Re: Re: Re: More /.{I->-1} craziness

*To*: mathgroup at smc.vnet.net*Subject*: [mg106273] Re: [mg106247] Re: [mg106203] Re: More /.{I->-1} craziness*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 7 Jan 2010 02:29:00 -0500 (EST)*References*: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

Some good points, David. When help says "You can enter a complex number in the form x + I y", it is seriously misleading, without the qualification you added below. x + I y is NOT a number (of any kind) when a and b are undefined, and neither is Complex[x, y]: NumericQ@Complex[x, y] False If they ARE defined, the result isn't necessarily complex (or even sensible): Complex[0, I] N@% Complex[0, I] Complex[0., 0. + 1. I] What the heck is that? Complex[0.`, 0.` + 1.` I] // Simplify Complex[0., 0. + 1. I] Bobby On Wed, 06 Jan 2010 04:59:15 -0600, David Park <djmpark at comcast.net> wrote: > I don't think that it is correct to expect that a mathematical object > has a > Head. Mathematica only gives us various representations of objects and > different representations have different Heads. Thus > > 3 + 4 I, ComplexPolar[5, ArcTan[4/3]] (in Presentations), 5 E^(I > ArcTan[4/3]), Complex[3,4] > > all represent the same mathematical object but all have different Heads. > (Plus, ComplexPolar, Times, Complex). > > What might be confusing is that Complex is a NUMBER and not a symbolic > expression. WRI could improve the Help for Complex by changing the first > note to: > > "You can enter a complex number in the form x + I y, where x and y are > Integer, Real, Rational or Complex numbers." > > "Expressions such as Complex[a,b] with Symbols are not meaningful and are > left unevaluated. Symbolic complex expressions contain Complex numbers > only > as subparts." > > And then, among the first examples, they might show: > > "Complex expressions may contain Complex numbers as subparts and can be > manipulated with routines such as Conjugate and ComplexExpand." > > x + I y > % // FullForm > ComplexExpand[Conjugate[%]] > % // FullForm > > x + I y > Plus[x,Times[Complex[0,1],y]] > x - I y > Plus[x,Times[Complex[0,-1],y]] > > Very few users would use Complex numbers in isolation without combining > them > in symbolic expressions. So why not stand users up and point them in the > right direction instead of just saying that the Help is 'formally > correct'? > > For those who use Help, of course. > > > David Park > djmpark at comcast.net > http://home.comcast.net/~djmpark/ > > > From: Richard Fateman [mailto:fateman at cs.berkeley.edu] > > [SNIP] > > Are you describing Mathematica here? It seems to me that it is an > exception that Head[a+b*I] is Plus, but Head[3+4I] is Complex. > > [SNIP] > > You assume that people read the documentation. This is provably false. > > RJF > > > -- DrMajorBob at yahoo.com