# Math-Bacovia

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

# EXAMPLE

```perl
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:

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

Output:

```ruby
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:

```perl
    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:

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

Example:

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

Output:

```ruby
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<full> 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.

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

Output:

```perl
Symbol("x")
```

Accepts the same options as the `alternatives()` method.

#### # `expand()`

Returns an expanded version of the self-expression.

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

Output:
```perl
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.

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

Output:
```ruby
3^log(1/2)
```

#### # `numeric()`

Evaluates the self-expression numerically and returns the result as a [Math::AnyNum](https://metacpan.org/release/Math-AnyNum) object.

```perl
my $x = Symbol('x', 13);
my $expr = ($x**2 - $x + 41);

say $expr->numeric;     #=> 197
```

# DEPENDENCIES

Math::Bacovia requires the following modules:

* [Math::AnyNum](https://metacpan.org/pod/Math::AnyNum)
* [List::UtilsBy](https://metacpan.org/pod/List::UtilsBy)
* [Set::Product::XS](https://metacpan.org/pod/Set::Product::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

* AnnoCPAN, Annotated CPAN documentation
  - http://annocpan.org/dist/Math-Bacovia

* CPAN Ratings
  - http://cpanratings.perl.org/d/Math-Bacovia

# LICENSE AND COPYRIGHT

Copyright (C) 2017-2018 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
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This license includes the non-exclusive, worldwide, free-of-charge
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otherwise transfer the Package with respect to any patent claims
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