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A.3.7 Iterators

Iterator notation.

Iterators are used in such functions as Sum, Table, Do and Range.

The iteration parameters imin, imax and di do not need to be integers. The variable i is given a sequence of values starting at imin, and increasing in steps of di, stopping when the next value of i would be greater than imax. The iteration parameters can be arbitrary symbolic expressions, so long as (imax-imin)/di is a number.

When several iteration variables are used, the limits for the later ones can depend on the values of earlier ones.

The variable i can be any symbolic expression; it need not be a single symbol. The value of i is automatically set up to be local to the iteration function. This is effectively done by wrapping a Block construct containing i around the iteration function.

The procedure for evaluating iteration functions is described in Section A.4.2.