File Coverage

blib/lib/Math/Symbolic.pm

Criterion	Covered	Total	%
statement	52	52	100.0
branch	8	8	100.0
condition			n/a
subroutine	15	15	100.0
pod	1	1	100.0
total	76	76	100.0

=encoding utf8

=head1 NAME

Math::Symbolic - Symbolic calculations

=head1 SYNOPSIS

  use Math::Symbolic;

  my $tree = Math::Symbolic->parse_from_string('1/2 * m * v^2');
  # Now do symbolic calculations with $tree.
  # ... like deriving it...

  my ($sub) = Math::Symbolic::Compiler->compile_to_sub($tree);

  my $kinetic_energy = $sub->($mass, $velocity);

=head1 DESCRIPTION

Math::Symbolic is intended to offer symbolic calculation capabilities
to the Perl programmer without using external (and commercial) libraries
and/or applications.

Unless, however, some interested and knowledgable developers turn up to
participate in the development, the library will be severely limited by
my experience in the area. Symbolic calculations are an active field of
research in CS.

There are several ways to construct Math::Symbolic trees. There are no
actual Math::Symbolic objects, but rather trees of objects of subclasses of
Math::Symbolic. The most general but unfortunately also the least intuitive
way of constructing trees is to use the constructors of
the Math::Symbolic::Operator, Math::Symbolic::Variable, and
Math::Symbolic::Constant classes to create (nested) objects of the
corresponding types.

Furthermore, you may use the overloaded interface to apply the standard
Perl operators (and functions, see L) to existing
Math::Symbolic trees and standard Perl expressions.

Possibly the most convenient way of constructing Math::Symbolic trees is
using the builtin parser to generate trees from expressions such as C<2 * x^5>.
You may use the Cparse_from_string()> class method for this.

Of course, you may combine the overloaded interface with the parser to
generate trees with Perl code such as C<$term * 5 * 'sin(omega*t+phi)'> which
will create a tree of the existing tree $term times 5 times the sine of
the vars omega times t plus phi.

There are several modules in the distribution that contain subroutines
related to calculus. These are not loaded by Math::Symbolic by default.
Furthermore, there are several extensions to Math::Symbolic available
from CPAN as separate distributions. Please refer to L
for an incomplete list of these.

For example, L come with C and
contains routines to compute Taylor Polynomials and the associated errors.

Routines related to vector calculus such as grad, div, rot, and Jacobi- and
Hesse matrices are available through the L
module. This module is also able to compute Taylor Polynomials of
functions of two variables, directional derivatives, total differentials,
and Wronskian Determinants.

Some basic support for linear algebra can be found in
L. This includes a routine to compute
the determinant of a matrix of C trees.

=head2 EXPORT

None by default, but you may choose to have the following constants
exported to your namespace using the standard Exporter semantics.
There are two export tags: :all and :constants. :all will export
all constants and the parse_from_string subroutine.

  Constants for transcendetal numbers:
    EULER (2.7182...)
    PI    (3.14159...)

  Constants representing operator types: (First letter indicates arity)
  (These evaluate to the same numbers that are returned by the type()
   method of Math::Symbolic::Operator objects.)
    B_SUM
    B_DIFFERENCE
    B_PRODUCT
    B_DIVISION
    B_LOG
    B_EXP
    U_MINUS
    U_P_DERIVATIVE (partial derivative)
    U_T_DERIVATIVE (total derivative)
    U_SINE
    U_COSINE
    U_TANGENT
    U_COTANGENT
    U_ARCSINE
    U_ARCCOSINE
    U_ARCTANGENT
    U_ARCCOTANGENT
    U_SINE_H
    U_COSINE_H
    U_AREASINE_H
    U_AREACOSINE_H
    B_ARCTANGENT_TWO

  Constants representing Math::Symbolic term types:
  (These evaluate to the same numbers that are returned by the term_type()
   methods.)
    T_OPERATOR
    T_CONSTANT
    T_VARIABLE

  Subroutines:
    parse_from_string (returns Math::Symbolic tree)

=cut

package Math::Symbolic;

use 5.006;
use strict;
use warnings;

use Carp;

use Math::Symbolic::ExportConstants qw/:all/;
use Math::Symbolic::AuxFunctions;

use Math::Symbolic::Base;
use Math::Symbolic::Operator;
use Math::Symbolic::Variable;
use Math::Symbolic::Constant;

use Math::Symbolic::Derivative;

use Math::Symbolic::Parser;
use Math::Symbolic::Compiler;

use Math::Symbolic::Custom;

require Exporter;

our @ISA = qw(Exporter);

our %EXPORT_TAGS = (
    all => [
        @{ $Math::Symbolic::ExportConstants::EXPORT_TAGS{all} },
        qw{&parse_from_string},
    ],
    constants => [ @{ $Math::Symbolic::ExportConstants::EXPORT_TAGS{all} }, ],
);
our @EXPORT_OK = ( @{ $EXPORT_TAGS{'all'} } );
our @EXPORT    = qw();

our $VERSION = '0.612';

=head1 CLASS DATA

The package variable $Parser will contain a Parse::RecDescent
object that is used to parse strings at runtime.

=cut

our $Parser = Math::Symbolic::Parser->new();

=head1 SUBROUTINES

=head2 parse_from_string

This subroutine takes a string as argument and parses it using
a Parse::RecDescent parser taken from the package variable
$Math::Symbolic::Parser. It generates a Math::Symbolic tree
from the string and returns that tree.

The string may contain any identifiers matching /[a-zA-Z][a-zA-Z0-9_]*/ which
will be parsed as variables of the corresponding name.

Please refer to L for more information.

=cut

sub parse_from_string {
    my $string = shift;
    croak "Missing string argument from parse_from_string() call"
      unless defined $string;
    if ($string eq 'Math::Symbolic') {
        if (@_) {
            $string = shift;
        }
        else {
          croak("Missing string argument from Math::Symbolic->parse_from_string() call");
        }
    }
    $string =~ s/\s+//gso;
    if ( not defined $Parser ) {
        $Parser = Math::Symbolic::Parser->new();
    }
    return $Parser->parse($string);
}

1;
__END__