZeroDimensionalG
See Also
Groebner
Groebner[IsZeroDimensional]
Groebner[MonomialOrder]
type
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