I'd like to bring Max::Expr to your attention. It parses math expressions into a tree of objects:

use strict;
use warnings;

use Data::Dumper;
use Math::Expr;

my $e=Parse("y=ax^2+bx+c");

print Dumper ($e);
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Output:

$VAR1 = bless( {
 'Breakable' => 0,
 'Val' => '=',
 'Opps' => [
   bless( {
    'Val' => 'y',
    'VarType' => 'Real'
   }, 'Math::Expr::Var' ),
   bless( {
    'Breakable' => 1,
    'Val' => '+',
    'Opps' => [
      bless( {
       'Breakable' => 1,
       'Val' => '+',
       'Opps' => [
        bless( {
         'Breakable' => 1,
         'Val' => '^',
         'Opps' => [
          bless( {
            'Val' => 'ax',
            'VarType' => 'Real'
          }, 'Math::Expr::Var' ),
          bless( {
            'Val' => '2'
          }, 'Math::Expr::Num' )
          ]
        }, 'Math::Expr::Opp' ),
        bless( {
         'Val' => 'bx',
         'VarType' => 'Real'
        }, 'Math::Expr::Var' )
       ]
      }, 'Math::Expr::Opp' ),
      bless( {
       'Val' => 'c',
       'VarType' => 'Real'
      }, 'Math::Expr::Var' )
     ]
   }, 'Math::Expr::Opp' )
  ]
 }, 'Math::Expr::Opp' );
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