conjugate(z) -> z -- should be nounform
(conjugate loaded from EIGEN)
Logged In: YES
The defn of conjugate is
conjugate(x) := sublis('([%i = - %i]), x)$
which is useful since it can be applied to lists and
matrices (among other objects) but it seems too simple-minded.
The defn above can yield a wrong answer if its argument is a
real function of a complex variable. E.g.,
conjugate('carg(a+b %i)) yields
'carg (a-b %i) -- oops.
Maybe the right answer is to kill off the existing defn and
replace it with conjugate(x) := realpart(x) -
realpart and imagpart know about lists and matrices, maybe
other objects, so the convenience of the existing defn
doesn't seem compelling. Also realpart and imagpart know
about carg (as they should).
Logged In: NO
I am not sure why you mention lists and matrices -- all
Maxima functions are supposed to handle those cases (though
admittedly they don't all do it).
For all *analytic* functions and real variables, the current
definition is correct, and often gives far smaller
expressions than using rectform would. However, it is
incorrect for non-analytic functions (like carg) and
For that matter, rectform also assumes that functions it
doesn't know always have pure-real values. Try, for
example, realpart(f(%i)) or rp(%i!).
It is straightforward enough to write a proper $conjugate
function that takes that into account -- most of the work
would in fact go into establishing the list of analytic
functions!: though there is in principle a Maxima feature
'analytic', it is not used at all currently.
It is not clear what the right thing to do about unknown
functions is. In general, Maxima assumes that functions and
variables are real-valued -- even if the function arguments
are non-real. We probably don't want rectform(f(x)) for
unknown f and x to return 'realpart(f(x)) +
'imagpart(f(x))*%i.... But returning that only if x is
known non-real seems arbitrary, too.
Consider realpart(f(x)) => f(x) ... where f turns out to be
Logged In: YES
Defn of conjugate in eigen.mac is superseded by defn in
share/linearalgebra/conjugate.lisp, which doesn't have the
problems of the eigen.mac defn (nor the problems of the
realpart/imagpart proposed alternative). Closing this bug
report as fixed.