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

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

use Math::Symbolic qw/:all/;

my $exp = Math::Symbolic->parse_from_string('10^(a(x)*a(x))');

print "Expression: 10^(a(x)*a(x))\n\n";
print "prefix notation and evaluation: (a=2)\n";
print $exp->to_string('prefix') . " = " . $exp->value(a => 2) . "\n\n";

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

my $n_tree = $exp->new('total_derivative', $exp, 'a');

print $n_tree->to_string('prefix') . " = " . $n_tree->value(a => 2) . "\n\n";

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

print "$derived = " . $derived->value(a => 2) . "\n\n";

print "Finally, we simplify the derived term as much as possible:\n";
my $simplified = $derived->simplify();
print "$simplified = " . $derived->value(a => 2) . "\n\n";


print "For a change, we derive the term to x.\n";
$n_tree = $exp->new('total_derivative', $exp, 'x');

print "$n_tree\n";

$derived = $n_tree->apply_derivatives();

print "The derived term becomes:\n";
print "$derived\n";

print "Which simplifies as:\n";
print $derived->simplify();

