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Re: pattern matching against the Dt function?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85289] Re: [mg85238] pattern matching against the Dt function?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 5 Feb 2008 06:08:20 -0500 (EST)
  • References: <200802040806.DAA27693@smc.vnet.net>

On 4 Feb 2008, at 09:06, Adam M. wrote:

> Hello,
>
> I'm having trouble matching the Dt function with a pattern, even  
> though
> it works for all other functions I've tried.
>
> (*It doesn't match Dt[b] here.*)
> In[101]:= {f[a], Dt[b]} /. Dt[n_]->n
> Out[101]= {f[a], Dt[b]}
>
> (*But it matches f[a] with no problem.*)
> In[100]:= {f[a], Dt[b]} /. f[n_]->n
> Out[100]= {a, Dt[b]}
>
> (*In a process of elimination, I tried another built-in function, D,  
> and
> it worked fine.*)
> In[99]:= {f[a], D[b]} /. D[n_]->n
> Out[99]= {f[a], b}
>
> (*I tried another function more than one character long, Sin, and that
> works.*)
> In[102]:= {f[a], Sin[b]} /. Sin[n_]->n
> Out[102]= {f[a], b}
>
> (*The full forms all seem to follow the same pattern.*)
> In[103]:= Sin[b] // FullForm
> Out[103]//FullForm= Sin[b]
>
> In[104]:= Dt[b] // FullForm
> Out[104]//FullForm= Dt[b]
>
> In[105]:= f[b] // FullForm
> Out[105]//FullForm= f[b]
>
> (*I thought it might be related to the evaluation of the Dt  
> function, so
> I tried Holding it. No luck.*)
> In[111]:= {f[a], Hold[Dt[b]]} /. Dt[n_]->n
> Out[111]= {f[a], Hold[Dt[b]]}
>
> (*However, it has no problem matching f[a] in a Hold.*)
> In[112]:= {Hold[f[a]], Dt[b]} /. f[n_]->n
> Out[112]= {Hold[a], Dt[b]}
>
> (*I tried looking at the attributes to find out if there was something
> special about the Dt function, but it doesn't seem like it...*)
> In[116]:= Attributes[Sin]
> Out[116]= {Listable, NumericFunction, Protected}
>
> In[117]:= Attributes[D]
> Out[117]= {Protected, ReadProtected}
>
> In[118]:= Attributes[Dt]
> Out[118]= {Protected}
>
> I've read every section on pattern matching in the documentation  
> center,
> and I'm at a complete loss to explain why I can't seem to match the Dt
> function with the Dt[n_] pattern when I can match these other  
> functions.
> I know I can use the _Dt pattern to match it, but then I don't get
> control over matching the arguments...
>
> Thank you.
>
> Very curious,
> -- Adam M.
>

Note that:

In[1]:= Dt[n_]
Out[1]= Dt[n]*Derivative[1, 0][Pattern][n, _]


This means that you have to use HoldPattern:


In[2]:= {f[a], Dt[b]} /. HoldPattern[Dt[n_]] -> n
Out[2]= {f(a), b}


and so on...


Andrzej Kozlowski


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