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Applying Functions to Lists
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Built-in
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Applying Functions to Lists and Other Expressions
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Applying Functions to Lists
Expressions
Functional Programming
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List Manipulation
Mathematica Syntax
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Apply
(@@)
Apply
[
f
,
expr
]
or
f
@@
expr
replaces the head of
expr
by
f
.
Apply
[
f
,
expr
,
levelspec
]
replaces heads in parts of
expr
specified by
levelspec
.
MORE INFORMATION
Apply
uses standard level specifications:
n
levels
1
through
n
Infinity
levels
1
through
Infinity
{
n
}
level
n
only
{
n
1
,
n
2
}
levels
n
1
through
n
2
The default value for
levelspec
in
Apply
is
{0}
.
f
@@@
expr
is equivalent to
Apply
[
f
,
expr
, {1}]
.
A positive level
n
consists of all parts of
expr
specified by
n
indices.
A negative level
-
n
consists of all parts of
expr
with depth
n
.
Level
-1
consists of numbers, symbols and other objects that do not have subparts.
Level
0
corresponds to the whole expression.
Apply
always effectively constructs a complete new expression, and then evaluates it.
Apply
operates on
SparseArray
objects just as it would on the corresponding ordinary lists.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
In[1]:=
Out[1]=
In[2]:=
Out[2]=
In[3]:=
Out[3]=
Apply
gets rid of a level of lists:
In[1]:=
Out[1]=
Scope
(10)
Generalizations & Extensions
(2)
Options
(1)
Applications
(3)
Properties & Relations
(5)
Possible Issues
(1)
SEE ALSO
Map
Scan
Level
Operate
MapThread
Total
Sequence
Function
TUTORIALS
Applying Functions to Lists and Other Expressions
MORE ABOUT
Applying Functions to Lists
Expressions
Functional Programming
Handling Arrays of Data
List Manipulation
Mathematica Syntax
RELATED LINKS
NKS|Online
(
A New Kind of Science
)
New in 1 | Last modified in 4
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Scope 