M union N returns the MultiSet which is the elementwise maximum of M and N by multiplicity.  For example, if a has multiplicity 2 in M and 3 in N then it will have multiplicity 3 in M union N.

Note that this definition of union preserves idempotency: M union M = M.  To obtain the MultiSet comprised of the totality of elements of a collection of MultiSets, use addition: M + N.

The `union`( M, N, ... ) command performs the n-ary union of its arguments.

At least one argument must be a MultiSet for this routine to be invoked.  Any other argument which is expected to be a MultiSet can be a MultiSet, a set or a list; in the latter two cases the argument is converted to a MultiSet before proceeding to evaluate this command.  IsGeneralized(M) must return the same value for all MultiSet arguments M, and all non-MultiSet arguments will be promoted to MultiSets with this same property.

$M≔\mathrm{MultiSet}\left(a=2\,b=5\,c=4\right)$

$M≔\left\{\left[a\,2\right]\,\left[b\,5\right]\,\left[c\,4\right]\right\}$

$N≔\mathrm{MultiSet}\left(a=4\,c=3\,d=7\right)$

$N≔\left\{\left[a\,4\right]\,\left[c\,3\right]\,\left[d\,7\right]\right\}$

$M\mathbf{union}N$

$\left\{\left[a\,4\right]\,\left[b\,5\right]\,\left[c\,4\right]\,\left[d\,7\right]\right\}$

$M\mathbf{union}N\mathbf{union}\left[b\,c\,c\,e\right]$

$\left\{\left[a\,4\right]\,\left[b\,5\right]\,\left[c\,4\right]\,\left[d\,7\right]\,\left[e\,1\right]\right\}$

The MultiSet/union command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.