#!/usr/bin/perl
use Data::Dumper;
#use strict;
my $DEBUG1=1;
my @eq1;
my @eq2;
my @eqn_set;
my @variables;
my @factored_eqns;

################################################################
#2 equations( variables are x1 and x2 )
#Representations 
#eq1 = 2*a*b*x1 + 4*a*c*x2 + 2*a*d*x2 + 4*a*e*x2
#eq2 = 4*m*n*x1 + 2*m*o*x2 + 4*m*p*x1 + 2*m*q*x2
################################################################
@eq1 = ("2*a*b*x1", "4*a*c*x2", "2*a*d*x1", "4*a*e*x2");
@eq2 = ("4*m*n*x1", "2*m*o*x2", "4*m*p*x1", "2*m*q*x2");

#################################################################
#Form the equation set
#################################################################
@eqn_set = (\@eq1, \@eq2);

##################################################################
#Return an array of hashes; hash 1 corresponds to a factored 
#form of eqn1; hash 2 corresponds to a factored form of eqn2
#Returns-
#@factored_eqns = (%factored_eqn1, %factored_eqn2);
#Where -
#$factored_eqn1{"x1"} = ("2*a*b", "2*a*d");
#$factored_eqn1{"x2"} = {"4*a*c", "4*a*e"};
#$factored_eqn2{"x1"} = ("4*m*n", "4*m*p");
#$factored_eqn3{"x2"} = {"2*m*o", "2*m*q"}; 
##################################################################
@variables = ("x1", "x2");
@factored_eqns = &factorize(\@eqn_set,\@variables);

###################################################################
#Now Dump the result of the factorization
###################################################################
my $item;
foreach $item (@factored_eqns){
    print Dumper \%{$item};
}

####################################################################
#The factorize subroutine ---
####################################################################
sub factorize{

    my @this_eqn_set        = @{$_[0]};
    my @this_variable_set   = @{$_[1]};
    my $equation;
    my $variable;
    my $term;
    my @factors = ();
    my %coefficient_array;
    my $ii=0;
    my @factored_rows=();

    #clear the coefficient array hash
    undef %coefficient_array;

    print "Factorize.....\n";

    #for each equation in the equation set
    foreach $equation (@this_eqn_set){ 
	#then for each variable in the eqution
	foreach $variable (@this_variable_set){
	    #then for each term in the equation
	    foreach $term (@{$equation}){
		
		#if the term contains the variable currently be factored
		if($term =~ /\*$variable/){
		    #extract the variable coefficient from the term
		    $term =~ s/\*$variable//;
		    #save the coefficient for that variable in that term for that equation
		    push (@factors, $term);
		}

	    }#End processing the term
	    
	    #save the coefficients for that variable in that row
	    $coefficient_array{$variable} = \@factors;
	    
	    #Debug to check that the coefficient array is getting populated
	    if($DEBUG1==1){
		print "DEBUG1: Coefficient Array Pass $ii -\n";
		print Dumper \%coefficient_array;
		print "D1*****D1******\n";
		$ii++;
	    }

	    #clear the factors array for the next variable
	    @factors=();

	    #the coefficient array at this satge should be a hash whose
	    #keys are the variables and values are the coefficient terms for
	    #that variable; we save the hash into the equation set retrun array
	    push(@factored_rows,%coefficient_array);

	}#End processing variable in the equation
	
	#reset the coefficient array for the the next equation
	undef %coefficient_array;
    
    }#End processing the equation of the equation set

    #return the factored rows to the calling routine
    return(@factored_rows);
}