166 lines
6.1 KiB
Perl
166 lines
6.1 KiB
Perl
package DDG::Goodie::CalcRoots;
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# ABSTRACT: compute the n-th root of a number
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use strict;
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use DDG::Goodie;
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use Lingua::EN::Numericalize;
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triggers any => 'root';
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zci is_cached => 1;
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zci answer_type => 'root';
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my $UPPER_BOUND = 1000000000; # 1 Billion
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handle query => sub {
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# The 'root' trigger is very ambigous so this regex provides the specific triggers
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return unless m/^((?:.*square|.*cube(?:d|)|.*th|.*rd|.*nd|.*st|.*[0-9]+)) root(?: of|) (?!of)(.*)/i;
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# Common phrases that won't be caught by str2nbr()
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my %function = (
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'square' => 2,
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'cubed' => 3,
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'cube' => 3,
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);
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# Seperate the exponent and base courtesy of the above regex
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my $exp = $1;
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my $base = $2;
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my $sign = "";
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# Figure out what number the exponent is
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if ($exp =~ m/negative\s|minus\s|\A-/i) {
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$sign = "-";
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$exp = $function{$'} ? $function{$'} : str2nbr($');
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}
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else {
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$exp = $function{$exp} ? $function{$exp} : str2nbr($exp);
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}
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# You can't take a zeroeth root
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return if $exp == 0;
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# There are separate cases here.
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# 1. Negative base and even exponent (imaginary numbers)
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# 2. Negative base and odd exponenet
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# 3. Positive base
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if ($base =~ m/negative\s|minus\s|\A-/i && $exp % 2 == 0) {
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# Figure out what number the base is
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$base = $';
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$base = str2nbr($base) if $base =~ /[^0-9]/;
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return unless $base =~ /[0-9]+/;
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# Solve using the absolute value of the base
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$base = abs($base);
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return unless $base < $UPPER_BOUND;
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my $calc = $base ** (1/$exp);
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if($sign eq "-"){$calc = -$calc;}
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# If the result is a whole number (n), the answer is n*i
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if (($calc - int($calc)) == 0) {
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return structured($sign . $exp, "-$base","The $sign$exp-root of -$base is $calc i", "$sign<sup>$exp</sup>√-$base = $calc<em>i</em>");
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}
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# Try and simplify the radical
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my $count = int(abs($calc));
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while ($count > 1) {
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# See if the current number raised to the given exponent is a factor of our base. If it is, the answer is n * i * exponent-root(the other factor)
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my $newBase = $base / ($count ** $exp);
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if ( ($newBase - int($newBase)) == 0) {
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return structured($sign . $exp,"-$base","The $sign$exp-root of -$base is $count * i * the $sign$exp-root of $newBase.", "$sign<sup>$exp</sup>√-$base = $sign$count<em>i</em>⋅<sup>$exp</sup>√$newBase");
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}
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$count--;
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}
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# Can't be solved or simplified via the above methods
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return structured($sign . $exp,"-$base","The $sign$exp-root of -$base is i * the $sign$exp-root of $base", "$sign<sup>$exp</sup>√-$base = $sign<em>i</em>⋅<sup>$exp</sup>√$base");
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}
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elsif ($base =~ m/negative\s|minus\s|\A-/i && $exp % 2 != 0) {
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# Solve normally
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$base = $';
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$base = str2nbr($base) if $base =~ m/[^0-9]/;
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$base =~ s/[^0-9\.]//g;
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return unless $base ne '' && $base < $UPPER_BOUND;
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my $calc = $base ** (1/$exp) * -1;
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if($sign eq "-"){$calc = -$calc;}
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my $secondsign = "-"; #sign of the calcuated answer
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if($calc>0){$secondsign="";}
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# Try and simplify the radical if answer is not a whole number
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unless(($calc - int($calc))==0){
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my $count = int(abs($calc));
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while ($count > 1) {
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# See if the current number raised to the given exponent is a factor of our base. If it is, we can give them a simplified version of the radical in addition to the answer.
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my $newBase = $base / ($count ** $exp);
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if ( ($newBase - int($newBase)) == 0) {
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return structured($sign . $exp,"-$base","The $sign$exp-root of -$base is $calc ($secondsign$count times the $sign$exp-root of $newBase).", qq|$sign<sup>$exp</sup>√-$base = <a href="javascript:;" onclick="document.x.q.value='$calc';document.x.q.focus();">$calc</a> ($secondsign$count⋅<sup>$exp</sup>√$newBase)|);
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}
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$count--;
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}
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}
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return structured($sign . $exp,"-$base","The $sign$exp-root of -$base is $calc.", qq|$sign<sup>$exp</sup>√-$base = <a href="javascript:;" onclick="document.x.q.value='$calc';document.x.q.focus();">$calc</a>|);
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}
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elsif ($exp =~ m/[0-9]+/) {
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# Solve normally
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$base = str2nbr($base) if $base =~ m/[^0-9]/;
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$base =~ s/[^0-9\.]//g;
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return unless $base ne '' && $base < $UPPER_BOUND;
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my $calc = $base ** (1/$exp);
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if($sign eq "-"){$calc = -$calc;}
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#If the answer is not a whole number, try to simplify the radical
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unless(($calc - int($calc))==0){
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my $count = int(abs($calc));
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while ($count > 1) {
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# See if the current number raised to the given exponent is a factor of our base. If it is, we can give them a simplified version of the radical in addition to the answer.
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my $newBase = $base / ($count ** $exp);
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if ( ($newBase - int($newBase)) == 0) {
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return structured($sign . $exp,$base,"The $sign$exp-root of $base is $calc ($sign$count times the $exp-root of $newBase).", qq|$sign<sup>$exp</sup>√$base = <a href="javascript:;" onclick="document.x.q.value='$calc';document.x.q.focus();">$calc</a> ($sign$count⋅<sup>$exp</sup>√$newBase)|);
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}
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$count--;
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}
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}
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return structured($sign . $exp,$base,"The $sign$exp-root of $base is $calc.", qq|$sign<sup>$exp</sup>√$base = <a href="javascript:;" onclick="document.x.q.value='$calc';document.x.q.focus();">$calc</a>|);
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}
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return;
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};
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sub structured{
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my($exp,$base,$text, $html) = @_;
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return $text,
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structured_answer => {
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data => {
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title => $html,
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subtitle => "Calculate $exp-root of $base",
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},
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templates => {
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group => 'text',
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options => {
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title_content => 'DDH.calc_roots.title',
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},
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},
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};
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}
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1;
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