Initial population.

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+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\MultiSetXmpTitle}{MultiSet}
+\newcommand{\MultiSetXmpNumber}{9.53}
+%
+% =====================================================================
+\begin{page}{MultiSetXmpPage}{9.53 MultiSet}
+% =====================================================================
+\beginscroll
+The domain \spadtype{Multiset(R)} is similar to \spadtype{Set(R)}
+except that multiplicities
+(counts of duplications) are maintained and displayed.
+Use the operation \spadfunFrom{multiset}{Multiset} to create
+%-% \HDindex{set!vs. multiset}{MultiSetXmpPage}{9.53}{MultiSet}
+multisets from lists.
+%-% \HDindex{multiset}{MultiSetXmpPage}{9.53}{MultiSet}
+All the standard operations from sets are available for
+multisets.
+An element with multiplicity greater than one has the
+multiplicity displayed first, then a colon, and then the element.
+
+\xtc{
+Create a multiset of integers.
+}{
+\spadpaste{s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10]\bound{s}}
+}
+\xtc{
+The operation \spadfunX{insert} adds an element to a multiset.
+}{
+\spadpaste{insert!(3,s)\bound{s1}\free{s}}
+}
+\xtc{
+Use \spadfunX{remove} to remove an element.
+If a third argument is present, it specifies how many instances
+to remove. Otherwise all instances of the element are removed.
+Display the resulting multiset.
+}{
+\spadpaste{remove!(3,s,1); s\bound{s2}\free{s1}}
+}
+\xtc{
+}{
+\spadpaste{remove!(5,s); s\bound{s2}\free{s1}}
+}
+\xtc{
+The operation \spadfun{count} returns the number of copies
+of a given value.
+}{
+\spadpaste{count(5,s)\free{s2}}
+}
+\xtc{
+A second multiset.
+}{
+\spadpaste{t := multiset [2,2,2,-9]\bound{t}}
+}
+\xtc{
+The \spadfun{union} of two multisets is additive.
+}{
+\spadpaste{U := union(s,t)\bound{U}}
+}
+\xtc{
+The \spadfun{intersect} operation gives the elements that are in
+common, with additive multiplicity.
+}{
+\spadpaste{I := intersect(s,t)\bound{I}}
+}
+\xtc{
+The \spadfun{difference} of \spad{s} and \spad{t} consists of
+the elements that \spad{s} has but \spad{t} does not.
+Elements are regarded as indistinguishable, so that if \spad{s}
+and \spad{t} have any element in common, the \spadfun{difference}
+does not contain that element.
+}{
+\spadpaste{difference(s,t)\free{s2 t}}
+}
+\xtc{
+The \spadfun{symmetricDifference} is the \spadfun{union}
+of \spad{difference(s, t)} and \spad{difference(t, s)}.
+}{
+\spadpaste{S := symmetricDifference(s,t)\bound{S}\free{s2 t}}
+}
+\xtc{
+Check that the \spadfun{union} of the \spadfun{symmetricDifference} and
+the \spadfun{intersect} equals the \spadfun{union} of the elements.
+}{
+\spadpaste{(U = union(S,I))@Boolean\free{S I U}}
+}
+\xtc{
+Check some inclusion relations.
+}{
+\spadpaste{t1 := multiset [1,2,2,3]; [t1 < t, t1 < s, t < s, t1 <= s]\free{t s2}}
+}
+\endscroll
+\autobuttons
+\end{page}
+%