(%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)
Aleksas
2012-02-04
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
Anonymous
2012-02-13
Thank you kindly for the detailed answer.
I seem to recall reading that maxima uses complex numbers by default. As a general comment I find it odd that polarform(%i) would not give the same result as just %i.
However I've learned something. Much appreciated.
Robert Dodier
2012-12-10
Diff:
--- old +++ new @@ -1,4 +1,3 @@ - \(%i1\) \(%i\)^\(4/3\) \(%o1\) 1
Robert Dodier
2012-12-10
Observed behavior is to be expected given the current assumptions about simplification of complex numbers. Marking this report "closed" accordingly.