michaelmusty/belyidb

A Database of Belyi Maps

belyidb's Issues

Base fields for Euclidean triples

Some of the Euclidean Belyi maps have incorrect base fields. These maps could are defined over QQ, as is clear from the defining equations, but their given base fields are number fields of degree > 1. (All the sixth cyclotomic field, I think.) Some examples:

http://beta.lmfdb.org/Belyi/3T1/%5B3%2C3%2C3%5D/3/3/3/g1/a
http://beta.lmfdb.org/Belyi/8T13/%5B6%2C3%2C2%5D/62/3311/2222/g0/a
http://beta.lmfdb.org/Belyi/9T11/%5B6%2C3%2C2%5D/621/333/22221/g0/a

passport representatives

The passport representatives s_1,s_2,s_3 of https://beta.lmfdb.org/Belyi/6T3/%5B6%2C2%2C2%5D/6/222/2211/g0/a
do not satisfy s_3s_2s_1=1. We have s_2s_3s_1 =1 but the function BelyiMap([s_1,s_3,s_2]) produces the error that it has failed a sanity check, but (s_2s_3s_1)^-1 = 1 and BelyiMap([s_1^-1, s_2^-1, s_3^-1]) works fine.

Save Euclidean

Matt Radosevich's code allows us to compute many many Euclidean Belyi maps.

How do they get saved? I only see the function GammasToBelyiDB; but I bet there's something somewhere in there, because we do display Euclidean Belyi maps in the LMFDB...

Compare to Elkin database

https://github.com/arsenelkin/Belyi-Maps

reformat existing database files

rewrite the existing files to:

• sort a,b,c
• sanity check powser bases
• include all 6 maps in S_3 orbit: phi, 1/phi, etc

Polredabs redundancy

The Belyi code already has a Polredabs function. There is another version here in BelyiDB. It's not a good idea to have competing versions.

I had problems with our old version of Polredabs, and I think everyone who is running BelyiDB will also run Belyi (probably it's a required dependency?), which means that we should use the Belyi version, and clean up the calls to it.

more robust pickling

Implement the ability to save part of a passport in such a way that it is impossible to overwrite existing data.

measuring complexity of maps and curves

Currently height.m measures complexity naively using Magma functions Height and/or CoefficientHeight.

belyi_db_improved

What the "improved" mean? How is it different than belyi_db? Which one is being used when we upload maps?