horner | R Documentation |

Horner's method for multivariate polynomials

horner(P,v)

`P` |
Free algebra polynomial |

`v` |
Numeric vector of coefficients |

This function is (almost) the same as `mvp::horner()`

.

Given a polynomial

\mjdeqnp(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

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
argument.

Robin K. S. Hankin

horner("x", 1:4) # note constant term is 1. horner("x+y",1:3) # note presence of xy and yx terms horner("1+x+xyX",1:3)

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