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Apply

Apply
or replaces the head of expr by f.
Apply
or replaces heads at level of expr by f.
Apply
replaces heads in parts of expr specified by levelspec.
  • Apply uses standard level specifications:
nlevels through n
Infinitylevels through Infinity
{n}level n only
{n1,n2}levels through
  • The default value for levelspec in Apply is .
  • is equivalent to Apply.
  • 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 consists of numbers, symbols, and other objects that do not have subparts.
  • Level 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.
Apply gets rid of a level of lists:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Apply gets rid of a level of lists:
In[1]:=
Click for copyable input
Out[1]=
Apply at level (default):
Apply at level :
The short form is equivalent to applying at level :
Apply at levels and :
Apply down to level (excluding level ):
Apply at levels through :
Apply at all levels, starting at level :
Apply also at level :
Negative levels:
Positive and negative levels can be mixed:
Different heads at each level:
Apply also inside heads at the levels specified:
Apply works with any head, not just List:
Apply works on sparse arrays:
Apply inside heads as well as arguments:
Display the factorization of an integer using superscripts:
Create a table from a list of range specifications:
Turn a function that takes several arguments into one that takes a list of arguments:
Leaves are visited before roots:
Total does effectively the same thing as applying Plus to a list:
Using in a pure function has the same effect as using Apply:
Three ways to apply a function at level :
Ordinary function application takes the list as a single argument:
Apply takes the elements of the list as separate arguments:
Applying to atomic objects that do not have subparts effectively does nothing:
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