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The MutableSet function returns a new MutableSet object.

If called with a single argument that is either a Maple set or a MutableSet object, the returned object contains the elements in the argument.

Otherwise, the returned object contains each distinct argument as an element.

The following functions modify the content The ms argument denotes a MutableSet object.

clear(ms) : Clear ms.

delete(ms,expr) : Delete expr from ms.

insert(ms,expr) : Insert expr into ms.

ms ,= expr : Insert expr into ms. Unlike the insert function, the ,= operator can accept a sequence of elements on the right hand side.

The following set functions combine MutableSet objects. Those prefixed with an ampersand (&) operate inplace on the first argument. These functions can be invoked as functions or inline operators. The ms1 and ms2 arguments denote MutableSet objects.

ms1 intersect ms2, or $\mathrm{ms1}\cap \mathrm{ms2}$, or `intersect`(ms1,ms2,...) : Return a new MutableSet object that is the intersection of the given MutableSets.

ms1 &intersect ms2 or `&intersect`(ms1,ms2,...) : Remove elements of ms1 that are not elements of ms2, etc., updating ms1.

ms1 minus ms2, or $\mathrm{ms1}\setminus \mathrm{ms2}$, or `minus`(ms1,ms2) : Return a new MutableSet object that contains the set difference of ms1 and ms2.

ms1 &minus ms2 or `&minus`(ms1,ms2) : Remove elements of ms2 from ms1, updating ms1.

ms1 union ms2, or $\mathrm{ms1}\cup \mathrm{ms2}$, or `union`(ms1,ms2,...) : Return a new MutableSet object that is the union of the given mutable sets.

ms1 &union ms2 or `&union`(ms1,ms2,...) : Combine the members of ms2, etc., with ms1, updating ms1.

The following functions inspect the content of a MutableSet object. The ms, ms1, and ms2 arguments denote MutableSet objects.

ms = other or `=`(ms,other) : When evaluated in a boolean context, returns true if ms and other are both MutableSet objects with identical content, false otherwise.

expr in ms or `in`(expr,ms) : Returns true if expr is a member of ms, false otherwise.

empty(ms) : Returns true if ms is empty, false otherwise.

entries(ms) : Returns an expression sequence of all the entries in ms, with each entry enclosed in a list by default.

has(ms,expr) : Returns true if any member of ms contains expr, false otherwise.

hastype(ms,typ) : Returns true if any member of ms contains an expression of the specified type, false otherwise.

indets(ms,typ) : Returns a Maple set of all indeterminates in ms. If the optional typ parameter is specified, then returns the expressions of type typ.

indices(ms) : Returns an expression sequence of all the indices of ms, with each index enclosed in a list by default.

lowerbound(ms) : Returns the lower index bound (always 1).

max(ms) : Returns the maximum element of ms. Behaves like max on sets.

member(expr,ms) : Returns true if expr is a member of ms, false otherwise. The three argument form of member is not supported.

min(ms) : Returns the minimum element of ms. Behaves like min on sets.

numelems(ms) : Returns the number of elements in ms.

numboccur(ms,expr) : Count the number of occurrences of expr in ms, either as an element or within elements.

`subset`(ms1,ms2), or ms1 subset ms2, or ms1 subset ms2 : Returns true if ms1 is a subset of ms2, false otherwise.

upperbound(ms) : Returns the upper index (same as the output of numelems).

Each of the above functions is already available in Maple for built-in Maple structures such as sets and Arrays. Please refer to the help page for each function for details on usage.

The map , select , remove , selectremove , and subs functions operate on a MutableSet object. Refer to their help pages for the calling sequences. By default they create a new MutableSet object, but if called with the inplace index option, they update the MutableSet object. The ms argument denotes a MutableSet object.

map(fcn,ms) : Apply a procedure, fcn, to each element of ms.

select(fcn,ms) : Select elements of ms for which fcn returns true.

remove(fcn,ms) : Remove elements of ms for which fcn returns true.

selectremove(fcn,dq) : Produce two MutableSets, one containing selected elements and the other removed elements.

subs(eqns,ms) : Substitute subexpressions in the content of ms.

The convert function can be used to convert a MutableSet object to and from other Maple structures.

convert(ms,typ) : Convert a MutableSet to the specified type

convert(expr,MutableSet) : Convert expr to a MutableSet object. expr must be a list , set , or rtable .

Integer indices can be used to extract or reassign a single element of a MutableSet. Reassigning an element may change its index.

Range indices are not supported.

The MutableSet object exports a ModuleIterator function, allowing a MutableSet object to be used in loops and iterations (seq , add , etc.).

Create a MutableSet with three elements.

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\right)$

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\right)$

Copy M1.

$\mathrm{M2}≔\mathrm{MutableSet}\left(\mathrm{M1}\right)$

$\mathrm{M2}≔\mathrm{MutableSet}\left(a\,b\,c\right)$

Create a MutableSet from a Maple set.

$\mathrm{M3}≔\mathrm{MutableSet}\left(\left\{b\,c\,d\right\}\right)$

$\mathrm{M3}≔\mathrm{MutableSet}\left(b\,c\,d\right)$

Delete the b element from M1 and insert a d element.

$\mathrm{delete}\left(\mathrm{M1}\,b\right)$

$\mathrm{MutableSet}\left(a\,c\right)$

$\mathrm{insert}\left(\mathrm{M1}\,d\right)$

$\mathrm{MutableSet}\left(a\,c\,d\right)$

Add $c$ to each element in $\mathrm{M2}$, doing so inplace.

$\mathrm{map}\left[\mathrm{inplace}\right]\left(\mathrm{`+`}\,\mathrm{M2}\,c\right)$

$\mathrm{MutableSet}\left(a+c\,b+c\,2c\right)$

Replace all occurrences of $c$ inside $\mathrm{M2}$ with $d$, doing so inplace.

$\mathrm{subs}\left[\mathrm{inplace}\right]\left(c=d\,\mathrm{M2}\right)$

$\mathrm{MutableSet}\left(2d\,a+d\,b+d\right)$

Create two MutableSet objects, then form their intersection.

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\,d\right)$

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\,d\right)$

$\mathrm{M2}≔\mathrm{MutableSet}\left(c\,d\,e\,f\right)$

$\mathrm{M2}≔\mathrm{MutableSet}\left(c\,d\,e\,f\right)$

$\mathrm{M3}≔\mathrm{M1}\mathbf{intersect}\mathrm{M2}$

$\mathrm{M3}≔\mathrm{MutableSet}\left(c\,d\right)$

Use the inplace form to update $\mathrm{M1}$ with the intersection of $\mathrm{M1}$ and $\mathrm{M2}$.

$\mathrm{M1}\&intersect\mathrm{M2}\:$

$\mathrm{M1}$

$\mathrm{MutableSet}\left(c\,d\right)$

Use member to determine whether a given element is a member of $\mathrm{M1}$.

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\,4\right)$

$\mathrm{M1}≔\mathrm{MutableSet}\left(4\,a\,b\,c\right)$

$\mathrm{member}\left(b\,\mathrm{M1}\right)$

$\mathrm{true}$

Use has to test for the occurrence of a subexpression in any of the members of the set.

$\mathrm{has}\left(\mathrm{M1}\,c\right)$

$\mathrm{true}$

$\mathrm{indets}\left(\mathrm{M1}\,\mathrm{numeric}\right)$

$\left\{4\right\}$

Create a MutableSet object by converting a Vector .

$\mathrm{M1}≔\mathrm{convert}\left(\mathrm{Vector}\left(10\,\mathrm{symbol}=v\right)\,\mathrm{MutableSet}\right)$

$\mathrm{M1}≔\mathrm{MutableSet}\left(v_1\,v_2\,v_3\,v_4\,v_5\,v_6\,v_7\,v_8\,v_9\,v_{10}\right)$

Convert M1 to a standard set.

$\mathrm{convert}\left(\mathrm{M1}\,\mathrm{set}\right)$

$\left\{v_1\,v_2\,v_3\,v_4\,v_5\,v_6\,v_7\,v_8\,v_9\,v_{10}\right\}$

Use indexing to extract each element of a MutableSet.

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\,d\right)$

$\mathrm{M1}≔\mathrm{MutableSet}\left(a\,b\,c\,d\right)$

$\mathrm{seq}\left(i=\mathrm{M1}\left[i\right]\,i=1..\mathrm{numelems}\left(\mathrm{M1}\right)\right)$

$1=a,2=b,3=c,4=d$

Reassign the value at the second index. Note that in the updated MutableSet, the new value is assigned a different index.

$\mathrm{M1}\left[2\right]≔23\:$

$\mathrm{seq}\left(i=\mathrm{M1}\left[i\right]\,i=1..\mathrm{numelems}\left(\mathrm{M1}\right)\right)$

$1=23,2=a,3=c,4=d$

Iterate through each element in M1.

$\left[\mathrm{seq}\left(x\,x\mathbf{in}\mathrm{M1}\right)\right]$

$\left[23\,a\,c\,d\right]$

Add the elements of M2.

$\mathrm{add}\left(x\,x\mathbf{in}\mathrm{M2}\right)$

$c+d+e+f$

$$\begin{gathered} \mathbf{for}x\mathbf{in}\mathrm{M2}\mathbf{do} \\ \mathrm{print}\left(x\right) \\ \mathbf{end}\mathbf{do} \end{gathered}$$

$c$

$d$

$e$

$f$

The MutableSet object provides an efficient way to construct a set an element at a time, in a loop. Doing so with standard Maple sets is inefficient in that each addition creates a new set. As such the operation is $\mathrm{O}\left(n^2\right)$ in time and memory, where $n$ is the number of elements. The following compares the memory and time required to create a set of ten thousand elements using standard sets and a MutableSet object.

MapleSets := proc(n :: posint)
local i, s;
s := {};
for i to n do
s := s union {i};
end do:
numelems(s);
end proc:
MutableSets := proc(n :: posint)
local i, s;
s := MutableSet();
for i to n do
insert(s,-i);
end do;
numelems(s);
end proc:

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MapleSets}\left(10000\right)\right)$

memory used=382.91MiB, alloc change=27.49MiB, cpu time=2.78s, real time=3.47s, gc time=1.33s

$10000$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MutableSets}\left(10000\right)\right)$

memory used=1.38MiB, alloc change=0 bytes, cpu time=41.00ms, real time=71.00ms, gc time=0ns

$10000$