horner {clifford} | R Documentation |
Horner's method for Clifford objects
horner(P,v)
P |
Multivariate polynomial |
v |
Numeric vector of coefficients |
Given a polynomial
p(x) = a_0 +a_1+a_2x^2+\cdots + a_nx^n
it is possible to express p(x)
in the algebraically equivalent
form
p(x) = a_0 + x\left(a_1+x\left(a_2+\cdots + x\left(a_{n-1} +xa_n
\right)\cdots\right)\right)
which is much more efficient for evaluation, as it requires only n
multiplications and n
additions, and this is optimal. The output
of horner()
depends on the signature()
.
Horner's method is not as cool for Clifford objects as it is for
(e.g.) multivariate polynomials or freealg
objects. This is
because powers of Clifford objects don't get more complicated as the
power increases.
Robin K. S. Hankin
horner(1+e(1:3)+e(2:3) , 1:6)
rcliff() |> horner(1:4)