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Re: Redefine Arg to return a value from 0 to 2 pi

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80421] Re: Redefine Arg to return a value from 0 to 2 pi
  • From: markholtuk at googlemail.com
  • Date: Wed, 22 Aug 2007 04:41:13 -0400 (EDT)
  • References: <faeash$f5i$1@smc.vnet.net>

I've always got the impression from this list that it's not
necessarily a good idea to mess around with built-in commands. The
thing to do is to define your own command e.g. myArg as follows:

myArg[z_] := Module[{z0 = z}, If[Im[z0] < 0,
         ArcTan[Re[z0], Im[z0]] + 2*Pi, ArcTan[Re[z0],
         Im[z0]]]];

This will then do what you want:

Plot[myArg[2*Exp[I*t]], {t, 0, 4*Pi}]

I'm sorry I can't explain why your approach doesn't work, but I'm sure
one of our resident guru's can/will.

Best wishes,

Mark

On Aug 21, 10:22 am, chuck009 <dmili... at comcast.com> wrote:
> I'm trying to redefine Arg to return a value from 0 to 2 pi.  However when I do so and then try and plot Arg[z], Mathematica seems to still use the old definition.  Can anybody help me?  This is my code:
>
> (* redefine Arg to return a value from 0 to 2 pi *)
>
> Unprotect[Arg]
> Arg[z_] := Module[{z0 = z}, If[Im[z0] < 0,
>          ArcTan[Re[z0], Im[z0]] + 2*Pi, ArcTan[Re[z0],
>            Im[z0]]]];
> Protect[Arg]
>
> (* check new definition -- this is correct *)
>
> ListPlot[Table[{t, Arg[2*Exp[I*t]]}, {t, 0, 4*Pi, 0.1}]]
>
> (* try and plot new definition of Arg -- Plot used the old definition (-pi to pi) *)
>
> Plot[Arg[2*Exp[I*t]], {t, 0, 4*Pi}]
>
> (* resore old definition of Arg *)
>
> Unprotect[Arg]
> Arg[z_] =.
> Protect[Arg]

Mark R. Holt, BA, PhD,
Room 3.28
Molecular Cardiology,
Cardiovascular Division and
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King's College London,
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LONDON, SE1 1UL.

Phone: +44 20 7848 6438
Fax:     +44 20 7848 6435




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