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isoTypes -- distinct isomorphism classes



Given a list of Macaulay2 objects for which areIsomorphic makes sense for any pair, this method determines the distinct isomorphism classes appearing in the list, by performing "upper-triangular" comparisons of pairs.

In particular, the output list (of representatives of each isomorphism class) is always ordered consistently with the order of the original list.

If the list has size $n$, and all objects are pairwise non-isomorphic, then ($n$ choose $2$) comparisons are made, while if all objects are isomorphic, then only $n-1$ comparisons are made.

i1 : M = uniformMatroid_3 5

o1 = a "matroid" of rank 3 on 5 elements

o1 : Matroid
i2 : L = {M / {0}, uniformMatroid_2 4, matroid random(QQ^2,QQ^4)}

o2 = {a "matroid" of rank 2 on 4 elements, a "matroid" of rank 2 on 4
     elements, a "matroid" of rank 2 on 4 elements}

o2 : List
i3 : isoTypes L

o3 = {a "matroid" of rank 2 on 4 elements}

o3 : List

See also

Ways to use isoTypes :

For the programmer

The object isoTypes is a method function.