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Re: Letting functions not evaluate

• To: mathgroup at smc.vnet.net
• Subject: [mg79491] Re: [mg79416] Letting functions not evaluate
• From: Carl Woll <carlw at wolfram.com>
• Date: Fri, 27 Jul 2007 06:08:22 -0400 (EDT)
• References: <200707260933.FAA05595@smc.vnet.net>

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].
>  
>

Use Condition (/;). For example:

g[x_, y_] := Mod[10, x y] /; IntegerQ[x y]

In[63]:= g[2, 3]
Out[63]= 4

In[64]:= g[2, 3.3] // FullForm
Out[64]//FullForm= g[2,3.3`]

Carl Woll
Wolfram Research

• References:
  • Letting functions not evaluate
    • From: Josh Burkart <jburkart@ucdavis.edu>