WOLFRAM LANGUAGE TUTORIAL
Constructing Lists
Lists are widely used in the Wolfram Language, and there are many ways to construct them.
| Range[n] | the list  |
| Table[expr,{i,n}] | the values of expr with i from  to n |
| Array[f,n] | the list  |
| NestList[f,x,n] |  with up to n nestings |
| Normal[SparseArray[{i1->v1,…},n]] | a length n list with element  being  |
| Apply[List,f[e1,e2,…]] | the list  |
Some explicit ways to construct lists.
This gives a table of the first five powers of 2.
| Out[1]= |  |
Here is another way to get the same result.
| Out[2]= |  |
This gives a similar list.
| Out[3]= |  |
SparseArray lets you specify values at particular positions.
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You can also use patterns to specify values.
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Often you will know in advance how long a list is supposed to be, and how each of its elements should be generated. And often you may get one list from another.
| Table[expr,{i,list}] | the values of expr with i taking on values from list |
| Map[f,list] | apply f to each element of list |
| MapIndexed[f,list] | give  for the i element |
| Cases[list,form] | give elements of list that match form |
| Select[list,test] | select elements for which  is True |
| Pick[list,sel,form] | pick out elements of list for which the corresponding elements of sel match form |
| TakeWhile[list,test] | give elements  from the beginning of list as long as  is True |
| list[[{i1,i2,…}]] or Part[list,{i1,i2,…}] |
| give a list of the specified parts of list |
Constructing lists from other lists.
This selects elements less than 5.
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This takes elements up to the first element that is not less than 5.
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This explicitly gives numbered parts.
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This picks out elements indicated by a
in the second list.
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Sometimes you may want to accumulate a list of results during the execution of a program. You can do this using Sow and Reap.
| Sow[val] | sow the value val for the nearest enclosing Reap |
| Reap[expr] | evaluate expr, returning also a list of values sown by Sow |
Using Sow and Reap.
This program iteratively squares a number.
| Out[10]= |  |
This does the same computation, but accumulating a list of intermediate results above 1000.
| Out[11]= |  |
An alternative but less efficient approach involves introducing a temporary variable, then starting with 
, and successively using AppendTo[t,elem].
