symdiff(3tcl)						 Symbolic differentiation for Tcl					     symdiff(3tcl)

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NAME

       symdiff - Symbolic differentiation for Tcl

SYNOPSIS

       package require Tcl  8.5

       package require grammar::aycock	1.0

       package require math::calculus::symdiff	1.0

       math::calculus::symdiff::symdiff expression variable

       math::calculus::jacobian variableDict

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DESCRIPTION

       The  math::calculus::symdiff  package provides a symbolic differentiation facility for Tcl math expressions. It is useful for providing de-
       rivatives to packages that either require the Jacobian of a set of functions or else are more efficient or stable when the Jacobian is pro-
       vided.

PROCEDURES

       The math::calculus::symdiff package exports the two procedures:

       math::calculus::symdiff::symdiff expression variable
	      Differentiates the given expression with respect to the specified variable. (See Expressions below for a discussion of the subset of
	      Tcl math expressions that are acceptable to math::calculus::symdiff.)  The result is a Tcl expression that evaluates the derivative.
	      Returns an error if expression is not a well-formed expression or is not differentiable.

       math::calculus::jacobian variableDict
	      Computes	the  Jacobian  of  a system of equations.  The system is given by the dictionary variableDict, whose keys are the names of
	      variables in the system, and whose values are Tcl expressions giving the values of those variables. (See	Expressions  below  for  a
	      discussion  of the subset of Tcl math expressions that are acceptable to math::calculus::symdiff. The result is a list of lists: the
	      i'th element of the j'th sublist is the partial derivative of the i'th variable with respect to the j'th variable. Returns an  error
	      if any of the expressions cannot be differentiated, or if variableDict is not a well-formed dictionary.

EXPRESSIONS

       The  math::calculus::symdiff package accepts only a small subset of the expressions that are acceptable to Tcl commands such as expr or if.
       Specifically, the only constructs accepted are:

       o      Floating-point constants such as 5 or 3.14159e+00.

       o      References to Tcl variable using $-substitution. The variable names must consist of alphanumerics and underscores: the ${...}  nota-
	      tion is not accepted.

       o      Parentheses.

       o      The +, -, *, /. and ** operators.

       o      Calls to the functions acos, asin, atan, atan2, cos, cosh, exp, hypot, log, log10, pow, sin, sinh. sqrt, tan, and tanh.

       Command substitution, backslash substitution, and argument expansion are not accepted.

EXAMPLES

	      math::calculus::symdiff::symdiff {($a*$x+$b)*($c*$x+$d)} x
	      ==> (($c * (($a * $x) + $b)) + ($a * (($c * $x) + $d)))
	      math::calculus::symdiff::jacobian {x {$a * $x + $b * $y}
				       y {$c * $x + $d * $y}}
	      ==> {{$a} {$b}} {{$c} {$d}}

BUGS, IDEAS, FEEDBACK
       This  document, and the package it describes, will undoubtedly contain bugs and other problems.	Please report such in the category math ::
       calculus of the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883].  Please also report any ideas for enhancements you may
       have for either package and/or documentation.

SEE ALSO

       math::calculus, math::interpolate

COPYRIGHT

       Copyright (c) 2010 by Kevin B. Kenny <kennykb@acm.org>
       Redistribution permitted under the terms of the Open Publication License <http://www.opencontent.org/openpub/>

math									1.0							     symdiff(3tcl)