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Re: pattern matching against the Dt function?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85260] Re: pattern matching against the Dt function?
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Tue, 5 Feb 2008 05:53:24 -0500 (EST)
  • References: <fo6h46$r20$1@smc.vnet.net>

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...
> 

Hi Adam,

The Trace[], On[] and Off[] functions can be helpful when debugging 
these things.

The reason why it doesn't match is that Dt[n_] gets evaluated:

In[1]:= Dt[f[x]]
Out[1]= Dt[n] (Pattern^(1,0))[n,_]

In[2]:= n_ // FullForm
Out[2]= Pattern[n,Blank[]]

In[3]:= Dt[n_]
Out[3]= Dt[n] (Pattern^(1,0))[n,_]

In[4]:= Dt[f[]]
Out[4]= 0

In[5]:= Dt[_] (* The FullForm of _ is Blank[] *)
Out[5]= 0

A workaround is using HoldPattern:

{f[a], Dt[b]} /. HoldPattern[Dt[n_]] -> n

I hope this helps,
Szabolcs


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