Sollya User's Manual

Name:

horner brings all polynomial subexpressions of an expression to Horner form

Usage:

horner(function) : function -> function

Parameters:

function represents the expression to be rewritten in Horner form

Description:

The command horner rewrites the expression representing the function function in a way such that all polynomial subexpressions (or the whole expression itself, if it is a polynomial) are written in Horner form. The command horner does not endanger the safety of computations even in Sollya's floating-point environment: the function returned is mathematically equal to the function function.

Example 1:

   > print(horner(1 + 2 * x + 3 * x^2));
   1 + x * (2 + x * 3)
   > print(horner((x + 1)^7));
   1 + x * (7 + x * (21 + x * (35 + x * (35 + x * (21 + x * (7 + x))))))

Example 2:

> print(horner(exp((x + 1)^5) - log(asin(x + x^3) + x)));
exp(1 + x * (5 + x * (10 + x * (10 + x * (5 + x))))) - log(asin(x * (1 + x^2)) + x)

See also: canonical, print, coeff, degree, autosimplify, simplifysafe