# NAME

Math::SymbolicX::Error - Parser extension for dealing with numeric errors

# SYNOPSIS

```
use Math::Symbolic qw/parse_from_string/;
use Math::SymbolicX::Error;
# Inlined Number::WithError declarations:
my $formula = parse_from_string('3 * error(3 +/- 0.2)^2 + error(1 +/- 0.1)');
print $formula->value();
# prints '2.80e+01 +/- 3.6e+00'
# High precision support using Math::BigFloat
my $high_precision = parse_from_string('3 * error_big(3e-12 +/- 0.2e-12');
print $high_precision->value();
# prints '9.00e-12 +/- 6.0e-13'
```

# DESCRIPTION

This module adds numeric error (or uncertainty) support to the Math::Symbolic parser. It does so by extending the parser grammar of the Math::Symbolic module (that is, the one stored in $Math::Symbolic::Parser) with certain special functions that create constants as Number::WithError objects. (Math::Symbolic::Variable objects have been able to contain objects since the very beginning.)

## MOTIVATION

All constants in strings that are parsed by Math::Symbolic::Parser are converted to Math::Symbolic::Constant objects holding the value associated to the constant in an ordinary Perl Scalar by default. Unfortunately, that means you are limited to real floating point numbers.

On the other hand, it might be necessary to attach a certain error to a number and calculate using error propagation. Math::SymbolicX::Error helps making this process more opaque. Since the Math::Symbolic::Constant objects can hold any object, you can build your trees by hand using Math::Complex objects instead of Perl Scalars for the value of the constants. But since the Math::Symbolic::Parser is by far the most convenient interface to Math::Symbolic, there had to be a reasonably simple way of introducing Number::WithError support to the parser. So here goes.

## USAGE

In order to numeric constants with errors in Math::Symbolic trees from the parser, you just load this extension module and wrap any of the functions listed hereafter around any constants that have an associated error.

The aforementioned functions are `error()`

and `error_big()`

. `error()`

turns its arguments into a Number::WithError object which is injected into the Math::Symbolic tree at the point in the parse tree at which the `error()`

function was found.

Similarily, `error_big()`

creates a Number::WithError object but with Math::BigFloat support. That is, arbitrary precision.

# AUTHOR

Steffen Mueller, <symbolic-module at steffen-mueller dot net<gt>

# COPYRIGHT AND LICENSE

Copyright (C) 2006-2008 by Steffen Mueller

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.8 or, at your option, any later version of Perl 5 you may have available.

# SEE ALSO

New versions of this module can be found on http://steffen-mueller.net or CPAN.

You should definately be familiar with Number::WithError before you start using this module because the objects that are returned from `$formula-`

value()> calls are Number::WithError objects.

Also have a look at Math::Symbolic, and at Math::Symbolic::Parser

Refer to Math::SymbolicX::ParserExtensionFactory for the implementation details.

Other parser extensions include big- and complex number support: Math::SymbolicX::BigNum, Math::SymbolicX::Complex