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Reference concatenation operator

The concatenation operator is written as a tilde. An expression using the

concatenation operator has the following syntax:

reference left ~ reference right

The result of such an expression is a reference list, which is an ordered list of

references. Some functions can take a reference list as an argument, SUM, MAX or

INDEX for example.

The reference concatenation is sometimes called 'union'. But it is not the union of the

two sets 'reference left' and 'reference right' as normally understood in set theory.

COUNT(A1:C3~B2:D2) returns 12 (=9+3), but it has only 10 cells when considered

as the union of the two sets of cells.

Notice that SUM(A1:C3;B2:D2) is different from SUM( A1:C3~B2:D2) although they

give the same result. The first is a function call with 2 parameters, each of them is

reference to a range. The second is a function call with 1 parameter, which is a

reference list.

Intersection operator

The intersection operator is written as an exclamation mark. An expression using the

intersection operator has the following syntax:

reference left ! reference right

If the references refer to single ranges, the result is a reference to a single range,

containing all cells, which are both in the left reference and in the right reference.

If the references are reference lists, then each list item from the left is intersected

with each one from the right and these results are concatenated to a reference list.

The order is to first intersect the first item from the left with all items from the right,

then intersect the second item from the left with all items from the right, and so on.

Examples

A2:B4 ! B3:D6

This results in a reference to the range B3:B4, because these cells are inside

A2:B4 and inside B3:D4.

(A2:B4~B1:C2) ! (B2:C6~C1:D3)

First the intersections A2:B4!B2:C6, A2:B4!C1:D3, B1:C2!B2:C6 and B1:C2!C1:D3

are calculated. This results in B2:B4, empty, B2:C2, and C1:C2. Then these results

are concatenated, dropping empty parts. So the final result is the reference list

B2:B4 ~ B2:C2 ~ C1:C2.

You can use the intersection operator to refer a cell in a cross tabulation in an

understandable way. If you have columns labeled 'Temperature' and 'Precipitation'

and the rows labeled 'January', 'February', 'March', and so on, then the following

expression

'February' ! !Temperature'

will reference to the cell containing the temperature in February.

The intersection operator (!) should have a higher precedence than the concatenation

operator (~), but do not rely on precedence.

Tip

Always put in parentheses the part that is to be calculated first.

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