isIntersectionOfSchubertDeterminantalIdeals I
Checks if the input ideal $I$ can be written as $I = I_{w_1} \cap ... \cap I_{w_k}$, where each $I_{w_i}$ is a Schubert determinantal ideal.
This function computes the antidiagonal initial ideal of $I$ (using the default term order in Macaulay2, which is antidiagonal), finds the primes in the decomposition of $I$, reads a permutation from each such prime, and checks if $I$ is the intersection of the Schubert determinantal ideals of those permutations.
The following theorems combine to guarantee that, if $I$ can be written as the intersection of Schubert determinantal ideals, it is exactly the intersection of the Schubert determinantal ideals found by the algorithm described above.



The object isIntersectionOfSchubertDeterminantalIdeals is a method function.