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MultiSet/union

MultiSet union operator

 Calling Sequence M union N union( M, N, ... )

Parameters

 M - MultiSet; a MultiSet, set, or list N - MultiSet; a MultiSet, set, or list ... - 0 or more additional MultiSets, sets or lists

Description

 • 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.

Examples

 > $M≔\mathrm{MultiSet}\left(a=2,b=5,c=4\right)$
 ${M}{≔}\left\{\left[{a}{,}{2}\right]{,}\left[{b}{,}{5}\right]{,}\left[{c}{,}{4}\right]\right\}$ (1)
 > $N≔\mathrm{MultiSet}\left(a=4,c=3,d=7\right)$
 ${N}{≔}\left\{\left[{a}{,}{4}\right]{,}\left[{c}{,}{3}\right]{,}\left[{d}{,}{7}\right]\right\}$ (2)
 > $M\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{union}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}N$
 $\left\{\left[{a}{,}{4}\right]{,}\left[{b}{,}{5}\right]{,}\left[{c}{,}{4}\right]{,}\left[{d}{,}{7}\right]\right\}$ (3)
 > $M\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{union}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}N\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{union}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left[b,c,c,e\right]$
 $\left\{\left[{a}{,}{4}\right]{,}\left[{b}{,}{5}\right]{,}\left[{c}{,}{4}\right]{,}\left[{d}{,}{7}\right]{,}\left[{e}{,}{1}\right]\right\}$ (4)

Compatibility

 • The MultiSet/union command was introduced in Maple 2016.