So here (20) is a simpler expression for derivative of arg:
(16) -> abs(x)==sqrt(x*conjugate(x))
Compiled code for abs has been cleared.
Compiled code for arg has been cleared.
1 old definition(s) deleted for function or rule abs
Type:
Void
(17) -> arg(x)==log(x/abs(x))/%i
1 old definition(s) deleted for function or rule arg
Type:
Void
(18) -> arg %i
Compiling function abs with type Complex(Integer) -> Expression(
Complex(Integer))
Compiling function arg with type Complex(Integer) -> Expression(
Complex(Integer))
(18) - %i log(%i)
Type:
Expression(Complex(Integer))
(19) -> complexNumeric %
(19) 1.5707963267_948966192
Type:
Complex(Float)
(20) -> D(arg(x),x)
Compiling function abs with type Variable(x) -> Expression(Integer)
Compiling function arg with type Variable(x) -> Expression(Complex(
Integer))
_
- %ix + %i x
(20) ------------
_
2xx
Type:
Expression(Complex(Integer))
In general I am a little uncertain if, how and when to deal with
simplifications of expressions like abs that can be expressed in terms of
more fundamental/elementary functions. What do you think?
Bill.
On 20 November 2014 09:41, Bill Page <bill.p...@newsynthesis.org> wrote:
> ...
>
> 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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