Hi, this is hopefully an easy question:
As a simple exercise, I'm trying to show that \int_0^{2\pi} e^{i (m-n)
x}dx = 2\pi\delta_{mn} for integer m, n.
Here's how I did it:
sage: var('m,n'); w = SR.wild(0);
sage: assume(n, 'integer');assume(m, 'integer')
sage: int = integrate(e^(i*(m-n)*x),x,0,2*pi)
sage: print int.limit(m=n)
sage: print int.subs({e^(w):cosh(w)+sinh(w)}).simplify_trig()
2*pi
0
The bit I don't like is using the substitution... it should not be
nesc. The problem, I think, lies at
sage: sin(2*pi*n).simplify_trig() # this works
sage: e^(i*2*pi*m).simplify_full() # this doesn't work
0
e^(2*I*pi*m)
Any suggestions?
--
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support+unsubscr...@googlegroups.com
For more options, visit this group at
http://groups.google.com/group/sage-support
URL: http://www.sagemath.org
