On 20 November 2014 01:54, Ondřej Čertík <ondrej.cer...@gmail.com> wrote:
>
> What you posted looks good. But we need to test it for arg(z), re(z),
> im(z) and any other non-analytic function that we can find.
>
(1) -> re(x)==(conjugate(x)+x)/2
Type:
Void
(2) -> im(x)==%i*(conjugate(x)-x)/2
Type:
Void
(3) -> arg(x)==log(x/abs(x))/%i
Type:
Void
(4) -> re %i
Compiling function re with type Complex(Integer) -> Fraction(Complex
(Integer))
(4) 0
Type:
Fraction(Complex(Integer))
(5) -> im %i
Compiling function im with type Complex(Integer) -> Fraction(Complex
(Integer))
(5) 1
Type:
Fraction(Complex(Integer))
(6) -> arg %i
Compiling function arg with type Complex(Integer) -> Expression(
Complex(Integer))
(6) - %i log(%i)
Type:
Expression(Complex(Integer))
(7) -> complexNumeric %
(7) 1.5707963267_948966192
Type:
Complex(Float)
(8) -> D(re(x),x)
Compiling function re with type Variable(x) -> Expression(Integer)
(8) 1
Type:
Expression(Integer)
(9) -> D(im(x),x)
Compiling function im with type Variable(x) -> Expression(Complex(
Integer))
(9) 0
Type:
Expression(Complex(Integer))
(10) -> D(arg(x),x)
Compiling function arg with type Variable(x) -> Expression(Complex(
Integer))
_ 2 2
%i xx - 2%i abs(x) + %i x
(10) ---------------------------
2
2x abs(x)
Type:
Expression(Complex(Integer))
I had a thought. I suppose that all non-analytic (nonholomorphic) functions
of interest can be written in terms of conjugate and some analytic
functions, e.g.
abs(x)=sqrt(x*conjugate(x))
so perhaps all we really need is to know how to differentiate conjugate
properly?
Bill
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