Horner's method for multivariate polynomials
Free algebra polynomial
Numeric vector of coefficients
This function is (almost) the same as
Given a polynomial\mjdeqn
p(x) = a_0 +a_1+a_2x^2+\cdots + a_nx^nomitted; see latex
it is possible to express p(x) in the algebraically equivalent form\mjdeqn
p(x) = a_0 + x\left(a_1+x\left(a_2+\cdots + x\left(a_n-1 +xa_n \right)\cdots\right)\right)omitted; see PDF
which is much more efficient for evaluation, as it requires only n
multiplications and n additions, and this is optimal. Function
horner() will take a
freealg object for its first
Robin K. S. Hankin
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