Kevin Ryde
and 1 contributors


Math::Polynomial::Horner -- stringize Math::Polynomial in Horner form


 use Math::Polynomial;
 my $poly = Math::Polynomial->new(7,8,0,9,4,5);

 use Math::Polynomial::Horner;
 print Math::Polynomial::Horner::as_string($poly, {times=>'*'});
 # ((((5*x + 4)*x + 9)*x^2 + 8)*x + 7)


This is a few lines of code to format Math::Polynomial objects as strings in Horner form. It uses parentheses to group terms for multiplications by x rather than powering.

Program Code

Horner form is quite good for computer evaluation. If you adjust times, power etc in the string config then it can be pasted into a program.

For Perl, the default "descending" comes out better than ascending because Perl evaluates left to right so the descending does each coefficient addition successively, whereas ascending pushes all the coefficients on the stack before working down through them.

An obvious optimization for evaluation is to watch for middle powers like x^2 in the synopsis above which arise from runs of zero coefficients, and hold them in temporary variables if needed more than once.

More sophisticated optimizations can be had from power trees or partly or completely factorizing the polynomial to find repeated roots. Some of that may be a bit difficult, and for that matter Math::Symbolic might be a better way to keep track of transformations applied.


$string = Math::Polynomial::Horner::as_string ($poly)
$string = Math::Polynomial::Horner::as_string ($poly, $sconfig)

Return $poly as a string in Horner form.

Optional $config is a hashref of stringize parameters the same as $poly->as_string takes, plus extra fields described below.


In addition to the basic string configurations of Math::Polynomial the following are recognised.

left_paren, string, default "("
right_paren, string, default ")"

Internal parentheses to use. prefix and suffix are used at the very start and end of the string so if you change left_paren and right_paren then you will probably change prefix and suffix too, perhaps to empty strings if you don't want an outermost set of parens.

    $str = Math::Polynomial::Horner::as_string
                { left_paren  => '[',
                  right_paren => ']',
                  prefix      => '',
                  suffix      => '' });

There's a couple of secret experimental options in the code too. power_by_times_upto prefers multiplications over powering when there's zero coefficients to be skipped. fold_sign_swap_end extends fold_sign to swap the order of the high term and following factor to turn for instance (-3*x + 1) into (1 - 3*x). It can save a negation if the high coefficient is -1 and the next is positive. And for_perl gives Perl code power operator and turns on fold_sign. Not sure if these are a good idea. The Perl style might not suit if using values or coefficients which are not plain numbers but instead an object, matrix, whatever.





Math-Polynomial-Horner is Copyright 2010, 2011, 2019 Kevin Ryde

Math-Polynomial-Horner is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-Polynomial-Horner is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-Polynomial-Horner. If not, see <>.