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Re: Letting functions not evaluate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79471] Re: [mg79416] Letting functions not evaluate
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 27 Jul 2007 05:57:59 -0400 (EDT)
  • References: <200707260933.FAA05595@smc.vnet.net>

On 26 Jul 2007, at 10:33, Josh Burkart wrote:

> Say I have a function f[x], and, for certain values of the argument  
> x, I don't want it to evaluate to anything. E.g., say
>
> f[x_]:=Mod[10,x],
>
> and if x is not an integer, then I want f[x] to yield simply f[x].  
> One way to achieve this is through pattern matching, i.e.,
>
> f[x_Integer]:=Mod[10,x]
>
> Although this works perfectly in this example, it is somewhat  
> limited. For instance, if I have a function taking two arguments  
> and I want to perform some check on both arguments together to see  
> whether the function should evaluate or not, pattern matching won't  
> work. E.g.,
>
> g[x_,y_]:=Mod[10,x*y]
>
> only if x*y is an integer (even if x and y individually aren't  
> integers). I think there's some way to do this more generally than  
> pattern matching, since for instance if I enter
>
> In[11]:= Integrate[Gamma[x]^5,x]//FullForm
> Out[11]//FullForm= Integrate[Power[Gamma[x],5],x]
>
> Mathematica just returns the input unevaluated after taking a  
> little time to decide it's not resolvable. Anyone know how to do  
> this? Using an If[] statement doesn't work, since
>
> In[1]:= f[x_]:=If[IntegerQ[x], Mod[10, x], f[x]]
> In[4]:= f[3]
> Out[4]= 1
> In[3]:= f[3.3]
> During evaluation of In[3]:= $IterationLimit::itlim: Iteration  
> limit of 4096 exceeded. >>
> Out[3]= Hold[f[3.3]]
>
> results in infinite recursion. HoldForm[] and Defer[] also produce  
> somewhat dissatisfactory results, since the FullForm[] of what they  
> return is actually HoldForm/Defer[blah blah].
>

For example:

f[x_, y_] /; Element[x*y, Integers] := Mod[x*y, 10]

f[1/2, 24]
  2

f[1/2, 3]
f[1/2, 3]

etc...

Andrzej Kozlowski


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