[GiNaC-devel] Implicit derivation of functions (re-submission)

[Vladimir V. Kisil]

	Dear All,

	I am resending the patch for implicit derivation of
  functions. Quote from the previous submission:
http://www.ginac.de/pipermail/ginac-devel/2013-November/002053.html

"   I wish to propose another GiNaC extension. Consider function
  abs(). Since it can be presented as abs(z)=sqrt(z*z.conjugate()), the
  derivative of abs(f) may be calculated as

  (abs(f))'=(f'*f.conjugate()+f*f'.conjugate())/2/abs(f)

  However, this formula cannot be packed into the present GiNaC code,
  since it only knows about the chain rule. Thus, the patch adds a
  possibility to define derivatives of functions in some general
  expression. In particular, the above derivative of abs() is
  defined. Example:

  cout << abs(log(z)).diff(z) << endl;
  // (before) -> D[0](abs)(log(z))*z^(-1)
  // (now) -> 1/2*(z^(-1)*conjugate(log(z))+log(z)*conjugate(z)^(-1))*abs(log(z))^(-1)
"
 This issue independently appeared in this discussion:
http://www.ginac.de/pipermail/ginac-devel/2014-April/002106.html

  If it is not included in the core code, then a user need to redefine
  the entire GiNaC function class to have this feature.

  Best wishes,
  Vladimir
-- 
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/
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