Wolfram: List. Create (Table)
Table
Use
Table
to generate a flat list or nested rectangular array (aka n-dimensional matrix). Like
Python list comprehension
but more powerful.
💡 TIP: Table
is the most powerful way to generate a list, and is most frequently used. Master it.
Table[expr, n]
-
a list with expr repeated n times.
Table[ x, {3}] (* {x, x, x} *)
Table[expr, {i, iMax}]
-
a list, each item is expr with the variable i successively taking on the values 1 through iMax (in steps of 1).
Table[ x, {x, 3}] (* {1, 2, 3} *)
Table[expr, {i, iMin, iMax}]
-
start with iMin.
Table[ x, {x, 6, 9}] (* {6, 7, 8, 9} *) Table[ 2 x + y , {x, 1, 4}] (* {2 + y, 4 + y, 6 + y, 8 + y} *)
Table[expr, {i, iMin, iMax, di}]
-
with increment di.
Table[ x, {x, 1, 3, 1/2}] (* {1, 3/2, 2, 5/2, 3} *) Table[ x, {x, 1, 3, 0.5}] (* {1., 1.5, 2., 2.5, 3.} *)
Table[expr, {i, ListOfValues}}]
-
a flat list. Each item use the given list of values ListOfValues.
Table[ x, {x, {3, 9, 2}}] (* {3, 9, 2} *)
Generating Nested List with Table
Table[expr, iterSpec1, iterSpec2, etc]
-
a nested list. For each i, loop over the variable in each iterSpec.
Table[expr, iterSpec1, iterSpec2]
is same as
Table[Table[expr, iterSpec2], iterSpec1]
the iterSpec can take any of the following form:
{n}
→ repeat n times.{var, max}
{var, min, max}
{var, min, max, step}
{var, listOfValues}
Table[ ff[x, y, z], {x, 2}, {y, 2}, {z, 2}] (* { { {ff[1, 1, 1], ff[1, 1, 2]}, {ff[1, 2, 1], ff[1, 2, 2]}}, { {ff[2, 1, 1], ff[2, 1, 2]}, {ff[2, 2, 1], ff[2, 2, 2]}}} *)
Examples
any part can be symbolic
Table[ Sin[x], {x, 0, 2 Pi, Pi/4}] (* {0, 1/Sqrt[2], 1, 1/Sqrt[2], 0, -(1/Sqrt[2]), -1, -(1/Sqrt[2]), 0} *)
generating a 3D matrix.

arbitrary expression
Table[ f[x+y] z, {x, 3}, {y, 3}] (* { {z*f[2], z*f[3], z*f[4]}, {z*f[3], z*f[4], z*f[5]}, {z*f[4], z*f[5], z*f[6]}} *)
WolframLang Loop, Iteration, Recursion
WolframLang List Operations
- Wolfram: List Operations
- Wolfram: List. Create (Table)
- Wolfram: Create Flat List (Range)
- Wolfram: List. Get Parts
- Wolfram: List. Add Element
- Wolfram: List. Delete Element
- Wolfram: List. Change Element
- Wolfram: List. Check Exist
- Wolfram: List. Filter
- Wolfram: List. Sort Reverse Order
- Wolfram: List. Reshape (split, group, flatten, transpose)
- Wolfram: List. Count, Group, Similar Items
- Wolfram: List. Combinatorics
- Wolfram: List. Join, Union, Intersection, Difference