# FixedPolynomials

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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.

## Getting started

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)
```

But this is not the fastest way possible. In order to achieve the best performance we need to precompute some things and also preallocate
intermediate storage. For this we have `GradientConfig`

and `JacobianConfig`

.
For single polynomial the API is as follows

```
cfg = GradientConfig(f) # this can be reused!
f(x) == evaluate(f, x, cfg)
# We can also compute the gradient of f at x
map(g -> g(x), ∇f) == gradient(f, x, cfg)
```

We also have support for systems of polynomials:

```
cfg = JacobianConfig([f, f]) # this can be reused!
[f(x), f(x)] == evaluate([f, f] x, cfg)
# We can also compute the jacobian of [f, f] at x
jacobian(f, x, cfg)
```