Hi all
I'm trying to exponentiate the small antisymmetric matrix (infinitesimal
rotation of angle x). Following the ideas of the thread «How does one
define a "real" variable», I try the following :
sage : var('x')
sage: assume(x,'real')
sage : X=matrix([ [0,1],[-1,0] ])
sage: R=exp(x*X)
sage: R
[ 1/2*(e^(2*I*x) + 1)*e^(-I*x) -1/2*(I*e^(2*I*x) - I)*e^(-I*x)]
[ 1/2*(I*e^(2*I*x) - I)*e^(-I*x) 1/2*(e^(2*I*x) + 1)*e^(-I*x)]
sage: R[0][0].simplify()
1/2*(e^(2*I*x) + 1)*e^(-I*x)
By the way, the following works :
sage : a=R[0][0]
sage: (a.real_part()+a.imag_part()).simplify_full()
cos(x)
How can automatize it ? Is it a way to perform this simplification to
each element of the matrix at once ?
Have a good afternoon
Laurent
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