Math-Bacovia

Math::Bacovia is a symbolic math library, with support for numerical evaluation (including support for complex numbers).

EXAMPLE

use 5.014;
use Math::Bacovia qw(:all);
my $x = Symbol('x');
my $y = Symbol('y');
say $x+$y;               #=> Sum(Symbol("x"), Symbol("y"))
say $x-$y;               #=> Difference(Symbol("x"), Symbol("y"))
say $x*$y;               #=> Product(Symbol("x"), Symbol("y"))
say $x/$y;               #=> Fraction(Symbol("x"), Symbol("y"))
say $x**$y;              #=> Power(Symbol("x"), Symbol("y"))
say Log($x);             #=> Log(Symbol("x"))
say Log($x)+Log($y);     #=> Log(Product(Symbol("x"), Symbol("y")))
say Exp($x);             #=> Exp(Symbol("x"))
say Exp($x)*Exp($y);     #=> Exp(Sum(Symbol("x"), Symbol("y")))
say "\n=> Sum:";
my $sum = Fraction(0, 1);
for my $n (1..10) {
    $sum += Fraction(1, $n);
}
say $sum;                     #=> Fraction(10628640, 3628800)
say $sum->numeric;            #=> 7381/2520
say "\n=> Product:";
my $prod = Product();
for my $n (1..3) {
    $prod *= Exp(Fraction(1, $n));
}
say $prod->pretty;            #=> (exp(1) * exp(1/2) * exp(1/3))
say $prod->simple->pretty;    #=> exp(11/6)
say $prod->numeric;           #=> 6.25470095193632871640207...
say "\n=> Alternative representations:";
say join ', ', Power(3, 5)->alternatives(full => 1);   #=> Power(3, 5), Exp(Product(Log(3), 5)), 243

DESCRIPTION

The types supported by this library are described bellow:

# Symbol(name, value=undef)

Represents a symbolic value. Optionally, it can have a numerical value (or any other value).

# Number(value)

Represents a numerical value.

# Fraction(numerator, denominator)

Represents a symbolic fraction.

# Difference(minuend, subtrahend)

Represents a symbolic subtraction.

# Power(base, power)

Represents a symbolic exponentiation in a symbolic base.

# Log(x)

Represents the natural logarithm of a symbolic value.

# Exp(x)

Represents the natural exponentiation of a symbolic value.

# Sum(a, b, c, ...)

Represents a summation of an arbitrary (finite) number of symbolic values.

# Product(a, b, c, ...)

Represents a product of an arbitrary (finite) number of symbolic values.

SPECIAL METHODS

An interesting feature is the support for alternative representations (provided by the method alternatives()),
which uses common mathematical identities to create symbolically equivalent expressions from the self-expression.

Bellow we describe the special methods provided by this library:

# alternatives()

Returns a list with alternative representations from the self-expression.

Example:

say for Exp(Log(Fraction(1,3)) * 2)->alternatives;

Output:

Exp(Product(2, Log(Fraction(1, 3))))
Power(Fraction(1, 3), 2)
Exp(Product(2, Log(1/3)))
Power(1/3, 2)

The options supported by this method are:

    log  => 1,    # will try to generate logarithmic alternatives
    full => 1,    # will try to generate more alternatives (it may be slow)

The options can be provided as:

$obj->alternatives(
    full => 1,
    log  => 1,
);

Example:

say for Power(3, 5)->alternatives(full => 1);

Output:

Power(3, 5)
Exp(Product(Log(3), 5))
243

WARNING: The number of alternative representations grows exponentially! For non-trivial expressions,
this process may take a very long time and use lots of memory. In combination with the B option
(set to a true value), the returned list may contain hundreds of even thousands of alternative representations.

# simple()

Returns a simplification of the self-expression.

say Exp(Log(Log(Exp(Exp(Log(Symbol('x')))))))->simple;

Output:

Symbol("x")

Accepts the same options as the alternatives() method.

# expand()

Returns an expanded version of the self-expression.

say Power(Fraction(5, 7), Fraction(1, 3))->expand(full => 1);

Output:

Exp(Product(Log(Fraction(5, 7)), Fraction(1, 3)))

Accepts the same options as the alternatives() method.

# pretty()

Returns a human-readable stringification of the self-expression.

say Power(3, Log(Fraction(1, 2)))->pretty;

Output:

3^log(1/2)

# numeric()

Evaluates the self-expression numerically and returns the result as a Math::AnyNum object.

my $x = Symbol('x', 13);
my $expr = ($x**2 - $x + 41);
say $expr->numeric;     #=> 197

DEPENDENCIES

Math::Bacovia requires the following modules:

• Math::AnyNum
• List::UtilsBy
• :XS">Set::XS

INSTALLATION

To install this module, run the following commands:

perl Build.PL
./Build
./Build test
./Build install

SUPPORT AND DOCUMENTATION

After installing, you can find documentation for this module with the
perldoc command.

perldoc Math::Bacovia

You can also look for information at:

• MetaCPAN
  • https://metacpan.org/pod/Math::Bacovia

LICENSE AND COPYRIGHT

Copyright (C) 2017-2019 Daniel Șuteu

This program is free software; you can redistribute it and/or modify it
under the terms of the the Artistic License (2.0). You may obtain a
copy of the full license at:

http://www.perlfoundation.org/artistic_license_2_0

Any use, modification, and distribution of the Standard or Modified
Versions is governed by this Artistic License. By using, modifying or
distributing the Package, you accept this license. Do not use, modify,
or distribute the Package, if you do not accept this license.

If your Modified Version has been derived from a Modified Version made
by someone other than you, you are nevertheless required to ensure that
your Modified Version complies with the requirements of this license.

This license does not grant you the right to use any trademark, service
mark, tradename, or logo of the Copyright Holder.

This license includes the non-exclusive, worldwide, free-of-charge
patent license to make, have made, use, offer to sell, sell, import and
otherwise transfer the Package with respect to any patent claims
licensable by the Copyright Holder that are necessarily infringed by the
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