> From: Kip Murray <[email protected]> > > TACIT DEFINITION OF VERBS DEFINES VERBS IN TERMS OF OTHER VERBS. This occurs > in > mathematics where you see h = f + g , h = f g, h = f o g, etc., but tacit > definition is not much used in math beyond differentiation formulas like (f + > g)' = f' + g', (f g)' = f' g + f g', (f o g)' = (f' o g) g' ; and you are > more > than likely to see the last expressed as f(g(x))' = f'(g(x)) g'(x) . > Likewise, > you are more likely to see (x^n)' = n x^(n-1) than (id^n)' = n id^(n-1) . > That > is, math is more likely to use informal definitions with x's than tacit > definitions without x's.
Tacit is not much used beyond differentiation formulas? How about Functional Analysis: http://mathworld.wolfram.com/L2-Space.html Convolution (half the formulas are tacit) http://mathworld.wolfram.com/Convolution.html Vector Algebra and Differential Geometry http://mathworld.wolfram.com/RadiusVector.html http://mathworld.wolfram.com/TangentVector.html I'd say it is consistently used part of the time after the nature of the arguments is presented and it facilitates shorter and cleaner notation. In general it is used whenever function itself is an object of transformation or calculation, such as whenever operators appear. Differentiation is just one of them. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
