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Re: Problem with evaluation of delayed rules

  • To: mathgroup at
  • Subject: [mg21678] Re: Problem with evaluation of delayed rules
  • From: Eckhard Hennig <hennig at>
  • Date: Fri, 21 Jan 2000 04:00:38 -0500 (EST)
  • Organization: ITWM
  • References: <85mkef$>
  • Sender: owner-wri-mathgroup at

Thanks to everyone who responded to my message regarding evaluation of
delayed rules in held expressions. Unfortunately, none of the proposed
solutions fully meets my requirements, either because Condition 1 (no
specific solution for "If") was not taken into account or because it doesn't
work for my particular application. What I posted was just a simple example,
and the actual problem is indeed a bit more complicated:

Let "equations" denote a list of mathematical expressions involving "If"
statements (or other control statements with HoldXXX attribute). In
"equations", I want to apply the following substitutions. All delayed rules
must be evaluated as soon as they apply because the variable "mnavar" (a
list of symbols) is local to a Block.

equations /.
  { Derivative[_][_][x_ /; x =!= $TimeVariable] -> 0,
    Derivative[k_][Voltage[a_, b_, _]][$TimeVariable]
    | Derivative[k_][Voltage[a_, b_, _]] :>
      D[mnavar[[a]] - mnavar[[b]], {$TimeVariable, k}],
    Voltage[a_, b_, _] :> mnavar[[a]] - mnavar[[b]],
    Derivative[k_][Current[__, i_]][$TimeVariable]
    | Derivative[k_][Current[__, i_]] :>
      D[BranchCurrentIdentifier[i], {$TimeVariable, k}],
    Current[__, i_] :> BranchCurrentIdentifier[i] }

Several responses to my original message suggested using a "Cases" statement
to build up a list of evaluated replacement rules dynamically and then apply
this list to the expression. This solution has two disadvantages: it needs
more memory and it does not work for more than one delayed rule at a time,
thus requiring repeated application of the "Cases" approach for each of the
above rules. In my application, these drawbacks are not acceptable because
the "equations" may be very large, so that memory efficiency and performance
is an important issue.

Any other solutions that don't involve specific solutions for the "If"
statement or degrade performance?

Best regards,


Dipl.-Ing. Eckhard Hennig      mailto:hennig at
Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
Erwin-Schroedinger-Strasse,  67663 Kaiserslautern,  Germany
  Voice: +49-(0)631-205-3126    Fax: +49-(0)631-205-4139

     ITWM - Makers of Analog Insydes for Mathematica

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