type for finite-dimensional ideals
set or list of polynomials
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).
A ≔ poly_algebra⁡x,y,z:
T ≔ MonomialOrder⁡A,tdeg⁡x,y,z:
F ≔ x2−2⁢x⁢z+5,x⁢y2+y⁢z3,3⁢y2−8⁢z3:
Thus far, no Groebner basis has been computed.
G ≔ Basis⁡F,T:
Download Help Document