[Maxima-bugs] [ maxima-Bugs-3483425 ] Imaginary unit to the power of 4/3

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Bugs item #3483425, was opened at 2012-02-02 18:48
Message generated for change (Comment added) made by aleksasd
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: https://www.google.com/accounts ()
Assigned to: Nobody/Anonymous (nobody)
Summary: Imaginary unit to the power of 4/3

Initial Comment:

(%i1)  (%i)^(4/3)
(%o1) 1

WxMaixima
System info
wxWidgets: 2.8.12
Unicode Support: no
Maxima version: 5.26.0 
Lisp: GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)

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Comment By: Aleksas (aleksasd)
Date: 2012-02-04 05:28

Message:
 After replace %i to polarform(%i)  or domain:complex; we get correct
result:

(%i1) polarform(%i)^(4/3);
(%o1) (sqrt(3)*%i)/2-1/2
(%i2) rectform(%);
(%o2) (sqrt(3)*%i)/2-1/2

 or
(%i3) domain:complex;
(%o3) complex
(%i4) (%i)^(4/3);
(%o4) (-1)^(2/3)
(%i5) rectform(%);
(%o5) (sqrt(3)*%i)/2-1/2

 Other example: integrate(exp(x^5),x,0,1)
 Wrong:
(%i6) domain:complex;
(%o6) complex
(%i7) integrate(exp(x^5),x,0,1);
(%o7) (%e^((2*%i*%pi)/5)*(gamma_incomplete(1/5,-1)-gamma(1/5)))/5
(%i8) float(rectform(%)),expand;
(%o8) 0.37851290892278-1.164942948399964*%i

 Correct:
(%i9) assume(k>1)$ declare(k,odd)$
(%i11) sol:integrate(exp(x^k),x,0,1);
"Is "(k-1)/k" an "integer"?"n;
(%o11) (gamma(1/k)/(-1)^(1/k)-gamma_incomplete(1/k,-1)/(-1)^(1/k))/k
(%i12) subst(k=5,sol);
(%o12) (gamma(1/5)/(-1)^(1/5)-gamma_incomplete(1/5,-1)/(-1)^(1/5))/5
(%i13) float(rectform(%)),expand;
(%o13) 1.1102230246251565*10^-16*%i+1.224893503635311
(%i14) realpart(%);
(%o14) 1.224893503635311
(%i15) quad_qags(exp(x^5), x, 0, 1);
(%o15) [1.224893503635311,5.5812865751276883*10^-11,21,0]

Aleksas D

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