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.\"
.IX Title "Math::Symbolic::Derivative 3pm"
.TH Math::Symbolic::Derivative 3pm "2021-01-07" "perl v5.32.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.nh
.SH "NAME"
Math::Symbolic::Derivative \- Derive Math::Symbolic trees
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 4
\&  use Math::Symbolic::Derivative qw/:all/;
\&  $derived = partial_derivative($term, $variable);
\&  # or:
\&  $derived = total_derivative($term, $variable);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module implements derivatives for Math::Symbolic trees.
Derivatives are Math::Symbolic::Operators, but their implementation
is drawn from this module because it is significantly more complex
than the implementation of most operators.
.PP
Derivatives come in two flavours. There are partial\- and total derivatives.
.PP
Explaining the precise difference between partial\- and total derivatives is
beyond the scope of this document, but in the context of Math::Symbolic,
the difference is simply that partial derivatives just derive in terms of
\&\fIexplicit\fR dependency on the differential variable while total derivatives
recongnize implicit dependencies from variable signatures.
.PP
Partial derivatives are faster, have been tested more thoroughly, and
are probably what you want for simpler applications anyway.
.SS "\s-1EXPORT\s0"
.IX Subsection "EXPORT"
None by default. But you may choose to import the \fBtotal_derivative()\fR
and \fBpartial_derivative()\fR functions.
.SH "CLASS DATA"
.IX Header "CLASS DATA"
The package variable \f(CW%Partial_Rules\fR contains partial
derivative rules as key-value pairs of names and subroutines.
.SH "SUBROUTINES"
.IX Header "SUBROUTINES"
.SS "partial_derivative"
.IX Subsection "partial_derivative"
Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.
third argument is an optional boolean indicating whether or not the
tree has to be cloned before being derived. If it is true, the
subroutine happily stomps on any code that might rely on any components
of the Math::Symbolic tree that was passed to the sub as first argument.
.SS "total_derivative"
.IX Subsection "total_derivative"
Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.
third argument is an optional boolean indicating whether or not the
tree has to be cloned before being derived. If it is true, the
subroutine happily stomps on any code that might rely on any components
of the Math::Symbolic tree that was passed to the sub as first argument.
.SH "AUTHOR"
.IX Header "AUTHOR"
Please send feedback, bug reports, and support requests to the Math::Symbolic
support mailing list:
math-symbolic-support at lists dot sourceforge dot net. Please
consider letting us know how you use Math::Symbolic. Thank you.
.PP
If you're interested in helping with the development or extending the
module's functionality, please contact the developers' mailing list:
math-symbolic-develop at lists dot sourceforge dot net.
.PP
List of contributors:
.PP
.Vb 3
\&  Steffen MXller, symbolic\-module at steffen\-mueller dot net
\&  Stray Toaster, mwk at users dot sourceforge dot net
\&  Oliver EbenhXh
.Ve
.SH "SEE ALSO"
.IX Header "SEE ALSO"
New versions of this module can be found on
http://steffen\-mueller.net or \s-1CPAN.\s0 The module development takes place on
Sourceforge at http://sourceforge.net/projects/math\-symbolic/
.PP
Math::Symbolic