Solver Expand (Or Multiply) Two Polynomial Expressions

Source code of 'Expand (Or Multiply) Two Polynomial Expressions'

This Solver (Expand (Or Multiply) Two Polynomial Expressions) was created by by jim_thompson5910(35256)

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==section input
This solver will show you how to expand or multiply out two polynomial expressions. For example, let's say you want to multiply out {{{(x^2+3y)(2x-3y^2+10z)}}}. Simply enter the two individual polynomials {{{x^2+3y}}} and {{{2x-3y^2+10z}}} into their respective parenthesis, and click 'solve' to see how to multiply it out.

(*[input 30 left=x^2+3y])(*[input 30 right=2x-3y^2+10z])

Simply change the expressions to whatever you want to multiply out.

Note: please keep things simple (ie don't enter square roots, logs, trig functions, etc...). Also, this solver doesn't support fractions yet. So please do any necessary simplifications before using this solver if you're dealing with fractions. Please keep in mind that this solver does very little error checking. So make sure that you're entering in the correct problem.

==section solution

perl

############# Subroutines

sub display
{
 my $exp=$_[0];
 $exp=~s/\*//g;
 $exp=~s/\+\-/\-/g;
 $exp=~s/\-\-/\+/g;
 $exp=~s/\^1($|\D)/$1/g;
 $exp=~s/(^|\D)1([a-z])/$1$2/g;
 return $exp;
}

## get terms in canonical form
sub monomial_standardize
{
   die "Needs one argument" if @_!=1;
   my $exp=$_[0];
   $exp=~s/\s//g;
   $exp=~s/^(\-?)([a-z])/$1 1$2/;
   $exp=~s/([a-z])(?=[a-z])/$1\^1$2/g;
   $exp=~s/(\d+)([a-z])/$1\*$2/g;
   $exp=~s/([a-z])$/$1\^1/;
   $exp=~s/\s//g;
   return $exp;
}

sub monomial_error_check
{
   die "Needs two arguments" if @_!=2;
   my ($exp,$flag)=@_;

## only check numerical values
   if($flag==1)
   {
      die "Error: Symbols are too close on \"$exp\"." if $exp=~m/\D\D/;
      $exp=~s/\/|\.|\-//g;
      die "Error: Non-numeric symbols detected \"$exp\"." if $exp=~m/\D/;
      return;
   }

die "Error: Symbols are too close on \"$exp\"." if $exp=~m/\W\W/;
}

sub monomial_multiplication
{
   die "Needs two arguments: exp1 and exp2" if @_!=2;
   my ($exp1,$exp2)=@_;

if($exp1!~m/[a-z]/)
   {
      $exp1="$exp1 x^0";
      $exp1=~s/\s//g;
   }
   if($exp2!~m/[a-z]/)
   {
      $exp2="$exp2 x^0";
      $exp2=~s/\s//g;
   }

die "Please no fractions (at this time)" if $exp1=~m/\// or $exp2=~m/\//;

monomial_error_check($exp1,0);
   monomial_error_check($exp2,0);

my %coefficient_hash;
   my ($standard_exp1,$standard_exp2)=(monomial_standardize($exp1),monomial_standardize($exp2));

my ($coefficient1,$var1)=$standard_exp1=~m/^(.*?)\*([a-z].*?)$/;
   monomial_error_check($coefficient1,1);

my @var_terms1=split(/\*/,$var1);
 for (my $i=0;$i<@var_terms1;$i++)
 {
 my ($var,$exponent)=$var_terms1[$i]=~m/([a-z])\^(.*)$/;
 die "No fractions allowed in exponent" if $exponent=~m/\//;
 monomial_error_check($exponent,1);
 $coefficient_hash{$var}+=$exponent;
 }

my ($coefficient2,$var2)=$standard_exp2=~m/^(.*?)\*([a-z].*?)$/;
   monomial_error_check($coefficient2,1);

my @var_terms2=split(/\*/,$var2);
 for (my $i=0;$i<@var_terms2;$i++)
 {
 my ($var,$exponent)=$var_terms2[$i]=~m/([a-z])\^(.*)$/;
 die "No fractions allowed in exponent" if $exponent=~m/\//;
 monomial_error_check($exponent,1);
 $coefficient_hash{$var}+=$exponent;
 }

my $final_coefficient=$coefficient1*$coefficient2; ## maybe use rational arithmetic here?
   my $ans=$final_coefficient;
   for my $i('a'..'z')
   {
      $ans.="*$i^$coefficient_hash{$i}" if $exp1=~m/$i/ or $exp2=~m/$i/;
   }
   $ans=~s/\*?[a-z]\^0//g;
   $ans=~s/([a-z])\^1(\D|$)/$1$2/g;
   $ans=~s/\*//g;
   return $ans;
}

####

## remove duplicates from an array
sub remove_duplicates {
my (@arr);
@arr=@_;

for(my $i=0;$i<@arr;$i++)
 {
 for(my $j=0;$j<@arr;$j++)
 {if($i!=$j)
 {if($arr[$i] eq $arr[$j])
 {splice(@arr,$i,1) if $i>$j;
 splice(@arr,$j,1) if $j>$i;
 }
 }
 }
 }

return @arr;
}

sub monomial_terms_sort
{
   die "Needs one argument: exp" if @_!=1;
   my $exp=$_[0];
   $exp=~s/\s//g;
   $exp=~s/([a-z])(?=[a-z])/$1\^1$2/g;
   $exp=~s/(\d+)([a-z])/$1\*$2/g;
   $exp=~s/([a-z])$/$1\^1/;
   my @terms=split(/\*/,$exp);
   my $coefficient=$1 if $exp=~m/^(\-?\d+)\*/;
   $exp=$coefficient;

for my $i('a'..'z')
 {
 for (my $j=0;$j<@terms;$j++)
 {
 if($terms[$j]=~m/$i/)
 {
 $exp.="*$terms[$j]";
 }
 }
 }
 $exp=~s/\*//g;
 $exp=~s/\^1(\D|$)/$1/g;
 $exp=~s/\s//g;
 return $exp;
}

sub combine_like_terms
{
 die "Needs one argument: exp" if @_!=1;
 my $exp=$_[0];
 $exp=~s/\-/\+\-/g;
 my @terms=split(/\+/,$exp);
 @terms=map{s/^(\-?)([a-z])/$1 1$2/;$_} @terms;
 @terms=map{s/\s//;$_} @terms;
 #my @coefficients
 my %coefficients;
 my @order=();
 for (my $i=0;$i<@terms;$i++)
 {
 my ($coefficient,$var)=$terms[$i]=~m/^(\-?\d+\.\d+|\-?\d+)(.*?)$/;
 $var=monomial_terms_sort($var);
 push(@order,$var);
 $coefficients{$var}+=$coefficient;
 }
 @order=remove_duplicates(@order);
 my $ans="";
 for (my $i=0;$i<@order;$i++)
 {
 $ans.="+$coefficients{$order[$i]}$order[$i]" if $coefficients{$order[$i]}!=0;
 }
 $ans=~s/^\+//;
 $ans=~s/\+\-/\-/g;
 $ans=~s/(^|\D)1([a-z])/$1$2/g;
 return $ans;

}

########## End Subroutines

########## Error Checking
my @functions=qw(sin cos tan csc sec cot log ln sqrt abs exp ro); 
if($left=~m/\// or $right=~m/\//)
{
 print "Error: This solver does not support fractions yet.";
 return;
}

if($left=~m/\)|$/ or $right=~m/$|\(/)
{
 print "Error: No need to enter parenthesis (they're already entered for you).";
 return;
}

for(my $i=0;$i<@functions;$i++)
{
 if($left=~m/$functions[$i]/ or $right=~m/$functions[$i]/)
 {
 print "Error: This solver does not support the function \"$functions[$i]\".";
 return;
 }
}

########## End Error Checking

#my ($left,$right)=("x+y+z","x-y-z");
($left,$right)=map{s/\s//g;$_} ($left,$right);
($left,$right)=map{s/\*//g;$_} ($left,$right);
my $original_exp="($left)($right)";

($left,$right)=map{s/\-/\+\-/g;$_} ($left,$right);
my @left_terms=split(/\+/,$left);
my @right_terms=split(/\+/,$right);
my @temp=map("$_($right)",@left_terms);
my $temp=display("".join("+",@temp)."");

## set up (A+B+C)(D+E+F)=A(D+E+F)+B(D+E+F)+C(D+E+F)
my @letters=('A'..'Z');
my @left_temp_letters=();
my @right_temp_letters=();
my $temp_original;
my $temp_expanded;
my $count=0;
for(my $i=0;$i<@left_terms;$i++)
{
 push(@left_temp_letters,$letters[$i]);
 $count++;
}
for(my $i=0;$i<@right_terms;$i++)
{
 push(@right_temp_letters,$letters[$count]);
 $count++;
}

$temp_original="(".join("+",@left_temp_letters).")(".join("+",@right_temp_letters).")";

my @left_temp_letters=map("$_(".join("+",@right_temp_letters).")",@left_temp_letters);
my $temp_expanded=display("".join("+",@left_temp_letters)."");

print " {{{$original_exp}}} Start with the given expression. ";

print " {{{",display($temp),"}}} Expand. Note: {{{$temp_original=$temp_expanded}}} ";
@temp=();
my @intermediate=();

for(my $i=0;$i<@left_terms;$i++)
{
 for(my $j=0;$j<@right_terms;$j++)
 {
 push(@temp,"($left_terms[$i])*($right_terms[$j])");
 my $product=monomial_multiplication($left_terms[$i],$right_terms[$j]);
 push(@intermediate,$product);
 }
}
$temp=display("".join("+",@temp)."");
print " {{{$temp}}} Distribute. ";

my $uncombined_expression=join("+",@intermediate);
$uncombined_expression=~s/\+\-/\-/g;

print " {{{",display($uncombined_expression),"}}} <a href=http://www.algebra.com/algebra/homework/Expressions-with-variables/monomial-arithmetic.solver>Multiply</a>. ";

my $ans=combine_like_terms(display($uncombined_expression));

if($uncombined_expression ne $ans)
{
 print " {{{$ans}}} Combine like terms. ";
}

print " ---------------------------------------------------- ";

print " Answer: ";

print " So {{{$original_exp=$ans}}} ";

==section output

==section check