Built-in Mathematica Symbol

Part ([[...]])

expr[[i]] or Part[expr, i]
gives the i

part of expr.

expr[[-i]]
counts from the end.

expr[[i, j, ...]] or Part[expr, i, j, ...]
is equivalent to expr[[i]][[j]]....

expr[[{i₁, i₂, ...}]]
gives a list of the parts i₁, i₂, ... of expr.

expr[[m;;n]]
gives parts m through n.

expr[[m;;n;;s]]
gives parts m through n in steps of s.

MORE INFORMATION

You can make an assignment like t[[spec]]=value to modify any part or sequence of parts in an expression. »

Part 0 of an expression is its head.

Common spans of parts include:

	expr[[m;;]]	part m through the end
	expr[[;;n]]	from the beginning to part n
	expr[[;;,j]]	column j
	expr[[m₁;;n₁,m₂;;n₂]]	submatrix

When expr is a list, expr[[{i₁, i₂, ...}]] gives a list of parts. In general, the head of expr is applied to the list of parts. »

You can get a nested list of parts from expr[[list₁, list₂, ...]]. Each part has one index from each list.

If any of the list_i are All or ;;, all parts at that level are kept.

Notice that lists are used differently in Part than in functions like Extract, MapAt and Position.

If expr is a SparseArray object, expr[[...]] gives the parts in the corresponding ordinary array. »

In StandardForm and InputForm, expr[[spec]] can be input as exprspec.

and can be entered as Esc [[ Esc and Esc ]] Esc or \[LeftDoubleBracket] and \[RightDoubleBracket].

In StandardForm, expr[[spec]] can be input as expr_[[spec]] or expr_spec.

EXAMPLES

CLOSE ALL

Basic Examples (10)

Pick out a part of a list:

Pick out a sequence of parts:

Pick out a part of a matrix:

The second row of a matrix:

The second column of a matrix:

An element 2 from the end of a list:

A list of parts:

Reassign a part:

Reassign a sequence of parts:

Part works with expressions of any kind, not just lists:

Part always operates on the FullForm of expressions:

Pick out a part of a list:

In[1]:=

Out[1]=

Pick out a sequence of parts:

In[1]:=

Out[1]=

Pick out a part of a matrix:

In[1]:=

Out[1]=

The second row of a matrix:

In[1]:=

Out[1]=

The second column of a matrix:

In[1]:=

Out[1]=

An element 2 from the end of a list:

A list of parts:

Reassign a part:

Reassign a sequence of parts:

Part works with expressions of any kind, not just lists:

Part always operates on the FullForm of expressions:

In[4]:=

Out[4]=

In[5]:=

Out[5]//FullForm=

Scope (10)

Equivalent forms:

Pick out parts 1 and 3:

Pick out parts 2 and 3 of parts 1 and 3:

Parts 1 through 3 from the end:

Shorter notation:

Parts extracted in steps of 2:

Enter in FullForm:

Enter using Esc [[ Esc and Esc ]] Esc:

Enter as a subscript:

Assign several parts at once:

Assign parts 2 and 3 to be x:

Assign different values to parts 1, 3 and 4:

All standard assignment operations work on parts:

Rearrange elements by reassigning parts:

For SparseArray objects, Part gives the parts in the corresponding ordinary array:

Rows or columns are represented as sparse vectors:

Values can also be set:

Generalizations & Extensions (3)

The zeroth part of an expression is its head:

Reassign the head:

Heads in the original expression are reused when "lists" of parts are extracted:

Applications (4)

Pick out the first solution from an equation:

Pick out all solutions for a univariate equation:

Go through the first 1000 primes, and count how many lie in each possible "mod 10 bin":

Another way to get the same result:

Apply a permutation:

Invert a permutation:

Properties & Relations (2)

Pick out parts cyclically by using Mod with offset 1:

Take picks out ranges of parts:

Possible Issues (4)

Part operates on the FullForm of expressions, not their formatted forms:

Position does not return part specifications in a form that can immediately be used by Part:

Extract extracts parts specified in the way returned by Position:

Successive part extraction is not always equivalent to direct part extraction:

Only parts that already exist can be reassigned: