# Introduction

FixedPolynomials.jl is a library for *really fast* evaluation of multivariate polynomials. Here are the latest benchmark results.

Since `FixedPolynomials`

polynomials are optimised for fast evaluation they are not suited for construction of polynomials. It is recommended to construct a polynomial with an implementation of MultivariatePolynomials.jl, e.g. DynamicPolynomials.jl, and to convert it then into a `FixedPolynomials.Polynomial`

for further computations.

## Tutorial

Here is an example on how to create a `Polynomial`

with `Float64`

coefficients:

```
using FixedPolynomials
import DynamicPolynomials: @polyvar
@polyvar x y z
f = Polynomial{Float64}(x^2+y^3*z-2x*y)
```

To evaluate `f`

you simply have to pass in a `Vector{Float64}`

```
x = rand(3)
f(x) # alternatively evaluate(f, x)
```

The only defined method is `evaluate(f::Polynomial{T}, x::AbstractVector{T})`

. This is intentional restrictive to avoid any unintended performance penalties.

`f`

has then the variable ordering as implied by `DynamicPolynomials.variables(x^2+y^3*z-2x*y)`

, i.e. `f([1.0, 2.0, 3.0])`

will evaluate `f`

with `x=1`

, `y=2`

and `z=3`

.

## Safety notes

For the evaluation multivariate variant of Horner's method is used. Due to that for polynomials with terms of degree over 43 we cannot guarantee an error of less than 1 ULP.