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isASMIdeal -- whether an ideal is an ASM ideal



Every ASM ideal can be written as an intersection of Schubert determinantal ideals. Given an ideal $I$, this function first uses schubertDecompose to find the set of permutations that must index the minimal primes of $I$ if indeed $I$ is an ASM ideal. Then $I$ is an ASM ideal if and only if $I=I_A$ for the ASM $A$ whose rank table is the determined by taking entrywise maxima (using entrywiseMaxRankTable) in the rank tables of the permutations found by schubertDecompose.

When this function returns true, it also stores the ASM $A$ so that $I=I_A$. The matrix $A$ can then be accessed using getASM.

i1 : I1=schubertDeterminantalIdeal {3,4,1,2};

o1 : Ideal of QQ[z   ..z   ]
                  1,1   4,4
i2 : I2=sub(schubertDeterminantalIdeal {3,2,4,1},ring I1);

o2 : Ideal of QQ[z   ..z   ]
                  1,1   4,4
i3 : I = intersect(I1,I2);

o3 : Ideal of QQ[z   ..z   ]
                  1,1   4,4
i4 : isASMIdeal I

o4 = true

Ways to use isASMIdeal :

For the programmer

The object isASMIdeal is a method function.