I came across a bit of code that uses the syntax /: and I don't know what it does. I can't find its documentation, or maybe I'm just not looking properly. The code snippet is something like:

F/:F[A___,b_?NumberQ B_, C___] := b*F[A,B,C]

(i.e. part of the definition of multi-linearity). How does this behave differently than the following?:

G[A___,b_?NumberQ B_, C___] := b*G[A,B,C]


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    $\begingroup$ In the spirit of teaching people how to fish: highlight the /: part of the expression. Press F1. The help file should give links to the relevant functions. $\endgroup$ – J. M. will be back soon May 3 '12 at 17:42
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    $\begingroup$ Or at the very least, try entering /: into the doc center and see what comes up $\endgroup$ – rm -rf May 3 '12 at 17:43
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    $\begingroup$ Check TagSet in docs $\endgroup$ – kglr May 3 '12 at 17:44
  • $\begingroup$ @J.M.,@R.M,@kguler: Thanks for the tips, I didn't know about the F1 thing. Having read those documentation pages, I still don't understand the difference between my two lines of code. $\endgroup$ – Ian Hincks May 3 '12 at 17:55
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    $\begingroup$ @IanHincks In this case, there is none. The docs mention that in the Scope section. For OwnValues (variables) and DownValues (functions), you can use SetDelayed (:=) with the same effect. But for UpValues (which are another kind of global rules), you need to use TagSetDelayed (/:), or perhaps UpSetDelayed (although I favor the former). $\endgroup$ – Leonid Shifrin May 3 '12 at 18:00

/: is the short-hand notation for TagSetDelayed, which is creating UpValues. It's useful for over-loading how a particular function behaves with a specific head. For example:

In[1]:= h /: Plus[x : h[arg1_, arg2_], y : h[arg3_, arg4_]] := Plus[arg1, arg2, arg3, arg4]

In[2]:= h[1, 2] + h[3, 4]
Out[2]= 10

The benefit being you don't have to Unprotect[Plus] to set the definition, and if you Remove[h] this definition will be wiped out as well.

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    $\begingroup$ Thanks @nikko. What purpose do the x and y serve in this example? It seems to work without them. $\endgroup$ – Ian Hincks May 3 '12 at 18:35
  • $\begingroup$ @IanHincks in this example, they don't serve any purpose, but they could be used to refer to the entire object matched by h[arg1_, arg2_]. So, if you had need of the entire pattern, you could use it. $\endgroup$ – rcollyer May 3 '12 at 18:36
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    $\begingroup$ In this case, it is TagSetDelayed rather than TagSet. The syntax in fact has to parts: s/:lhs:=rhs or s/:lhs=rhs, so /: alone is not enough to tell which one it is. Also, a correct statement is that TagSetDelayed (or TagSet) can create UpValues (but it can also create OwnValues, DownValues and SubValues, in which case, the tag part is redundant). $\endgroup$ – Leonid Shifrin May 3 '12 at 18:43
  • $\begingroup$ yes, sorry the x: and y: are superfluous here. $\endgroup$ – nikko May 3 '12 at 18:45

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