maresb

### Keybase proof

I hereby claim:

  * I am maresb on github.
  * I am maresb (https://keybase.io/maresb) on keybase.
  * I have a public key ASA8DYv0J6fm3Bi7xz9WsJQyyYXhkOWM18rNTCEl72au-Ao

To claim this, I am signing this object:

maresb

# These are the vectors in Schiemann's S2 lattice of length <= sqrt(8).

# This is (loosely) a Protein Data Bank format file.
# <https://en.wikipedia.org/wiki/Protein_Data_Bank_(file_format)>

# I tried to find an embedding with rational coordinates, but I don't think
# it's possible. Here I use (1 + sqrt(61)) / 4 = 2.2026 and
# (1 - sqrt(61)) / 4 = -1.7026.

maresb

# These are the vectors in Schiemann's S1 lattice of length <= sqrt(8).

# This is (loosely) a Protein Data Bank format file.
# <https://en.wikipedia.org/wiki/Protein_Data_Bank_(file_format)>

# I tried to find an embedding with rational coordinates, but I don't think
# it's possible. Here I use sqrt(7) = 2.6458.


# To verify correctness, note that the Gram matrix can be generated in PARI/GP

maresb

/*

An exploration of Alexander Schiemann's pair of inequivalent 4D lattices with
identical theta functions.

Context: <https://math.stackexchange.com/questions/4428707>

Ben Mares, 2022

maresb

Diagnosing dependency problems on other platforms with conda-lock

Source: conda-forge/dvc-feedstock#240 (comment)

The exact procedure is as follows.

Use the following as a template:

maresb

from typing import Dict, List, Union

from sqlalchemy import Column
from sqlalchemy.orm import (
    ColumnProperty,
    InstrumentedAttribute,
    MapperProperty,
    RelationshipProperty,
)
from sqlmodel.main import SQLModelMetaclass

maresb

"""Make boto3 automatically check the shared credentials file for updates.

In some situations, the ~/.aws/credentials file may be periodically updated. For
example, this is the case with the "AWS managed temporary credentials" which are
provided to AWS Cloud9 environments. (See
<https://docs.aws.amazon.com/cloud9/latest/user-guide/how-cloud9-with-iam.html#auth-and-access-control-temporary-managed-credentials>.)

Example usage of this module is:

import boto3