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.\" ========================================================================
.\"
.IX Title "Differentiate 3pm"
.TH Differentiate 3pm "2004-12-18" "perl v5.10.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.SH "NAME"
Math::Calculus::Differentiate \- Algebraic Differentiation Engine
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&  use Math::Calculus::Differentiate;
\&
\&  # Create an object.
\&  my $exp = Math::Calculus::Differentiate\->new;
\&  
\&  # Set a variable and expression.
\&  $exp\->addVariable(\*(Aqx\*(Aq);
\&  $exp\->setExpression(\*(Aqx^2 + 5*x\*(Aq) or die $exp\->getError;
\&  
\&  # Differentiate and simplify.
\&  $exp\->differentiate or die $exp\->getError;;
\&  $exp\->simplify or die $exp\->getError;;
\&  
\&  # Print the result.
\&  print $exp\->getExpression; # Prints 2*x + 5
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module can take an algebraic expression, parse it into a tree structure, modify
the tree to give a representation of the differentiated function, simplify the tree
and turn the tree back into an output of the same form as the input.
.PP
It supports differentiation of expressions including the +, \-, *, / and ^ (raise to
power) operators, bracketed expressions to enable correct precedence and the functions
ln, exp, sin, cos, tan, sec, cosec, cot, sinh, cosh, tanh, sech, cosech, coth, asin,
acos, atan, asinh, acosh and atanh.
.SH "EXPORT"
.IX Header "EXPORT"
None by default.
.SH "METHODS"
.IX Header "METHODS"
.IP "new" 4
.IX Item "new"
.Vb 1
\&  $exp = Math::Calculus::Differentiate\->new;
.Ve
.Sp
Creates a new instance of the differentiation engine, which can hold an individual
expression.
.IP "addVariable" 4
.IX Item "addVariable"
.Vb 1
\&  $exp\->addVariable(\*(Aqx\*(Aq);
.Ve
.Sp
Sets a certain named value in the expression as being a variable. A named value must be
an alphabetic chracter.
.IP "setExpression" 4
.IX Item "setExpression"
.Vb 1
\&  $exp\->setExpression(\*(Aqx^2 + 5*x);
.Ve
.Sp
Takes an expression in human-readable form and stores it internally as a tree structure,
checking it is a valid expression that the module can understand in the process. Note that
the engine is strict about syntax. For example, note above that you must write 5*x and not
just 5x. Whitespace is allowed in the expression, but does not have any effect on precedence.
If you require control of precedence, use brackets; bracketed expressions will always be
evaluated first, as you would normally expect. The module follows the \s-1BODMAS\s0 precedence
convention. Returns undef on failure and a true value on success.
.IP "getExpression" 4
.IX Item "getExpression"
.Vb 1
\&  $expr = $exp\->getExpression;
.Ve
.Sp
Returns a textaul, human readable representation of the expression that is being stored.
.IP "differentiate" 4
.IX Item "differentiate"
.Vb 1
\&  $exp\->differentiate(\*(Aqx\*(Aq);
.Ve
.Sp
Differentiates the expression that was stored with setExpression with respect to the variable
passed as a parameter. Returns undef on failure and a true value on success.
.IP "simplify" 4
.IX Item "simplify"
.Vb 1
\&  $exp\->simplify;
.Ve
.Sp
Attempts to simplify the expression that is stored internally. It is a very good idea to call
this after calling differentiate, as the tree will often not be in the most compact possible
form, and this will affect the readability of output from getExpression and the performance
of future calls to differentiate if you are intending to obtain higher derivatives. Returns
undef on failure and a true value on success.
.IP "getTraceback" 4
.IX Item "getTraceback"
.Vb 1
\&  $exp\->getTraceback;
.Ve
.Sp
When setExpression and differentiate are called, a traceback is generated to describe
what these functions did. If an error occurs, this traceback can be extremely useful
in helping track down the source of the error.
.IP "getError" 4
.IX Item "getError"
.Vb 1
\&  $exp\->getError;
.Ve
.Sp
When any method other than getTraceback is called, the error message stored is cleared, and
then any errors that occur during the execution of the method are stored. If failure occurs,
call this method to get a textual representation of the error.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
The author of this module has a website at <http://www.jwcs.net/~jonathan/>, which has
the latest news about the module and a web-based frontend to allow you to test the module
out for yourself.
.SH "AUTHOR"
.IX Header "AUTHOR"
Jonathan Worthington, <jonathan@jwcs.net>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2004 by Jonathan Worthington
.PP
This library is free software; you can redistribute it and/or modify
it under the same terms as Perl itself, either Perl version 5.8.1 or,
at your option, any later version of Perl 5 you may have available.
.SH "POD ERRORS"
.IX Header "POD ERRORS"
Hey! \fBThe above document had some coding errors, which are explained below:\fR
.IP "Around line 55:" 4
.IX Item "Around line 55:"
\&'=item' outside of any '=over'
.IP "Around line 150:" 4
.IX Item "Around line 150:"
You forgot a '=back' before '=head1'