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By Leonid Shifrin

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In some rare cases one can also introduce variables with composite heads. These are stored in SubValues attached to their symbolic head. The latter two types of variables are usually used in more special circumstances, since DownValues and SubValues are normally associated with functions rather than variable definitions. You will be better off not using DownValues or SubValues - based variables until you understand exactly when and for which purpose they are beneficial. Once the global definition is given to a variable, it remains there until another definition of the same type is entered to replace it, or until it is cleared.

Due to symbolic nature of Mathematica, these values can be of any type, either atoms or normal expressions (there is no notion of "type" in Mathematica as such - see below). The built - in function which reflects the possible assignment made to a "proper" variable is called OwnValues. For example : a 3; OwnValues a HoldPattern a 3 The equal sign here represents an assignment operator, which we will cover shortly. Another way to characterize the "proper" variables is that their definitions are stored in OwnValues.

In cases when we have more than one iterator, we create a nested list where the innermost iterators correspond to the outermost lists. As we see, the bounds of the more outermost iterators may depend on the variables of more innermost ones, in which case the lists will have sublists of different lengths. This is where we start seeing that lists are more general than (multidimensional) arrays since the sublists are not bound to have the same dimensions. Also, notice that lists created by Table are not bound to be lists of numbers - they can be lists of functions: Clear i, x ; Table x ^ i, i, 1, 10 x, x2 , x3 , x4 , x5 , x6 , x7 , x8 , x9 , x10 Here, for example, we created a 3x3 matrix of monomials: Clear i, j, x ; Table x ^ i j , i, 1, 3 , j, 1, 3 x2 , x3 , x4 , x3 , x4 , x5 , x4 , x5 , x6 One more comment about Table is that it is a scoping construct in the sense that it localizes its iterator variables.

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