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SandBoxWirtinger

Edit detail for SandBoxWirtinger revision 3 of 21

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Editor: Bill Page Time: 2014/08/13 23:48:46 GMT+0
Note:

changed:
-conjugate:=operator('conjugate)
)lib FSPECX
abs2sqrt := rule abs(a+%i*b)==sqrt(a^2+b^2)


changed:
-  eval(D(eval(ex,z=x+%i*y),x)/2-%i*D(eval(ex,z=x+%i*y),y)/2,[x'=z/2+conjugate(z)/2,y'=z/2-conjugate(z)/2])
  eval(D(eval(ex,z=x+%i*y),x)/2-%i*D(eval(ex,z=x+%i*y),y)/2,[x=z/2+conjugate(z)/2,y=z/2-conjugate(z)/2])

added:

\begin{axiom}
diff(sin(x),x)
diff'(sin(x),x)
diff(sqrt(x^2),x)
diff'(sqrt(x^2),x)
z*conjugate(z)
z::Expression Complex Integer
diff(z*conjugate(z),z)
eval(z*conjugate(z),z=x+%i*y)
D(%,x)/2
eval(z*conjugate(z),z=x+%i*y)
D(%,y)/2
diff'(z*conjugate(z),z)
\end{axiom}

Ref.

http://en.wikipedia.org/wiki/Wirtinger_derivatives

fricas

)lib FSPECX

   FunctionalSpecialFunction is now explicitly exposed in frame initial

   FunctionalSpecialFunction will be automatically loaded when needed 
      from /var/aw/var/LatexWiki/FSPECX.NRLIB/FSPECX
abs2sqrt := rule abs(a+%i*b)==sqrt(a^2+b^2)

$\label{eq1}{abs \left({{i \ b}+ a}\right)}\mbox{\rm = =}{\sqrt{{{b}^{2}}+{{a}^{2}}}}$

(1)

Type: RewriteRule?(Integer,Complex(Integer),Expression(Complex(Integer)))

fricas

diff(ex,z) ==
  eval(D(eval(ex,z=x+%i*y),x)/2-%i*D(eval(ex,z=x+%i*y),y)/2,[x=z/2+conjugate(z)/2,y=z/2-conjugate(z)/2])

Type: Void

fricas

diff'(ex,z) ==
  eval(D(eval(ex,z=x+%i*y),x)/2+%i*D(eval(ex,z=x+%i*y),y)/2,[x=z/2+conjugate(z)/2,y=z/2-conjugate(z)/2])

Type: Void

fricas

diff(sin(x),x)

fricas

Compiling function diff with type (Expression(Integer),Variable(x))
       -> Expression(Complex(Integer))

$\label{eq2}\cos \left({x}\right)$

(2)

Type: Expression(Complex(Integer))

fricas

diff'(sin(x),x)

fricas

Compiling function diff' with type (Expression(Integer),Variable(x))
       -> Expression(Complex(Integer))

$\label{eq3}0$

(3)

Type: Expression(Complex(Integer))

fricas

diff(sqrt(x^2),x)

$\label{eq4}x \over{\sqrt{{x}^{2}}}$

(4)

Type: Expression(Complex(Integer))

fricas

diff'(sqrt(x^2),x)

$\label{eq5}0$

(5)

Type: Expression(Complex(Integer))

fricas

z*conjugate(z)

$\label{eq6}{z}^{2}$

(6)

Type: Expression(Integer)

fricas

z::Expression Complex Integer

$\label{eq7}z$

(7)

Type: Expression(Complex(Integer))

fricas

diff(z*conjugate(z),z)

fricas

Compiling function diff with type (Expression(Integer),Variable(z))
       -> Expression(Complex(Integer))

$\label{eq8}2 \ z$

(8)

Type: Expression(Complex(Integer))

fricas

eval(z*conjugate(z),z=x+%i*y)

$\label{eq9}-{{y}^{2}}+{2 \ i \ x \ y}+{{x}^{2}}$

(9)

Type: Expression(Complex(Integer))

fricas

D(%,x)/2

$\label{eq10}{i \ y}+ x$

(10)

Type: Expression(Complex(Integer))

fricas

eval(z*conjugate(z),z=x+%i*y)

$\label{eq11}-{{y}^{2}}+{2 \ i \ x \ y}+{{x}^{2}}$

(11)

Type: Expression(Complex(Integer))

fricas

D(%,y)/2

$\label{eq12}- y +{i \ x}$

(12)

Type: Expression(Complex(Integer))

fricas

diff'(z*conjugate(z),z)

fricas

Compiling function diff' with type (Expression(Integer),Variable(z))
       -> Expression(Complex(Integer))

$\label{eq13}0$

(13)

Type: Expression(Complex(Integer))