I am wanting to hand off a holomorphic function to an external library, but
the library only works with real numbers (operations with C++ doubles).
Thus I wish to have Sage compute functions u and v for which f(x+i y) =
u(x,y) + i v(x,y) such that u and v are expressed only in terms of
operations on real numbers, i.e., without the imaginary unit i. I am
impressed by how far I can get by simply calling f(x+i y).real_part(), but
abs(x+I*y) is not rewritten as sqrt(x+I*y). A simple example session to
illustrate:
sage: y, z = var('y, z')
sage: assume(x, 'real')
sage: assume(y, 'real')
sage: abs(x+I*y)
abs(x + I*y)
sage: abs(x+I*y).real_part()
abs(x + I*y)
sage: norm(x+I*y)
x^2 + y^2
sage: log(x+I*y).real_part()
log(abs(x + I*y))
sage: sin(x+I*y).real_part()
cosh(y)*sin(x)
Is there a simple way to do what I am trying to do? Perhaps by asking Sage
to replace abs(z) with sqrt(norm(z))?
Best,
Robert
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