#!/usr/bin/perl
use strict;
use warnings;

use lib 'lib';
use Data::Dumper;

use Math::Symbolic qw/:all/;

my $var = Math::Symbolic::Variable->new();
my $a = $var->new('x' => 3.14159);

my $c = Math::Symbolic::Constant->new();
my $two = $c->new(2);

print "Vars: x=" . $a->value() .
           " (Value is optional)\n\n";

my $op  = Math::Symbolic::Operator->new();
#my $sin = $op->new('sin', $op->new('*', $two, $a));
my $sin = $op->new('sinh', $op->new('*', $two, $a));


print "Expression: sinh(2*x)\n\n";

print "prefix notation and evaluation:\n";
print $sin->to_string('prefix') . " = " . $sin->value() . "\n\n";

print "Now, we derive this partially to x: (prefix again)\n";

my $n_tree = $op->new( {
	type => U_P_DERIVATIVE,
	operands => [$sin, $a],
} );

print $n_tree->to_string('prefix') . " = " . $sin->value() . "\n\n";

print "Now, we apply the derivative to the term: (infix)\n";
my $derived = $n_tree->apply_derivatives();

print "$derived" . " = " . $derived->value() . "\n\n";

print "Finally, we simplify the derived term as much as possible:\n";
$derived = $derived->simplify();
print "$derived = " . $derived->value() . "\n\n";


print "Now, we do this three more times:\n";
for (1..3) {
	$derived = $op->new( {
		type => U_P_DERIVATIVE,
		operands => [$derived, $a],
	} )->apply_derivatives()->simplify();
}

print "$derived = " . $derived->value() . "\n\n";


