Bug introduced after 11.3, in or before 12.3, persisting through 13.0.

Consider the following sample:

{Re, Im}[u'[t]] // Through // ComplexExpand

In v9.0.1 u'[t] is assumed as real:

enter image description here

But at least since v12.3.1 the behavior changes:

enter image description here

Is this a bug or incompatible change?

Is there a simple way to bring back the old behavior? (This answer of mine is broken at the moment due to the change. )

  • $\begingroup$ The docs indicate no update to ComplexExpand since V6.0, so you should report it. $\endgroup$
    – Michael E2
    Jun 24 at 17:31
  • $\begingroup$ I get the first (desired) result on 11.3.0 for Mac OS X. $\endgroup$
    – march
    Jun 24 at 17:33
  • $\begingroup$ Possible workaround: Activate@ComplexExpand[{Re, Im}[Inactivate[u'[t]]] // Through] $\endgroup$
    – Michael E2
    Jun 24 at 17:35
  • $\begingroup$ A workaround: Simplify[{Re, Im}[u'[t]] // Through, u'[t] \[Element] Reals]. Or, to have the assumptions persist and just use Simplify: $Assumptions = $Assumptions && u'[t] \[Element] Reals; {Re, Im}[u'[t]] // Through // Simplify $\endgroup$
    – thorimur
    Jun 24 at 20:35
  • 2
    $\begingroup$ Filing a bug report for this. $\endgroup$ Jun 24 at 20:48

2 Answers 2


Comments have identified this as a bug; in the meantime, a simple way to bring back the old behavior for ComplexExpand in a given session can be obtained by adding the following definition to ComplexExpand. This builds on Michael E2's (in)activation workaround; I noticed that it really is just the Derivative symbol itself that gives us grief, so we can restrict our inactivation to Derivative per se.

Unprotect[complexExpandIntercept, ComplexExpand];
complexExpandIntercept = True;
ComplexExpand[args___] := 
 Block[{complexExpandIntercept = False}, 
    ComplexExpand @@ Inactivate[{args}, Derivative], 
    Derivative]] /; complexExpandIntercept
Protect[complexExpandIntercept, ComplexExpand];
{Re, Im}[u'[t]] // Through // ComplexExpand

(* Out: {Derivative[1][u][t], 0} *)

Note: for a brief moment this answer was incorrect due to flipped booleans; now it should be fixed. :)


Here another workaround that may be safe (as it would likely affect only expressions containing u'):

ComplexExpand[Null]; (* autoload ComplexExpandDump *)
Block[{System`ComplexExpandDump`ConjugateFunctions = 
   Append[System`ComplexExpandDump`ConjugateFunctions, u']},
 ComplexExpand[{Re, Im}[u'[t]] // Through]]
(*  {u'[t], 0}  *)
  • $\begingroup$ I think you mean ComplexExpand[u'[t] // Re] :) ? Then, it seems that we need to use ComplexExpand at least once before using the solution, otherwise System`ComplexExpandDump`ConjugateFunctions won't be loaded. $\endgroup$
    – xzczd
    Jun 25 at 2:01
  • $\begingroup$ @xzczd Thanks! (It turns out internally it complex-expands the real and imaginary parts of u'[t] anyway, so that at some point I dropped the Re and Im.) $\endgroup$
    – Michael E2
    Jun 25 at 3:09

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