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MathGroup Archive 2006

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Re: preclude mathematical meaning of OverBar etc

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67402] Re: preclude mathematical meaning of OverBar etc
  • From: Peter Pein <petsie at dordos.net>
  • Date: Thu, 22 Jun 2006 06:21:17 -0400 (EDT)
  • References: <e7aos7$922$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Martin Schoenecker schrieb:
> Dear group,
> 
> I would like to use OverBar, SuperStar etc. to define characteristic or 
> modified values for the same, "plain" variable.  Unfortunately, as every 
> expression, they become a mathematical meaning which is not what I 
> intend, e.g. for a substitution:
> 
> test
> 
> In[19]:=
> subsfun = u -> Function[{x, t},
>      OverHat[l]*OverTilde[u][
>        OverTilde[x][x], OverTilde[t][
>         t]]]
> subsvar = OverTilde[t] ->
>     Function[t, t/OverHat[t]]
> resubsvar = t/OverHat[t] ->
>     OverTilde[t]
> 
> Out[19]=
> u -> Function[{x, t}, OverHat[l]*
>      OverTilde[u][OverTilde[x][x],
>       OverTilde[t][t]]]
> 
> Out[20]=
> OverTilde[t] -> Function[t,
>     t/OverHat[t]]
> 
> Out[21]=
> t/OverHat[t] -> OverTilde[t]
> 
> In[22]:=
> D[u[x, t], t]
> % /. subsfun
> % /. subsvar
> % /. resubsvar
> 
> Out[22]=
> Derivative[0, 1][u][x, t]
> 
> Out[23]=
> OverHat[l]*Derivative[1][
>      OverTilde[t]][t]*
>    Derivative[0, 1][OverTilde[u]][
>     OverTilde[x][x], OverTilde[t][t]]
> 
> Out[24]=
> OverHat[l]*(1/OverHat[t] -
>     (t*Derivative[1][OverHat][t])/
>      OverHat[t]^2)*
>    Derivative[0, 1][OverTilde[u]][
>     OverTilde[x][x], t/OverHat[t]]
> 
> Out[25]=
> OverHat[l]*(1/OverHat[t] -
>     (t*Derivative[1][OverHat][t])/
>      OverHat[t]^2)*
>    Derivative[0, 1][OverTilde[u]][
>     OverTilde[x][x], OverTilde[t]]
> 
> where I get the derivative of the OverHat term, which is not desired. 
> How to overcome this?  Is there another possibility than to use 
> Symbolize with Utilities`Notation`?  Thanks for any hints,
> 
> Martin
> 
Hi Martin,

either do a SetAttributes[#,Constant]&/@{OverHat,OverBar} before calling D[] or use Dt with option Constants:

Dt[u[x, t] /. subsfun /. subsvar, t, Constants ->
     {x, OverTilde, OverHat}] /. resubsvar

(OverHat[l]*Derivative[0, 1][OverTilde[u]][OverTilde[x][x], OverTilde[t]])/OverHat[t]


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