Download Symbolic Math Toolbox User's Guide

Simplifications and Substitutions
Simplifications and Substitutions
There are several functions that simplify symbolic expressions and are used to
perform symbolic substitutions:
Simplifications
Here are three different symbolic expressions.
syms x
f = x^3-6*x^2+11*x-6
g = (x-1)*(x-2)*(x-3)
h = -6+(11+(-6+x)*x)*x
Here are their prettyprinted forms, generated by
pretty(f), pretty(g), pretty(h)
3
2
x - 6 x + 11 x - 6
(x - 1) (x - 2) (x - 3)
-6 + (11 + (-6 + x) x) x
These expressions are three different representations of the same
mathematical function, a cubic polynomial in x.
Each of the three forms is preferable to the others in different situations. The
first form, f, is the most commonly used representation of a polynomial. It is
simply a linear combination of the powers of x. The second form, g, is the
factored form. It displays the roots of the polynomial and is the most accurate
for numerical evaluation near the roots. But, if a polynomial does not have such
simple roots, its factored form may not be so convenient. The third form, h, is
the Horner, or nested, representation. For numerical evaluation, it involves the
fewest arithmetic operations and is the most accurate for some other ranges of
x.
The symbolic simplification problem involves the verification that these three
expressions represent the same function. It also involves a less clearly defined
objective — which of these representations is “the simplest”?
2-41