List operations¶
Most objects that can be of variable size are represented as lists (linked lists internally). Yacas does implement arrays, which are faster when the number of elements in a collection of objects doesn’t change. Operations on lists have better support in the current system.

Head
(list)¶ returns the first element of a list
This function returns the first element of a list. If it is applied to a general expression, it returns the first operand. An error is returned if
list
is an atom. Example
In> Head({a,b,c}) Out> a; In> Head(f(a,b,c)); Out> a;

Tail
(list)¶ returns a list without its first element
 Example
In> Tail({a,b,c}) Out> {b,c};

Length
(list)¶ 
Length
(string) The length of a list or string
 Example
In> Length({a,b,c}) Out> 3; In> Length("abcdef"); Out> 6;

Map
(fn, list)¶ apply an nary function to all entries in a list
This function applies
fn
to every list of arguments to be found inlist
. So the first entry oflist
should be a list containing the first, second, third, … argument tofn
, and the same goes for the other entries oflist
. The function can either be given as a string or as a pure function (seeApply()
for more information on pure functions). Example
In> Map("+",{{a,b},{c,d}}); Out> {a+c,b+d};
See also

MapSingle
(fn, list)¶ apply a unary function to all entries in a list
The function
fn
is successively applied to all entries inlist
, and a list containing the respective results is returned. The function can be given either as a string or as a pure function (seeApply()
for more information on pure functions).The
/@
operator provides a shorthand forMapSingle()
. Example
In> MapSingle("Sin",{a,b,c}); Out> {Sin(a),Sin(b),Sin(c)}; In> MapSingle({{x},x^2}, {a,2,c}); Out> {a^2,4,c^2};

MakeVector
(var, n)¶ vector of uniquely numbered variable names
A list of length
n
is generated. The first entry contains the identifiervar
with the number 1 appended to it, the second entry containsvar
with the suffix 2, and so on until the last entry which containsvar
with the numbern
appended to it. Example
In> MakeVector(a,3) Out> {a1,a2,a3};
See also

Select
(pred, list)¶ select entries satisfying some predicate
Select()
returns a sublist oflist
which contains all the entries for which the predicatepred
returnsTrue
when applied to this entry. Example
In> Select("IsInteger",{a,b,2,c,3,d,4,e,f}) Out> {2,3,4};

Nth
(list, n)¶ return the
n
th element of a listThe entry with index
n
fromlist
is returned. The first entry has index 1. It is possible to pick several entries of the list by takingn
to be a list of indices.More generally,
Nth
returns then
th operand of the expression passed as first argument.An alternative but equivalent form of
Nth(list, n)
islist[n]
. Example
In> lst := {a,b,c,13,19}; Out> {a,b,c,13,19}; In> Nth(lst, 3); Out> c; In> lst[3]; Out> c; In> Nth(lst, {3,4,1}); Out> {c,13,a}; In> Nth(b*(a+c), 2); Out> a+c;

Reverse
(list)¶ return the reversed list (without touching the original)
 Param list
list to reverse
This function returns a list reversed, without changing the original list. It is similar to
DestructiveReverse()
, but safer and slower. Example
In> lst:={a,b,c,13,19} Out> {a,b,c,13,19}; In> revlst:=Reverse(lst) Out> {19,13,c,b,a}; In> lst Out> {a,b,c,13,19};
See also

List
(expr1, expr2, ...)¶ construct a list
A list is constructed whose first entry is
expr1
, the second entry isexpr2
, and so on. This command is equivalent to the expression{expr1, expr2, ...}
. Example
In> List(); Out> {}; In> List(a,b); Out> {a,b}; In> List(a,{1,2},d); Out> {a,{1,2},d};

UnList
(list)¶ convert a list to a function application
This command converts a list to a function application. The first entry of
list
is treated as a function atom, and the following entries are the arguments to this function. So the function referred to in the first element oflist
is applied to the other elements.Note that
list
is evaluated before the function application is formed, but the resulting expression is left unevaluated. The functionsUnList()
andHold()
both stop the process of evaluation. Example
In> UnList({Cos, x}); Out> Cos(x); In> UnList({f}); Out> f(); In> UnList({Taylor,x,0,5,Cos(x)}); Out> Taylor(x,0,5)Cos(x); In> Eval(%); Out> 1x^2/2+x^4/24;

Listify
(expr)¶ convert a function application to a list
The parameter
expr
is expected to be a compound object, i.e. not an atom. It is evaluated and then converted to a list. The first entry in the list is the toplevel operator in the evaluated expression and the other entries are the arguments to this operator. Finally, the list is returned. Example
In> Listify(Cos(x)); Out> {Cos,x}; In> Listify(3*a); Out> {*,3,a};

Concat
(list1, list2, ...)¶ concatenate lists
The lists
list1
,list2
, … are evaluated and concatenated. The resulting big list is returned. Example
In> Concat({a,b}, {c,d}); Out> {a,b,c,d}; In> Concat({5}, {a,b,c}, {{f(x)}}); Out> {5,a,b,c,{f(x)}};
See also

Delete
(list, n)¶ delete an element from a list
This command deletes the
n
th element fromlist
. The first parameter should be a list, whilen
should be a positive integer less than or equal to the length oflist
. The entry with indexn
is removed (the first entry has index 1), and the resulting list is returned. Example
In> Delete({a,b,c,d,e,f}, 4); Out> {a,b,c,e,f};
See also

Insert
(list, n, expr)¶ insert an element into a list
The expression
expr
is inserted just before then
th entry inlist
. The first parameterlist
should be a list, whilen
should be a positive integer less than or equal to the length oflist
plus one. The expressionexpr
is placed between the entries inlist
with indicesn1
andn
. There are two border line cases: ifn
is 1, the expressionexpr
is placed in front of the list (just as by the:()
operator); ifn
equals the length oflist
plus one, the expressionexpr
is placed at the end of the list (just as byAppend()
). In any case, the resulting list is returned. Example
In> Insert({a,b,c,d}, 4, x); Out> {a,b,c,x,d}; In> Insert({a,b,c,d}, 5, x); Out> {a,b,c,d,x}; In> Insert({a,b,c,d}, 1, x); Out> {x,a,b,c,d};
See also

Replace
(list, n, expr)¶ replace an entry in a list
The
n
th entry oflist
is replaced by the expressionexpr
. This is equivalent to callingDelete()
andInsert()
in sequence. To be precise, the expressionReplace(list, n, expr)
has the same result as the expressionInsert(Delete(list, n), n, expr)
. Example
In> Replace({a,b,c,d,e,f}, 4, x); Out> {a,b,c,x,e,f};
See also

FlatCopy
(list)¶ copy the top level of a list
A copy of
list
is made and returned. The list is not recursed into, only the first level is copied. This is useful in combination with the destructive commands that actually modify lists in place (for efficiency).The following shows a possible way to define a command that reverses a list nondestructively.
 Example
In> reverse(l_IsList) < DestructiveReverse(FlatCopy(l)); Out> True; In> lst := {a,b,c,d,e}; Out> {a,b,c,d,e}; In> reverse(lst); Out> {e,d,c,b,a}; In> lst; Out> {a,b,c,d,e};

Contains
(list, expr)¶ test whether a list contains a certain element
This command tests whether
list
contains the expressionexpr
as an entry. It returnsTrue
if it does andFalse
otherwise. Only the top level oflist
is examined. The parameterlist
may also be a general expression, in that case the toplevel operands are tested for the occurrence ofexpr
. Example
In> Contains({a,b,c,d}, b); Out> True; In> Contains({a,b,c,d}, x); Out> False; In> Contains({a,{1,2,3},z}, 1); Out> False; In> Contains(a*b, b); Out> True;

Find
(list, expr)¶ get the index at which a certain element occurs
This commands returns the index at which the expression
expr
occurs inlist
. Ifexpr
occurs more than once, the lowest index is returned. Ifexpr
does not occur at all, 1 is returned. Example
In> Find({a,b,c,d,e,f}, d); Out> 4; In> Find({1,2,3,2,1}, 2); Out> 2; In> Find({1,2,3,2,1}, 4); Out> 1;
See also

Append
(list, expr)¶ append an entry at the end of a list
The expression
expr
is appended at the end oflist
and the resulting list is returned.Note that due to the underlying data structure, the time it takes to append an entry at the end of a list grows linearly with the length of the list, while the time for prepending an entry at the beginning is constant.
 Example
In> Append({a,b,c,d}, 1); Out> {a,b,c,d,1};
See also

RemoveDuplicates
(list)¶ remove any duplicates from a list
This command removes all duplicate elements from a given list and returns the resulting list. To be precise, the second occurrence of any entry is deleted, as are the third, the fourth, etc.
 Example
In> RemoveDuplicates({1,2,3,2,1}); Out> {1,2,3}; In> RemoveDuplicates({a,1,b,1,c,1}); Out> {a,1,b,c};

Swap
(list, i1, i2)¶ swap two elements in a list
This command swaps the pair of entries with entries
i1
andi2
inlist
. So the element at indexi1
ends up at indexi2
and the entry ati2
is put at indexi1
. Both indices should be valid to address elements in the list. Then the updated list is returned.Swap()
works also on generic arrays. Example
In> lst := {a,b,c,d,e,f}; Out> {a,b,c,d,e,f}; In> Swap(lst, 2, 4); Out> {a,d,c,b,e,f};
See also

Count
(list, expr)¶ count the number of occurrences of an expression
This command counts the number of times that the expression
expr
occurs inlist
and returns this number. Example
In> lst := {a,b,c,b,a}; Out> {a,b,c,b,a}; In> Count(lst, a); Out> 2; In> Count(lst, c); Out> 1; In> Count(lst, x); Out> 0;
See also

FillList
(expr, n)¶ fill a list with a certain expression
This command creates a list of length
n
in which all slots contain the expressionexpr
and returns this list. Example
In> FillList(x, 5); Out> {x,x,x,x,x};
See also

Drop
(list, n)¶ 
Drop
(list, n) 
Drop
(list, {m, n}) drop a range of elements from a list
This command removes a sublist of
list
and returns a list containing the remaining entries. The first calling sequence drops the firstn
entries inlist
. The second form drops the lastn
entries. The last invocation drops the elements with indicesm
throughn
. Example
In> lst := {a,b,c,d,e,f,g}; Out> {a,b,c,d,e,f,g}; In> Drop(lst, 2); Out> {c,d,e,f,g}; In> Drop(lst, 3); Out> {a,b,c,d}; In> Drop(lst, {2,4}); Out> {a,e,f,g};

Take
(list, n)¶ 
Take
(list, n) 
Take
(list, {m, n}) take a sublist from a list, dropping the rest
This command takes a sublist of
list
, drops the rest, and returns the selected sublist. The first calling sequence selects the firstn
entries inlist
. The second form takes the lastn
entries. The last invocation selects the sublist beginning with entry numberm
and ending with then
th entry. Example
In> lst := {a,b,c,d,e,f,g}; Out> {a,b,c,d,e,f,g}; In> Take(lst, 2); Out> {a,b}; In> Take(lst, 3); Out> {e,f,g}; In> Take(lst, {2,4}); Out> {b,c,d};

Partition
(list, n)¶ partition a list in sublists of equal length
This command partitions
list
into nonoverlapping sublists of lengthn
and returns a list of these sublists. The firstn
entries inlist
form the first partition, the entries from positionn+1
up to2n
form the second partition, and so on. Ifn
does not divide the length oflist
, the remaining entries will be thrown away. Ifn
equals zero, an empty list is returned. Example
In> Partition({a,b,c,d,e,f,}, 2); Out> {{a,b},{c,d},{e,f}}; In> Partition(1 .. 11, 3); Out> {{1,2,3},{4,5,6},{7,8,9}};
See also

Flatten
(expression, operator)¶ flatten expression w.r.t. some operator
Flatten()
flattens an expression with respect to a specific operator, converting the result into a list. This is useful for unnesting an expression.Flatten()
is typically used in simple simplification schemes. Example
In> Flatten(a+b*c+d, "+"); Out> {a,b*c,d}; In> Flatten({a,{b,c},d}, "List"); Out> {a,b,c,d};
See also

UnFlatten
(list, operator, identity)¶ inverse operation of
Flatten()
UnFlatten()
is the inverse operation ofFlatten()
. Given a list, it can be turned into an expression representing for instance the addition of these elements by callingUnFlatten()
with+
as argument to operator, and 0 as argument to identity (0 is the identity for addition, since a+0=a). For multiplication the identity element would be 1. Example
In> UnFlatten({a,b,c},"+",0) Out> a+b+c; In> UnFlatten({a,b,c},"*",1) Out> a*b*c;
See also

Type
(expr)¶ return the type of an expression
The type of the expression
expr
is represented as a string and returned. So, ifexpr
is a list, the string"List"
is returned. In general, the toplevel operator ofexpr
is returned. If the argumentexpr
is an atom, the result is the empty string""
. Example
In> Type({a,b,c}); Out> "List"; In> Type(a*(b+c)); Out> "*"; In> Type(123); Out> "";

NrArgs
(expr)¶ return number of toplevel arguments
This function evaluates to the number of toplevel arguments of the expression
expr
. The argumentexpr
may not be an atom, since that would lead to an error. Example
In> NrArgs(f(a,b,c)) Out> 3; In> NrArgs(Sin(x)); Out> 1; In> NrArgs(a*(b+c)); Out> 2;

VarList
(expr)¶ 
VarListArith
(expr)¶ 
VarListSome
(expr, list)¶ list of variables appearing in an expression
The command
VarList()
returns a list of all variables that appear in the expressionexpr
. The expression is traversed recursively.The command
VarListSome()
looks only at arguments of functions in thelist
. All other functions are considered opaque (as if they do not contain any variables) and their arguments are not checked. For example,VarListSome(a + Sin(bc))
will return{a, b, c}
, butVarListSome(a*Sin(bc), {*})
will not look at arguments ofSin()
and will return{a,Sin(bc)}
. HereSin(bc)
is considered a variable because the functionSin()
does not belong tolist
.The command “func:VarListArith returns a list of all variables that appear arithmetically in the expression
expr
. This is implemented throughVarListSome()
by restricting to the arithmetic functions+
,
,*
,/
. Arguments of other functions are not checked.Note that since the operators
+
and
are prefix as well as infix operators, it is currently required to useAtom("+")
to obtain the unevaluated atom+
. Example
In> VarList(Sin(x)) Out> {x}; In> VarList(x+a*y) Out> {x,a,y}; In> VarListSome(x+a*y, {Atom("+")}) Out> {x,a*y}; In> VarListArith(x+y*Cos(Ln(x)/x)) Out> {x,y,Cos(Ln(x)/x)} In> VarListArith(x+a*y^21) Out> {x,a,y^2};
See also
IsFreeOf()
,IsVariable()
,FuncList()
,HasExpr()
,HasFunc()

FuncList
(expr)¶ list of functions used in an expression
The command
FuncList()
returns a list of all function atoms that appear in the expressionexpr
. The expression is recursively traversed. Example
In> FuncList(x+y*Cos(Ln(x)/x)) Out> {+,*,Cos,/,Ln};

FuncListArith
(expr)¶ list of functions used in an expression
FuncListArith()
is defined throughFuncListSome()
to look only at arithmetic operations+
,
,*
,/
. Example
In> FuncListArith(x+y*Cos(Ln(x)/x)) Out> {+,*,Cos};

FuncListSome
(expr, list)¶ list of functions used in an expression
The command
FuncListSome()
does the same asFuncList()
, except it only looks at arguments of a givenlist
of functions. All other functions become opaque (as if they do not contain any other functions). For example,FuncList(a + Sin(bc))
will see that the expression has a{}
operation and return {{+,Sin,}}, butFuncListSome(a + Sin(bc), {+})
will not look at arguments ofSin()
and will return{+,Sin}
.Note that since the operators
+
and
are prefix as well as infix operators, it is currently required to useAtom("+")
to obtain the unevaluated atom+
. Example
In> FuncListSome({a+b*2,c/d},{List}) Out> {List,+,/};

PrintList
(list[, padding])¶ print list with padding
Prints
list
and inserts thepadding
string between each pair of items of the list. Items of the list which are strings are printed without quotes, unlikeWrite()
. Items of the list which are themselves lists are printed inside braces{}
. If padding is not specified, standard one is used “, ” (comma, space). Example
In> PrintList({a,b,{c, d}}, `` .. ``) Out> `` a .. b .. { c .. d}``;
See also

Table
(body, var, from, to, step)¶ evaluate while some variable ranges over interval
This command generates a list of values from
body
, by assigning variablevar
values fromfrom
up toto
, incrementingstep
each time. So, the variablevar
first gets the valuefrom
, and the expressionbody
is evaluated. Then the valuefrom``+``step
is assigned tovar
and the expressionbody
is again evaluated. This continues, incrementingvar
withstep
on every iteration, untilvar
exceedsto
. At that moment, all the results are assembled in a list and this list is returned. Example
In> Table(i!, i, 1, 9, 1); Out> {1,2,6,24,120,720,5040,40320,362880}; In> Table(i, i, 3, 16, 4); Out> {3,7,11,15}; In> Table(i^2, i, 10, 1, 1); Out> {100,81,64,49,36,25,16,9,4,1};
See also
For()
,MapSingle()
, ..:,TableForm()

TableForm
(list)¶ print each entry in a list on a line
This functions writes out the list
list
in a better readable form, by printing every element in the list on a separate line. Example
In> TableForm(Table(i!, i, 1, 10, 1)); 1 2 6 24 120 720 5040 40320 362880 3628800 Out> True;
See also
Destructive operations¶
Destructive commands run faster than their nondestructive counterparts because the latter copy the list before they alter it.

DestructiveAppend
(list, expr)¶ destructively append an entry to a list
This is the destructive counterpart of
Append()
. This command yields the same result as the corresponding call toAppend()
, but the original list is modified. So if a variable is bound tolist
, it will now be bound to the list with the expressionexpr
inserted. Example
In> lst := {a,b,c,d}; Out> {a,b,c,d}; In> Append(lst, 1); Out> {a,b,c,d,1}; In> lst Out> {a,b,c,d}; In> DestructiveAppend(lst, 1); Out> {a,b,c,d,1}; In> lst; Out> {a,b,c,d,1};

DestructiveDelete
(list, n)¶ delete an element destructively from a list
This is the destructive counterpart of :func`Delete`. This command yields the same result as the corresponding call to
Delete()
, but the original list is modified. So if a variable is bound tolist
, it will now be bound to the list with then
th entry removed. Example
In> lst := {a,b,c,d,e,f}; Out> {a,b,c,d,e,f}; In> Delete(lst, 4); Out> {a,b,c,e,f}; In> lst; Out> {a,b,c,d,e,f}; In> DestructiveDelete(lst, 4); Out> {a,b,c,e,f}; In> lst; Out> {a,b,c,e,f};
See also

DestructiveInsert
(list, n, expr)¶ insert an element destructively into a list
This is the destructive counterpart of
Insert()
. This command yields the same result as the corresponding call toInsert()
, but the original list is modified. So if a variable is bound tolist
, it will now be bound to the list with the expressionexpr
inserted. Example
In> lst := {a,b,c,d}; Out> {a,b,c,d}; In> Insert(lst, 2, x); Out> {a,x,b,c,d}; In> lst; Out> {a,b,c,d}; In> DestructiveInsert(lst, 2, x); Out> {a,x,b,c,d}; In> lst; Out> {a,x,b,c,d};
See also

DestructiveReplace
(list, n, expr)¶ replace an entry destructively in a list
 Param list
list of which an entry should be replaced
 Param n
index of entry to replace
 Param expr
expression to replace the
n
th entry with
This is the destructive counterpart of
Replace()
. This command yields the same result as the corresponding call toReplace()
, but the original list is modified. So if a variable is bound tolist
, it will now be bound to the list with the expressionexpr
inserted. Example
In> lst := {a,b,c,d,e,f}; Out> {a,b,c,d,e,f}; In> Replace(lst, 4, x); Out> {a,b,c,x,e,f}; In> lst; Out> {a,b,c,d,e,f}; In> DestructiveReplace(lst, 4, x); Out> {a,b,c,x,e,f}; In> lst; Out> {a,b,c,x,e,f};
See also

DestructiveReverse
(list)¶ reverse a list destructively
This command reverses
list
in place, so that the original is destroyed. This means that any variable bound tolist
will now have an undefined content, and should not be used any more. The reversed list is returned. Example
In> lst := {a,b,c,13,19}; Out> {a,b,c,13,19}; In> revlst := DestructiveReverse(lst); Out> {19,13,c,b,a}; In> lst; Out> {a};
See also
Set operations¶

Intersection
(l1, l2)¶ return the intersection of two lists
The intersection of the lists
l1
andl2
is determined and returned. The intersection contains all elements that occur in both lists. The entries in the result are listed in the same order as inl1
. If an expression occurs multiple times in bothl1
andl2
, then it will occur the same number of times in the result. Example
In> Intersection({a,b,c}, {b,c,d}); Out> {b,c}; In> Intersection({a,e,i,o,u}, {f,o,u,r,t,e,e,n}); Out> {e,o,u}; In> Intersection({1,2,2,3,3,3}, {1,1,2,2,3,3}); Out> {1,2,2,3,3};
See also

Union
(l1, l2)¶ return the union of two lists
The union of the lists
l1
andl2
is determined and returned. The union contains all elements that occur in one or both of the lists. In the resulting list, any element will occur only once. Example
In> Union({a,b,c}, {b,c,d}); Out> {a,b,c,d}; In> Union({a,e,i,o,u}, {f,o,u,r,t,e,e,n}); Out> {a,e,i,o,u,f,r,t,n}; In> Union({1,2,2,3,3,3}, {2,2,3,3,4,4}); Out> {1,2,3,4};
See also

Difference
(l1, l2)¶ return the difference of two lists
The difference of the lists
l1
andl2
is determined and returned. The difference contains all elements that occur inl1
but not inl2
. The order of elements inl1
is preserved. If a certain expression occursn1
times in the first list andn2
times in the second list, it will occurn1n2
times in the result ifn1
is greater thann2
and not at all otherwise. Example
In> Difference({a,b,c}, {b,c,d}); Out> {a}; In> Difference({a,e,i,o,u}, {f,o,u,r,t,e,e,n}); Out> {a,i}; In> Difference({1,2,2,3,3,3}, {2,2,3,4,4}); Out> {1,3,3};
See also
Associative map¶

Assoc
(key, alist)¶ return element stored in association list
The association list
alist
is searched for an entry stored with indexkey
. If such an entry is found, it is returned. Otherwise the atomEmpty
is returned.Association lists are represented as a list of twoentry lists. The first element in the twoentry list is the key, the second element is the value stored under this key.
The call
Assoc(key, alist)
can (probably more intuitively) be accessed asalist[key]
. Example
In> writer := {}; Out> {}; In> writer[``Iliad``] := ``Homer``; Out> True; In> writer[``Henry IV``] := ``Shakespeare``; Out> True; In> writer[``Ulysses``] := ``James Joyce``; Out> True; In> Assoc(``Henry IV``, writer); Out> {``Henry IV``,``Shakespeare``}; In> Assoc(``War and Peace``, writer); Out> Empty;
See also
AssocIndices()
,[]()
,:=()
,AssocDelete()

AssocIndices
(alist)¶ return the keys in an association list
All the keys in the association list
alist
are assembled in a list and this list is returned. Example
In> writer := {}; Out> {}; In> writer[``Iliad``] := ``Homer``; Out> True; In> writer[``Henry IV``] := ``Shakespeare``; Out> True; In> writer[``Ulysses``] := ``James Joyce``; Out> True; In> AssocIndices(writer); Out> {``Iliad``,``Henry IV``,``Ulysses``};
See also

AssocDelete
(alist, key)¶ 
AssocDelete
(alist, {key, value}) delete an entry in an association list
The key {
key
} in the association listalist
is deleted. (The list itself is modified.) If the key was found and successfully deleted, returnsTrue
, otherwise if the given key was not found, the function returnsFalse
.The second, longer form of the function deletes the entry that has both the specified key and the specified value. It can be used for two purposes:
to make sure that we are deleting the right value;
if several values are stored on the same key, to delete the specified entry (see the last example).
At most one entry is deleted.
 Example
In> writer := {}; Out> {}; In> writer[``Iliad``] := ``Homer``; Out> True; In> writer[``Henry IV``] := ``Shakespeare``; Out> True; In> writer[``Ulysses``] := ``James Joyce``; Out> True; In> AssocDelete(writer, ``Henry IV``) Out> True; In> AssocDelete(writer, ``Henry XII``) Out> False; In> writer Out> {{``Ulysses``,``James Joyce``}, {``Iliad``,``Homer``}}; In> DestructiveAppend(writer, {``Ulysses``, ``Dublin``}); Out> {{``Iliad``,``Homer``},{``Ulysses``,``James Joyce``}, {``Ulysses``,``Dublin``}}; In> writer[``Ulysses``]; Out> ``James Joyce``; In> AssocDelete(writer,{``Ulysses``,``James Joyce``}); Out> True; In> writer Out> {{``Iliad``,``Homer``},{``Ulysses``,``Dublin``}};
See also
Sorting¶

BubbleSort
(list, compare)¶ sort a list
This command returns
list
after it is sorted usingcompare
to compare elements. The functioncompare
should accept two arguments, which will be elements oflist
, and compare them. It should returnTrue
if in the sorted list the second argument should come after the first one, andFalse
otherwise.The function
BubbleSort()
uses the socalled bubble sort algorithm to do the sorting by swapping elements that are out of order. This algorithm is easy to implement, though it is not particularly fast. The sorting time is proportional to \(n^2\) where \(n\) is the length of the list. Example
In> BubbleSort({4,7,23,53,2,1}, "<"); Out> {2,1,4,7,23,53};
See also

HeapSort
(list, compare)¶ sort a list
This command returns
list
after it is sorted usingcompare
to compare elements. The functioncompare
should accept two arguments, which will be elements oflist
, and compare them. It should returnTrue
if in the sorted list the second argument should come after the first one, andFalse
otherwise.The function
HeapSort()
uses theheapsort algorithm
and is much faster for large lists. The sorting time is proportional to \(n\ln(n)\) where \(n\) is the length of the list. Example
In> HeapSort({4,7,23,53,2,1}, ``>``); Out> {53,23,7,4,1,2};
See also
Stack and queue operations¶

Push
(stack, expr)¶ add an element on top of a stack
This is part of a simple implementation of a stack, internally represented as a list. This command pushes the expression
expr
on top of the stack, and returns the stack afterwards. Example
In> stack := {}; Out> {}; In> Push(stack, x); Out> {x}; In> Push(stack, x2); Out> {x2,x}; In> PopFront(stack); Out> x2;
See also

Pop
(stack, n)¶ remove an element from a stack
This is part of a simple implementation of a stack, internally represented as a list. This command removes the element with index
n
from the stack and returns this element. The top of the stack is represented by the index 1. Invalid indices, for example indices greater than the number of element on the stack, lead to an error. Example
In> stack := {}; Out> {}; In> Push(stack, x); Out> {x}; In> Push(stack, x2); Out> {x2,x}; In> Push(stack, x3); Out> {x3,x2,x}; In> Pop(stack, 2); Out> x2; In> stack; Out> {x3,x};
See also

PopFront
(stack)¶ remove an element from the top of a stack
This is part of a simple implementation of a stack, internally represented as a list. This command removes the element on the top of the stack and returns it. This is the last element that is pushed onto the stack.
 Example
In> stack := {}; Out> {}; In> Push(stack, x); Out> {x}; In> Push(stack, x2); Out> {x2,x}; In> Push(stack, x3); Out> {x3,x2,x}; In> PopFront(stack); Out> x3; In> stack; Out> {x2,x};

PopBack
(stack)¶ remove an element from the bottom of a stack
This is part of a simple implementation of a stack, internally represented as a list. This command removes the element at the bottom of the stack and returns this element. Of course, the stack should not be empty.
 Example
In> stack := {}; Out> {}; In> Push(stack, x); Out> {x}; In> Push(stack, x2); Out> {x2,x}; In> Push(stack, x3); Out> {x3,x2,x}; In> PopBack(stack); Out> x; In> stack; Out> {x3,x2};
See also
Global stack¶
The functions below operate on a global stack, currently implemented as a list
that is not accessible externally (it is protected through
LocalSymbols()
).

GlobalPop
()¶ 
GlobalPop
(var) restore variables using a global stack
GlobalPop()
removes the last pushed value from the stack. If a variable name is given, the variable is assigned, otherwise the popped value is returned. If the global stack is empty, an error message is printed.See also

GlobalPush
(expr)¶ save variables using a global stack
 Example
In> GlobalPush(3) Out> 3; In> GlobalPush(Sin(x)) Out> Sin(x); In> GlobalPop(x) Out> Sin(x); In> GlobalPop(x) Out> 3; In> x Out> 3;
See also