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(1) Symbolic complex algebra in mathematica and (2) Dsolve
*To*: mathgroup at yoda.ncsa.uiuc.edu
*Subject*: (1) Symbolic complex algebra in mathematica and (2) Dsolve
*From*: ken yip <yip-ken at CS.YALE.EDU>
*Date*: Thu, 22 Nov 90 18:00:16 EST
(1) I hope I am not correct about this. I want to define a complex quantity
z = x + I y
so that
Re[z] ==> x
Im[z] ==> y
Conjugate[z] ==> x - I y
etc. Mathematica doesn't seem to know how to do this even after I define
x and y to be real by
x/: RealQ[x] = True
(Of course, this does not change the head of x which is still Symbol.)
Next I tried to define some transformation rules, but then I couldn't
find a way to specify the pattern variable to be of type real AND symbol.
(2) I want to solve a simple harmonic equation with boundary conditions:
DSolve[{x'[t] == y[t], y'[t] == k^2 x[t], y'[-h] == 0},{x[t],y[t]}, t]
But mathematica seems to ignore the boundary constraint.
Any wisdom?
P.S. Originally I plan to use Mathematica to help me solve some
linear non-homogenous PDEs, but after a few hours playing witb it,
I am becoming increasingly frustrated with many of the simple things
it can't do. Is that due to my insufficient knowledge of mathematica
or is that due to mathematica itself?
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