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Re: Setting upvalues, using ^:=, such that they get actually used

In article <gn11lk$86h$1 at>,
 Niko < at> wrote:

> Ok, I stumbled across Upvalues today and I thought they were gorgeous
> for my case.
> My case is this: I need the intersection of two really large sets, it
> looks like this:
> Intersection[sym[l], sym[q]]
> Now, they are really two large to compute them. I can compute the
> intersection faster myself. So, I tossed along and defined something
> like this:
> Intersection[sym[a_], sym[b_]] ^:= 42
> Unfortunately, Mathematica has a strong preference for using the
> downvalue of sym for the computation, regardless of the order I use
> for input.
> If I undefine "sym", things work fine, but that is of course a whole
> lot less elegant. Is there a way to "push" the priority of the upvalue
> definition, so it gets used whenever possible?

Not sure whether the following fully addresses your problem, but you 
could add the attribute *HoldAll* to the function *Intersection[]*. For 

In[1]:= Intersection[sym[l], sym[q]]

Out[1]= sym[]

In[2]:= Intersection[sym[a_], sym[b_]] ^:= 42

In[3]:= Intersection[sym[l], sym[q]]

Out[3]= 42

In[4]:= sym[x_] := RandomInteger[{1, 10}, RandomInteger[{1, 5}]]

In[5]:= Intersection[sym[l], sym[q]]

Out[5]= {1, 2}

In[6]:= SetAttributes[Intersection, HoldAll]
Intersection[sym[l], sym[q]]

Out[7]= 42


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