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