symdiff(n)             Symbolic differentiation for Tcl             symdiff(n)



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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
       derivatives to packages that either require the Jacobian of a set of
       functions or else are more efficient or stable when the Jacobian is
       provided.

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 ${...}
              notation 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(n)
