Special ideals used for benchmarking
We bundle a couple of special ideals useful for benchmarking of the Gröbner walk.
newell_patch — Functionnewell_patch(k::QQField, n::Int=1)
newell_patch(k::QQBarFieldElem, n::Int=1)Return the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface.
Here $n$ must be an integer between 1 and 32.
The specific generators for each patch have been taken from [Tra04].
newell_patch — Functionnewell_patch(k::Field, n::Int=1)Return the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface.
Here $n$ must be an integer between 1 and 32.
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.
newell_patch_with_orderings — Functionnewell_patch_with_orderings(k::Field, n::Int=1)Return the ideal corresponding to the implicitization of the $n$-th bi-cubic patch describing the Newell's teapot as a parametric surface.
Here $n$ must be an integer between 1 and 32.
Additionally return 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.