J = groebnerFamily M
J = groebnerFamily(M, L)
Given a monomial ideal $M$ in a polynomial ring $R$, this computes the parameter families of homogeneous ideals where $M$ could be their initial ideal. These families are obtained from either the standard monomials to the generators of $M$, or the standard monomials smaller than the generators of $M$ but of the same degree as these generators. In the former case we obtain a family of all ideals where $M$ could be their initial ideal. In the latter case, we obtain such a family with respect to a given term order.
|
|
|
|
|
|
|
|
Here, $F$ is the family of homogeneous ideals having $M$ as their initial ideal, under the term order of the ring of $M$.
The optional argument AllStandard is boolean, taking the value $true$ to compute the family of all homogeneous ideals with a given initial ideal and the value $false$ to compute the family with respect to a given order. The default value for this argument is false.
If $L$ is not given, then it is computed using standardMonomials (if AllStandard is true), or smallerMonomials (if AllStandard is false).
|
|
Note that $F$ and $F_2$ are the same family, in this case.
The object groebnerFamily is a method function with options.