Special ideals used for benchmarking

We bundle a couple of special ideals useful for benchmarking of the Gröbner walk.

newell_patch — Function

newell_patch(k::Union{QQField, QQBarFieldElem}, n::Int=1)

Let $n$ be an integer between 1 and 32. Returns the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface.

The specific generators for each patch have been taken from [Tra04].

source

newell_patch — Function

newell_patch(k::Field, n::Int=1)

Let $n$ be an integer between 1 and 32. Returns the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface.

The specific generators for each patch have been taken from [Tra04].

For fields $k\neq\mathbb{Q},\bar{\mathbb{Q}}$, this gives a variant of the ideal with integer coefficients.

source

newell_patch_with_orderings — Function

newell_patch_with_orderings(k::Field, n::Int=1)

Let $n$ be an integer between 1 and 32. Returns the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface. Additionally returns suitable start and target orderings, e.g. for use with the Gröbner walk.

The specific generators for each patch have been taken from [Tra04].

For fields $k\neq\mathbb{Q},\bar{\mathbb{Q}}$, this gives a variant of the ideal with integer coefficients.

source