The function 'exponentialize' should do what you want.
(%i1) display2d : false;
(%o1) FALSE
(%i2) exponentialize([cos(a),sin(b), cosh(a+b)]);
(%o2)
[(%E^(%I*a)+%E^-(%I*a))/2,-%I*(%E^(%I*b)-%E^-(%I*b))/2,(%E^(b+a)+%E^(-b-a))/2]
To return to trigonometric form, use 'demoivre'
(%i3) demoivre(%);
(%o3) [COS(a),SIN(b),(%E^(b+a)+%E^(-b-a))/2]
[The function 'demoivre' doesn't convert noncomplex exponentials
to hyperbolic form.]
(%i4) build_info();
Maxima version: 5.9.0.9beta1
Maxima build date: 13:27 6/29/2004
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL 2.7.0
Barton
Albert Reiner <areiner@tph.tuwien.ac.at>
Sent by: maxima-admin@math.utexas.edu
06/30/2004 04:39 AM
To: maxima@www.ma.utexas.edu
cc:
Subject: [Maxima] sin, cos into exponentials
Hi,
I am new to maxima, and despite spending quite some time with the
reference manual I do not see how to replace any occurrence of sine
and cosine by the corresponding exponentials; e.g., 3 sin(a) + cos(b)
should be turned into a sum of exp(%i*a), exp(-%i*a), exp(%i*b), and
exp(-%i*b).
TIA for any hints or pointers!
Albert.
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