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Multiple-Link Functions

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Example 1
Example 2
Example 3
Example 1
a
1
b
-1
Example 2
r
α
1.05
Example 3
function f
sin
cos
tan
arccos
a
1
b
-1
Multiple-link functions are functions that have arguments grouped in more than one pair of brackets. They appear in expressions of the type
f〈p,q,…〉[a,b,…](x,y,…)
. Definitions of multiple-link functions enable the classification of arguments as either parameters or variables.
Example 1. The identity
L[m,b](x)=mx+b
defines a double-link function, where
L
is a two-parameter family of linear functions.
Example 2. A formula for rotating the vector
r
around the axis given by the unit vector
ω
through the angle
α
is
Rot[ω,α][r]:=(r·ω)ω+(r-(r·ω)ω)cos(α)+(ω×r)sin(α)
, involving dot and cross products of vectors.
Example 3. The identity
∫f(a,b)=
b
∫
a
f(x)dx
defines the definite integral of a function
f
from
a
to
b,
which avoids using the bound (or dummy) variable
x
.
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