Bug introduced after 12.0.1, in or before 12.3, persisting through 13.0. Fixed in 13.2.0 or earlier.
Consider the following sample:
{Re, Im}[u'[t]] // Through // ComplexExpand
In v9.0.1 u'[t] is assumed as real:
But at least since v12.3.1 the behavior changes:
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. )
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},
Activate[
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} *)
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.
$\endgroup$
u'[t] anyway, so that at some point I dropped the Re and Im.)
$\endgroup$
ComplexExpandsince V6.0, so you should report it. $\endgroup$Activate@ComplexExpand[{Re, Im}[Inactivate[u'[t]]] // Through]$\endgroup$Simplify[{Re, Im}[u'[t]] // Through, u'[t] \[Element] Reals]. Or, to have the assumptions persist and just useSimplify:$Assumptions = $Assumptions && u'[t] \[Element] Reals; {Re, Im}[u'[t]] // Through // Simplify$\endgroup$