Letting functions not evaluate
- To: mathgroup at smc.vnet.net
- Subject: [mg79416] Letting functions not evaluate
- From: Josh Burkart <jburkart at ucdavis.edu>
- Date: Thu, 26 Jul 2007 05:33:19 -0400 (EDT)
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].
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