Re: Getting Symbolic Real and Imag Parts? (Once Again)
- To: mathgroup at smc.vnet.net
- Subject: [mg33508] Re: Getting Symbolic Real and Imag Parts? (Once Again)
- From: aes <siegman at stanford.edu>
- Date: Sun, 24 Mar 2002 01:44:03 -0500 (EST)
- Organization: Stanford University
- References: <a7cs6t$hv8$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Thanks to several people who emailed me to point out that the way to get symbolic real and imag parts of an expression is Real part = ComplexExpand[Re[expr]] Imag part = ComplexExpand[Im[expr]] and also my apologies for belatedly realizing that I had raised this question once before, months ago; gotten the same answer; and forgotten it. It's now stored in my online collection on Mathematica hints and kinks. Might as well also repeat the same comment that I made last time, however, namely that writing the expression in this form seems syntactically bizarre, not so say nonsensical. The expression ComplexExpand[Re[Sin[a + I b]]] would normally be interpreted as saying, in words, "Do a complex expansion of the real part of the sine of a + I B", presumably producing a complex result, including adding a "+ I 0" to make the result complex. What's really wanted, however, and what's actually accomplished by this expression, is instead, "Take the real part of the complex expansion of the sine of a + I b", a result you would expect to be written as Re[ComplexExpand[Sin[a+I b]]] It's sort of like having to write Log[Sin[z]] when what you want is Sin[Log[z]] > OK, so you can use ComplexExpand expand to find the symbolic real and imag > parts of an expression -- e.g. the input > > zComplex = ComplexExpand[ Sin[a+I b], TargetFunctions->{Re,Im}] > > gives as output > > Cosh[b] Sin[a] + I Cos[a] Sinh[b] > > as desired. But now, how do I get Mathematica to peel out the symbolically > real and > imaginary parts of this? -- that is, what inputs > > zR = ??? > > zI = ??? > > will give as outputs > > Cosh[b] Sin[a] > > and > > Cos[a] Sinh[b] > > (Maybe an example in the ComplexExpand Help file would be helpful?)