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MathGroup Archive 1992

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Re: Plotting x^(1/3), etc.

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Plotting x^(1/3), etc.
  • From: fateman at peoplesparc.berkeley.edu (Richard Fateman)
  • Date: Mon, 20 Apr 92 10:50:25 PDT

Kelly's definition is circular.  It defines Power in terms of Power.

	From mathgroup-adm at yoda.physics.unc.edu Fri Apr 17 23:38:02 1992
	From: roach at wri.com
	Subject: Re: Plotting x^(1/3), etc.
	To: mathgroup at yoda.physics.unc.edu
	Status: RO

	     The definition of Power that Mathematica uses is

	     x^y == E^(y*Log[x])

	where Log is the principle branch of the logarithm.
.....
So, what is E^(1/2)? 
since E = 2.71828 ...  is E^(1/2)  + or -  1.64872.. ?

If the definition is Exp[ ...]  where Exp[x] is understood
to be defined uniquely by the power series 1+x+..., then that helps 
a little. 

I think Kelly's hope that a simple characterization of "^" in Mathematica
can be used by all is not consistent with Mathematica's
simplification of x^0 and 0^0.  If x^0 is 1, then how could a
PARTICULAR value of x, namely x=0, change it to Indeterminate?

 Richard














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