Multiple-Link Functions

Multiple-link functions are functions that have arguments grouped in more than one pair of brackets. They appear in expressions of the type . Definitions of multiple-link functions enable the classification of arguments as either parameters or variables.
Example 1. The identity
defines a double-link function, where is a two-parameter family of linear functions.
Example 2. A formula for rotating the vector around the axis given by the unit vector through the angle is , involving dot and cross products of vectors.
Example 3. The identity
defines the definite integral of a function from to which avoids using the bound (or dummy) variable .


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Mathematica has recently introduced the operator-form functions SortBy[f], MaximalBy[f], TakeLargestBy[f,n] and so on.
[1] S. Leśniewski, S. Leśniewski's Lecture Notes in Logic (J. Srzednicki and Z. Stachniak, eds.), Boston: Kluwer Academic, 1988 p. 31.
[2] S. Leśniewski, Stanisław Leśniewski, Collected Works (S. J. Surma, J. T. Srzednicki and D. I. Barnett, eds.), Boston: Kluwer Academic, 1992 p. 475
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