# 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 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)
* [Set::Product::XS](https://metacpan.org/pod/Set::Product::XS)
* [List::UtilsBy::XS](https://metacpan.org/pod/List::UtilsBy::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 È˜uteu
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
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your Modified Version complies with the requirements of this license.
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