horner function

Horner's method

Horner's method for multivariate polynomials

horner(P,v)

Arguments

• P: Multivariate polynomial
• v: Numeric vector of coefficients

Details

Given a polynomial

it is possible to express $p(x)$ in the algebraically equivalent form

which is much more efficient for evaluation, as it requires only $n$

multiplications and $n$ additions, and this is optimal. But this is not implemented here because it's efficient. It is implemented because it works if $x$ is itself a (multivariate) polynomial, and that is the second coolest thing ever. The coolest thing ever is the Reduce() function.

Author(s)

Robin K. S. Hankin

See Also

ooom

Examples

horner("x",1:5)
horner("x+y",1:3)

w <- as.mvp("x+y^2")
stopifnot(1 + 2*w + 3*w^2 == horner(w,1:3))  # note off-by-one issue

"x+y+x*y" |> horner(1:3) |> horner(1:2)