## table of contents

math::calculus::symdiff(3tcl) | Symbolic differentiation for Tcl | math::calculus::symdiff(3tcl) |

# NAME¶

math::calculus::symdiff - Symbolic differentiation for Tcl

# SYNOPSIS¶

package require **Tcl 8.5**

package require **grammar::aycock 1.0**

package require **math::calculus::symdiff 1.0.1**

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

**math::calculus::jacobian** *variableDict*

# 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:

- Floating-point constants such as
**5**or**3.14159e+00**. - References to Tcl variable using $-substitution. The variable names must
consist of alphanumerics and underscores: the
**${...}**notation is not accepted. - Parentheses.
- The
**+**,**-**,*****,**/**. and******operators. - 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 Trackers*
[http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for
enhancements you may have for either package and/or documentation.

When proposing code changes, please provide *unified diffs*,
i.e the output of **diff -u**.

Note further that *attachments* are strongly preferred over
inlined patches. Attachments can be made by going to the **Edit** form of
the ticket immediately after its creation, and then using the left-most
button in the secondary navigation bar.

# 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/>

1.0.1 | tcllib |