G'day jess195,
Welcome to the monastery.
"I need to check what user enters against my answer. Say I have x + 1 as a correct answer, but user entered 1 + x. How can I build something that would check for all associativity and commutativity in a given equation?"
My thoughts on this was to substitute the variables with real values and then compare the results.
However, looking at some of your subsequent replies in this thread, I'm wondering if you really do want to compare two answers or generate a list of all possible answers:
assuming the former, here's some code I've been playing around with that you can possibly adapt to your needs.
#!/usr/bin/env perl
use strict;
use warnings;
use constant DEBUG => 0;
use constant FUZZINESS => 1e15;
use Scalar::Util 'looks_like_number';
my %vals = map { $_ => rand } 'a' .. 'z';
my @equations = (
'x + y',
'x  y',
'x * y',
'x / y',
'x % y',
'x ^ y',
'x * (y + z)',
'x / (y + z)',
'(x + y) * (x + y)',
'(x + y) * (x  y)',
);
EQUATION:
for my $equation (@equations) {
TRY:
while (1) {
print '' x 40, "\n";
print "Base equation: $equation\n";
print 'Try/Skip/Quit (t/s/q) [t]: ';
my $choice = <>;
next EQUATION if $choice =~ /^s/i;
last EQUATION if $choice =~ /^q/i;
print 'Equivalent equation: ';
my $try = <>;
chomp $try;
if (equivalent($equation, $try)) {
print "'$equation' and '$try' are equivalent.\n";
print 'Try again (y/n) [n]: ';
my $choice = <>;
next TRY if $choice =~ /^y/i;
last TRY;
}
else {
print "'$equation' and '$try' are not equivalent.\n";
next TRY;
}
}
}
sub equivalent {
my ($equation, $try) = @_;
my $eqn_val = get_value($equation);
return 0 unless defined $eqn_val;
my $try_val = get_value($try);
return 0 unless defined $try_val;
return abs($eqn_val  $try_val) < FUZZINESS ? 1 : 0;
}
sub get_value {
my $in_equation = shift;
print "get_value($in_equation)\n" if DEBUG;
(my $equation = $in_equation) =~ s/([az])/$vals{$1}/g;
$equation =~ s/\^/**/g;
print "SUBS: $equation\n" if DEBUG;
my $value = eval {
eval $equation;
};
if ($@) {
warn $@;
return undef;
}
if (not defined $value && length $value && looks_like_number $valu
+e) {
warn "!!! BAD EQUATION: '$in_equation'\n";
return undef;
}
print "VALUE: $value\n" if DEBUG;
return $value;
}
Here's some example output:
'x + y' and 'y + x' are equivalent.
...
'x  y' and 'y  x' are not equivalent.
...
'x  y' and 'xy' are equivalent.
...
'x * (y + z)' and 'x*y + x*z' are equivalent.
...
'x * (y + z)' and 'z * x + y * x' are equivalent.
...
'x / (y + z)' and 'x/y + x/z' are not equivalent.
...
'(x + y) * (x + y)' and 'x^2 + 2*x*y + y^2' are equivalent.
...
'(x + y) * (x  y)' and 'x^2 + y^2' are not equivalent.
...
'(x + y) * (x  y)' and 'x^2  y^2' are equivalent.
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
 a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

For: 

Use: 
 &   & 
 <   < 
 >   > 
 [   [ 
 ]   ] 
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.

