Real Circles Tangent to 3 Conics
The file Certify_136_Real_Solutions.jl certifies an instance of three conics that have 136 real tritangent circles with parameters described in Theorem 1.4.
The file Hill_Climbing.jl runs the hill climbing algorithm described in Algorithm 2.
The file certify.csv gives the certification data needed for the proof of Theorem 3.1 and
the file certify.jl computes the certification for each instance.
The page Hill_Climb_Data_Generation generates the hill climbing data needed in Section 4 outlined in Algorithm 3. It is a notebook that generates hill climbing data as a CSV file where the 1st 18 columns are the input to the hill climbing algorithm and the last 18 columns are the output of the hill climbing algorithm after one step.
The page Real_Solution_Counts is a notebook that takes the CSV file output by Hill_Climb_Data_Generation and produces a CSV file where the 1st 18 columns are the input to the hill-climbing algorithm, the next 18 columns are the output of the hill climbing algorithm after one step, and the final column is the number of real solutions.
The file data_hill_climbing.csv gives the data set \(\mathcal{D}_1\) used in Section 4.
The file data_random.csv gives the data set \(\mathcal{D}_2\) used in Section 4.
The page neural_count trains the machine learning model outlined in Section 4 using the data sets \(\mathcal{D}_1, \mathcal{D}_2\) and \(\mathcal{D}_1 \cup \mathcal{D}_2\).
The page analysis is used to find the prediction errors on the validation data.
Project page created: 10/11/2022
Project contributors: Paul Breiding, Julia Lindberg, Wern Juin Gabriel Ong, Linus Sommer
Software used: Julia (v.1.7)
Corresponding author of this page: Julia Lindberg, julia.lindberg@mis.mpg.de