I have written a sub routine to factorize a set of equations symbolically. What appears to be happening is that in the subroutine, I am factoring an equation passed as an argument and storing the variable and coefficients associated with that variable in a hash; whose key is the variable and value is the array of coefficients. Within the routine I am using Dumper to check how the hash is getting populated. On factorizing with respect to the first variable, I see the coefficients get recorded correctly in the hash. When the next variable is factored and recorded in the has, I see the coefficients of the next variable get recorded correctly but the firs variable coefficients appears to have been clobbered.. Finally the subroutine returns an array of hashes has recorded the coefficients in an array ( value ) with respect to the variables (keys) for each equation ( equation set ). I am also having difficulty accessing the contents of the returned array of hashes from the subroutine... Any helps would be very appreciated; code is attached below -

#!/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 t
+hat 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 populate
+d
        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 f
+or
        #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);
}
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