[Maxima-bugs] [ maxima-Bugs-816166 ] rectform/carg doesn't normalize exp(%i*n) (also asin, log)

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Bugs item #816166, was opened at 2003-10-01 18:24
Message generated for change (Comment added) made by dgildea
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Category: Lisp Core - Complex
Group: None
>Status: Closed
>Resolution: Works For Me
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: rectform/carg doesn't normalize exp(%i*n) (also asin, log)

Initial Comment:
  carg(exp(%i*x)) => x (OK?)
  carg(exp(%i*10.0)) => 10.0 (No?)

  carg(exp(%i*-%pi)) => %pi (OK)
  float(carg(exp(%i*-%pi))) => 3.14 (OK)
  carg(exp(%i*float(-%pi))) => -3.14 (?)

  float(carg(asin(-%i*10))) => -1.57 (OK)
  carg(asin(-%i*10)),numer => 4.71 (No!)

  float(rectform(log(-%i*10))) => 2.30 - 1.57*%I (OK)
  rectform(log(-%i*10)),numer => 2.30+4.71*%I (No!)

Presumably the principal values is what is wanted.  I will 
correct that.

This is related to the fact that carg(exp(%i*x)) doesn't 
normalize x to (-pi,pi] when x is not an explicit multiple 
of pi:

  carg(exp(%i*10)) => 10
  carg(exp(%i*x)) => x
but
  carg(exp(%i*(3*%pi-x))) => %pi-x

How far should this go?  I think it's pretty clear for the 
float/bfloat case, but how about carg(exp(%i*10))?  
Should that really return 10-4*%pi?  Currently, it goes 
the other way around!: exp(%i*(10-4*%pi)) actually 
simplifies to exp(%i*10)....


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>Comment By: Dan Gildea (dgildea)
Date: 2009-02-24 18:20

Message:
In current cvs:

(%i6) carg(exp(%i*x));
(%o6) x

(%i7) carg(exp(%i*10.0));
(%o7) -2.566370614359173

(%i8) carg(exp(%i*-%pi));
(%o8) %pi

(%i9) float(carg(exp(%i*-%pi)));
(%o9) 3.141592653589793

(%i10) carg(exp(%i*float(-%pi)));
(%o10) -3.141592653589793

(%i11) float(carg(asin(-%i*10)));
(%o11) -1.570796326794897

(%i12) float(carg(asin(-%i*10)));
(%o12) -1.570796326794897

(%i13) float(rectform(log(-%i*10)));
(%o13) 2.302585092994046-1.570796326794897*%i

(%i14) rectform(log(-%i*10)),numer;
(%o14) log(10)-%i*%pi/2

not sure why that last one didn't come out numerically:

(%i18) log(-%i*10),numer;
(%o18) 2.302585092994046-1.570796326794897*%i


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Comment By: Barton Willis (willisbl)
Date: 2005-07-18 06:42

Message:
Logged In: YES 
user_id=895922

How about 'nummod'?  See my recent Maxima
list posting and "Concrete Mathematics" by
Graham, Knuth, and Patashnik, Section 3.4

(%i1) load("C:/maxima/nummod/nummod.lisp")$
(%i2) f(x) := %pi - nummod(%pi-x,2*%pi)$
(%i3) f(-%pi);
(%o3) %pi
(%i4) f(0);
(%o4) 0
(%i5) f(%pi);
(%o5) %pi
(%i6) f(%pi + 1/10^9);
(%o6) 1/1000000000-%pi
(%i7) f(%pi - 1/10^9);
(%o7) %pi-1/1000000000
(%i8) 

Barton

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Comment By: Robert Dodier (robert_dodier)
Date: 2005-07-16 03:15

Message:
Logged In: YES 
user_id=501686

Well, how about carg (exp (%i*10)) => 'mod (10, 2*%pi)  ??

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