Built-in Mathematica Symbol

Table

Table[expr, {i_max}]
generates a list of i_max copies of expr.

Table[expr, {i, i_max}]
generates a list of the values of expr when i runs from 1 to i_max.

Table[expr, {i, i_min, i_max}]
starts with i=i_min.

Table[expr, {i, i_min, i_max, di}]
uses steps di.

Table[expr, {i, {i₁, i₂, ...}}]
uses the successive values i₁, i₂, ....

Table[expr, {i, i_min, i_max}, {j, j_min, j_max}, ...]
gives a nested list. The list associated with i is outermost. »

MORE INFORMATION

You can use Table to build up vectors, matrices, tensors and other arrays.

Table uses the standard Mathematica iteration specification.

Table evaluates its arguments in a nonstandard way.

Table[expr, spec] first evaluates spec, then localizes the variable specified, and successively assigns values to it, each time evaluating expr.

Table effectively uses Block to localize values or variables.

Table[expr, spec₁, spec₂] is effectively equivalent to Table[Table[expr, spec₂], spec₁].

EXAMPLES

CLOSE ALL

Basic Examples (6)

A table of the first ten squares:

A table with i running from 0 to 20 in steps of 2:

A list of ten x's:

Make a 4×3 matrix:

Plot a table:

Arrange a table in a column:

A table of the first ten squares:

In[1]:=

Out[1]=

A table with i running from 0 to 20 in steps of 2:

A list of ten x's:

Make a 4×3 matrix:

Out[2]//MatrixForm=

Plot a table:

In[1]:=

Out[1]=

Arrange a table in a column:

In[1]:=

Out[1]=

Scope (5)

The index in the table can run backwards:

Make a triangular array:

Make a 3x2x4 array, or tensor:

Iterate over an existing list:

Make an array from existing lists:

Generalizations & Extensions (2)

The table index can have symbolic values:

The variables need not just be symbols:

Applications (5)

Make a table of graphics:

Generate the corners of a polygon:

Make Pascal's triangle:

Properties & Relations (13)

Print the values of the table index while the table is being generated:

Monitor the values by showing them in a temporary cell:

Range gives the sequence of values of a table iterator:

Do evaluates the same sequence of expressions as Table, but does not return them:

Sum effectively applies Plus to results from Table:

Array iterates over successive integers:

Map applies a function to successive elements in a list:

Table can substitute successive elements in a list into an expression:

Using multiple iteration specifications is equivalent to nesting Table functions:

Feed in parameters for tables:

Use Apply to splice a complete iterator specification into Table:

With can insert the specification for a single iterator:

Possible Issues (6)

For some step sizes, output from Table may not include the upper limit given:

Table requires iterator specifications to be given explicitly:

Table normally reevaluates at each step:

The Evaluate is needed to force evaluation of the table before it is fed to Plot:

Values of Table variables do not get substituted inside held expressions:

Use With to insert values:

Formatting wrappers such as Grid give expressions that are no longer lists: