### Install pyknotid

Source: https://pyknotid.readthedocs.io/en/latest/sources/overview.html

Install the pyknotid package using pip. Ensure cython is installed if you want to use the optimized cython modules.

```bash
$ pip install pyknotid

```

--------------------------------

### Database Connection Setup

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/catalogue/identify.html

Sets up the database connection method. It checks for an existing connection or establishes a new one.

```python
from . import database as db
from pyknotid.catalogue.database import Knot
from pyknotid.catalogue import converters

if hasattr(db.db, 'get_conn'):
    connection_method = db.db.get_conn
else:
    connection_method = db.db.connection
connection_method()
```

--------------------------------

### Peewee SelectBase Query Execution and Fetching

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Provides methods for executing queries and fetching results, including peeking at the first row, getting the first N rows, retrieving a single scalar value, counting rows, checking for existence, and getting a single row.

```python
class SelectBase(_HashableSource, Source, SelectQuery):
    def _get_hash(self):
        return hash((self.__class__, self._alias or id(self)))

    def _execute(self, database):
        if self._cursor_wrapper is None:
            cursor = database.execute(self)
            self._cursor_wrapper = self._get_cursor_wrapper(cursor)
        return self._cursor_wrapper

    @database_required
    def peek(self, database, n=1):
        rows = self.execute(database)[:n]
        if rows:
            return rows[0] if n == 1 else rows

    @database_required
    def first(self, database, n=1):
        if self._limit != n:
            self._limit = n
            self._cursor_wrapper = None
        return self.peek(database, n=n)

    @database_required
    def scalar(self, database, as_tuple=False):
        row = self.tuples().peek(database)
        return row[0] if row and not as_tuple else row

    @database_required
    def count(self, database, clear_limit=False):
        clone = self.order_by().alias('_wrapped')
        if clear_limit:
            clone._limit = clone._offset = None
        try:
            if clone._having is None and clone._windows is None and \
               clone._distinct is None and clone._simple_distinct is not True:
                clone = clone.select(SQL('1'))
        except AttributeError:
            pass
        return Select([clone], [fn.COUNT(SQL('1'))]).scalar(database)

    @database_required
    def exists(self, database):
        clone = self.columns(SQL('1'))
        clone._limit = 1
        clone._offset = None
        return bool(clone.scalar())

    @database_required
    def get(self, database):
        self._cursor_wrapper = None
        try:
            return self.execute(database)[0]
        except IndexError:
            pass
```

--------------------------------

### Create Example Knots and Links

Source: https://pyknotid.readthedocs.io/en/latest/sources/overview.html

Generate example knotted space curves using functions like `torus_knot`, `torus_link`, and `figure_eight`. This snippet shows how to create different types of knots and links and perform basic checks.

```python
from pyknotid.make import torus_knot, torus_link, figure_eight

k = torus_knot(p=5, q=2)
k.identify()  # [<Knot 5_1>]

from pyknotid.make import torus_link

l = torus_link(p=2, q=8)  # a 2-component link
l.linking_number()  # 8

from pyknotid.make import figure_eight

k = figure_eight()
k.determinant()  # 5

```

--------------------------------

### Establish MySQL Database Connection

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Establishes a connection to the MySQL database using the installed driver. Raises an error if the MySQL driver is not available.

```python
def _connect(self):
        if mysql is None:
            raise ImproperlyConfigured('MySQL driver not installed!')
        return mysql.connect(db=self.database, **self.connect_params)
```

--------------------------------

### Get Model Instance by Primary Key

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves a single instance of the model using its primary key. This is a shortcut for `get` when you know the primary key value.

```python
@classmethod
    def get_by_id(cls, pk):
        return cls.get(cls._meta.primary_key == pk)
```

--------------------------------

### Get Database Download Directory

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/catalogue/getdb.html

Returns the directory where the knots database will be downloaded. This path is determined using the appdirs library.

```python
from pyknotid.catalogue.getdb import download_target_dir

dir = download_target_dir()
print(f'Database will be downloaded to: {dir}')
```

--------------------------------

### VisPy Canvas Setup for Mesh Rendering

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/visualise.html

Configures and displays a mesh on a VisPy canvas. This snippet sets up the camera and adds the mesh to the scene for interactive viewing.

```python
from vispy.scene import TurntableCamera, Mesh
# Assuming 'mesh' is a VisPy Mesh object and 'vispy_canvas' is an initialized canvas
# from pyknotid.visualise.vispy_utils import ensure_vispy_canvas, clear_vispy_canvas, vispy_canvas

# Placeholder for mesh and canvas initialization if not in context:
# vertices = np.random.rand(10, 3)
# indices = [[0, 1, 2], [0, 2, 3]]
# mesh = Mesh(vertices, indices)
# ensure_vispy_canvas()
# clear_vispy_canvas()

vispy_canvas.view.camera = TurntableCamera(fov=0, elevation=90.)
vispy_canvas.view.add(mesh)
vispy_canvas.show()

```

--------------------------------

### Get or Create Model Instance

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Attempts to retrieve a model instance based on the provided keyword arguments. If found, it returns the instance and `False`. If not found, it creates a new instance using the provided arguments and optional defaults, saves it, and returns the new instance and `True`. Handles potential `IntegrityError` during creation by retrying retrieval.

```python
@classmethod
    def get_or_create(cls, **kwargs):
        defaults = kwargs.pop('defaults', {})
        query = cls.select()
        for field, value in kwargs.items():
            query = query.where(getattr(cls, field) == value)

        try:
            return query.get(), False
        except cls.DoesNotExist:
            try:
                if defaults:
                    kwargs.update(defaults)
                with cls._meta.database.atomic():
                    return cls.create(**kwargs), True
            except IntegrityError as exc:
                try:
                    return query.get(), False
                except cls.DoesNotExist:
                    raise exc
```

--------------------------------

### Get Peewee Tables Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Placeholder method to retrieve a list of table names. Raises NotImplementedError if not implemented.

```python
def get_tables(self, schema=None):
    raise NotImplementedError
```

--------------------------------

### Get Peewee SQL Context Options

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the current context options for generating SQL, including field types, operations, and quoting settings.

```python
def get_context_options(self):
    return {
        'field_types': self._field_types,
        'operations': self._operations,
        'param': self.param,
        'quote': self.quote,
        'compound_select_parentheses': self.compound_select_parentheses,
        'conflict_statement': self.conflict_statement,
        'conflict_update': self.conflict_update,
        'for_update': self.for_update,
        'limit_max': self.limit_max,
    }
```

--------------------------------

### Get Exterior Manifold

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/representations/representation.html

Retrieves the knot complement manifold as a SnapPy class, providing access to SnapPy's tools. Requires Spherogram and potentially SnapPy to be installed.

```python
return self.planar_diagram().as_spherogram().exterior()
```

--------------------------------

### Model Query Helper Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes the ModelQueryHelper, setting the database if not already defined.

```python
super(_ModelQueryHelper, self).__init__(*args, **kwargs)
        if not self._database:
            self._database = self.model._meta.database
```

--------------------------------

### Context Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes the Context with a stack for states, SQL components, values, an AliasManager, and an initial State.

```python
class Context(object):
    def __init__(self, **settings):
        self.stack = []
        self._sql = []
        self._values = []
        self.alias_manager = AliasManager()
        self.state = State(**settings)
```

--------------------------------

### Get Peewee Foreign Keys Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Placeholder method to retrieve foreign key information for a table. Raises NotImplementedError if not implemented.

```python
def get_foreign_keys(self, table, schema=None):
    raise NotImplementedError
```

--------------------------------

### Create a New Model Instance and Save

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Creates a new instance of the model with the provided query parameters and immediately saves it to the database. `force_insert=True` ensures it's an insert operation.

```python
@classmethod
    def create(cls, **query):
        inst = cls(**query)
        inst.save(force_insert=True)
        return inst
```

--------------------------------

### retrieve_space_curve

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/representations/representation.html

Retrieves the space curve representation of a knot given specific starting and connection information. It handles cases with one or two possible starting lines.

```APIDOC
## retrieve_space_curve

### Description
Retrieves the space curve representation of a knot. It determines the path of the curve by following connected lines and their associated arc numbers and heights.

### Method
This is a method of the Representation class, called as an instance method.

### Parameters
*   **first** (Node) - The starting node for curve retrieval.
*   **next** (Node) - The next node in the sequence from the 'first' node.
*   **initial_arc_number** (int) - The starting arc number for the curve.
*   **heights** (dict) - A dictionary mapping (start_node, end_node, arc_number) to height values.

### Returns
(numpy.ndarray) - An array representing the segments of the space curve.
```

--------------------------------

### Get a Single Model Instance or None

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves a single instance of the model, returning `None` if no matching record is found. This is a safe alternative to `get` that avoids exceptions.

```python
@classmethod
    def get_or_none(cls, *query, **filters):
        try:
            return cls.get(*query, **filters)
        except DoesNotExist:
            pass
```

--------------------------------

### Peewee Database Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a Peewee database instance, setting up connection parameters and handling deferred initialization.

```python
def __init__(self, database, thread_safe=True, autorollback=False,
                 field_types=None, operations=None, autocommit=None, **kwargs):
    self._field_types = merge_dict(FIELD, self.field_types)
    self._operations = merge_dict(OP, self.operations)
    if field_types:
        self._field_types.update(field_types)
    if operations:
        self._operations.update(operations)

    self.autorollback = autorollback
    self.thread_safe = thread_safe
    if thread_safe:
        self._state = _ConnectionLocal()
        self._lock = threading.Lock()
    else:
        self._state = _ConnectionState()
        self._lock = _NoopLock()

    if autocommit is not None:
        __deprecated__('Peewee no longer uses the "autocommit" option, as ' 
                       'the semantics now require it to always be True. ' 
                       'Because some database-drivers also use the ' 
                       '"autocommit" parameter, you are receiving a ' 
                       'warning so you may update your code and remove ' 
                       'the parameter, as in the future, specifying ' 
                       'autocommit could impact the behavior of the ' 
                       'database driver you are using.')

    self.connect_params = {}
    self.init(database, **kwargs)

def init(self, database, **kwargs):
    if not self.is_closed():
        self.close()
    self.database = database
    self.connect_params.update(kwargs)
    self.deferred = not bool(database)
```

--------------------------------

### Get SQLite Table Foreign Keys

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves metadata for foreign key constraints on a specified SQLite table. It uses the `foreign_key_list` PRAGMA to get constraint details.

```python
def get_foreign_keys(self, table, schema=None):
        cursor = self.execute_sql('PRAGMA "%s".foreign_key_list("%s")' %
                                  (schema or 'main', table))
        return [ForeignKeyMetadata(row[3], row[2], row[4], table)
                for row in cursor.fetchall()]
```

--------------------------------

### Create All Tables

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Creates all tables defined in the schema. Supports a 'safe' mode to prevent errors if tables already exist.

```python
if safe and not cls._meta.database.safe_create_index \
           and cls.table_exists():
            return
        cls._schema.create_all(safe, **options)
```

--------------------------------

### ModelRaw Get Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves a single instance from a raw query. Raises Model.DoesNotExist if no matching instance is found, providing the SQL and parameters used.

```python
def get(self):
        try:
            return self.execute()[0]
        except IndexError:
            sql, params = self.sql()
            raise self.model.DoesNotExist('%s instance matching query does '
                                          'not exist:\nSQL: %s\nParams: %s' % 
                                          (self.model, sql, params))
```

--------------------------------

### PostgreSQL Database Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a PostgreSQL database connection, optionally registering Unicode types and setting client encoding. Requires the `psycopg2` driver.

```python
def init(self, database, register_unicode=True, encoding=None, **kwargs):
        self._register_unicode = register_unicode
        self._encoding = encoding
        self._need_server_version = True
        super(PostgresqlDatabase, self).init(database, **kwargs)
```

--------------------------------

### Get Single Instance with Pagination

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves a single instance by applying pagination to limit results to one. Raises Model.DoesNotExist if no record is found, including the SQL and parameters.

```python
def get(self):
        clone = self.paginate(1, 1)
        clone._cursor_wrapper = None
        try:
            return clone.execute()[0]
        except IndexError:
            sql, params = clone.sql()
            raise self.model.DoesNotExist('%s instance matching query does ' 
                                          'not exist:\nSQL: %s\nParams: %s' % 
                                          (clone.model, sql, params))
```

--------------------------------

### Begin Peewee Database Connection

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Ensures the database connection is established, connecting if it's currently closed.

```python
def begin(self):
    if self.is_closed():
        self.connect()
```

--------------------------------

### Get Schema

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the schema name associated with the model's metadata.

```python
@property
    def schema(self):
        return self._schema
```

--------------------------------

### SqliteDatabase Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes the SqliteDatabase, setting up pragmas, timeout, and other connection parameters. It handles pragmas provided as a dictionary or a list of tuples.

```python
def __init__(self, database, *args, **kwargs):
        self._pragmas = kwargs.pop('pragmas', ())
        super(SqliteDatabase, self).__init__(database, *args, **kwargs)
        self._aggregates = {}
        self._collations = {}
        self._functions = {}
        self._table_functions = []
        self._extensions = set()
        self._attached = {}
        self.register_function(_sqlite_date_part, 'date_part', 2)
        self.register_function(_sqlite_date_trunc, 'date_trunc', 2)
```

```python
def init(self, database, pragmas=None, timeout=5, **kwargs):
        if pragmas is not None:
            self._pragmas = pragmas
        if isinstance(self._pragmas, dict):
            self._pragmas = list(self._pragmas.items())
        self._timeout = timeout
        super(SqliteDatabase, self).init(database, **kwargs)
```

--------------------------------

### Get Peewee Transaction Depth

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the current number of nested transactions.

```python
def transaction_depth(self):
    return len(self._state.transactions)
```

--------------------------------

### Get Default Data for Insert

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns a dictionary of default values for insertable fields.

```python
def get_default_data(self):
        return {}
```

--------------------------------

### Link Class Initialization

Source: https://pyknotid.readthedocs.io/en/latest/sources/spacecurves/link.html

Initializes a Link instance with a list of lines and an optional verbose flag.

```APIDOC
## Link(lines, verbose=True)

### Description
Class for holding the vertices of multiple lines, providing helper methods for convenient manipulation and analysis. The data is stored internally as multiple :class:`Knot`s.

### Parameters
#### Parameters
- **lines** (list of nx3 array-like or Knots) – List with the points of each line.
- **verbose** (bool) – Whether to print information during processing. Defaults to True.
```

--------------------------------

### AliasManager GetItem

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Allows dictionary-style access to retrieve an alias using the get method.

```python
    def __getitem__(self, source):
        return self.get(source)
```

--------------------------------

### close

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/spacecurves/spacecurve.html

Adds the starting point to the end of the curve, ensuring it ends exactly where it began.

```APIDOC
## close

### Description
Adds the starting point to the end of the curve, so that it ends exactly where it began.

### Method
N/A (This is a method of a class)

### Parameters
None

### Request Example
N/A

### Response
N/A (Modifies the object in-place)
```

--------------------------------

### Peewee _ModelWriteQueryHelper Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a helper class for write operations (INSERT, UPDATE, DELETE) on models. It inherits from _ModelQueryHelper and sets up the model context for write queries.

```python
def __init__(self, model, *args, **kwargs):
        self.model = model
        super(_ModelWriteQueryHelper, self).__init__(model, *args, **kwargs)
```

--------------------------------

### Get SQLite Binary Type

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the appropriate type for binary data in SQLite, which is `sqlite3.Binary`.

```python
def get_binary_type(self):
        return sqlite3.Binary
```

--------------------------------

### Schema Manager Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes the SchemaManager with a model, an optional database, and context options.

```python
def __init__(self, model, database=None, **context_options):
        self.model = model
        self._database = database
        context_options.setdefault('scope', SCOPE_VALUES)
        self.context_options = context_options
```

--------------------------------

### Model Initialization and Configuration

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Defines the constructor for Peewee models, handling initial data population and tracking dirty fields. Includes class methods for aliasing and selecting fields.

```python
def __init__(self, *args, **kwargs):
        if kwargs.pop('__no_default__', None):
            self.__data__ = {}
        else:
            self.__data__ = self._meta.get_default_dict()
        self._dirty = set(self.__data__)
        self.__rel__ = {}

        for k in kwargs:
            setattr(self, k, kwargs[k])

    def __str__(self):
        return str(self._pk) if self._meta.primary_key is not False else 'n/a'

    @classmethod
    def validate_model(cls):
        pass

    @classmethod
    def alias(cls, alias=None):
        return ModelAlias(cls, alias)

    @classmethod
    def select(cls, *fields):
        is_default = not fields
        if not fields:
            fields = cls._meta.sorted_fields
        return ModelSelect(cls, fields, is_default=is_default)
```

--------------------------------

### Close the Curve

Source: https://pyknotid.readthedocs.io/en/latest/sources/spacecurves/spacecurve.html

Appends the starting point to the end of the curve, ensuring it closes exactly where it began.

```python
close()
```

--------------------------------

### from_qwer()

Source: https://pyknotid.readthedocs.io/en/latest/genindex.html

Creates a Cell from qwer data.

```APIDOC
## from_qwer()

### Description
Creates a Cell from qwer data.

### Method
N/A (Class method of Cell)

### Endpoint
N/A (SDK Class Method)

### Parameters
N/A

### Request Example
N/A

### Response
N/A
```

--------------------------------

### Get Dirty Fields of a Peewee Instance

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns a list of field names that have been modified on the model instance.

```python
@property
def dirty_fields(self):
    return [f for f in self._meta.sorted_fields if f.name in self._dirty]
```

--------------------------------

### Initialize Insert Query

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes an INSERT query with the table, data to insert, and optional columns or conflict handling.

```python
def __init__(self, table, insert=None, columns=None, on_conflict=None,
                 **kwargs):
        super(Insert, self).__init__(table, **kwargs)
        self._insert = insert
        self._columns = columns
        self._on_conflict = on_conflict
        self._query_type = None
```

--------------------------------

### Get Primary Key of Model Instance

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the primary key value of the current model instance.

```python
def get_id(self):
        return getattr(self, self._meta.primary_key.name)

    _pk = property(get_id)
```

--------------------------------

### Get Entity

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns an Entity object representing the model's table, including schema if specified.

```python
@property
    def entity(self):
        if self._schema:
            return Entity(self._schema, self.table_name)
        else:
            return Entity(self.table_name)
```

--------------------------------

### CompositeKey Get Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the composite key value for a given instance as a tuple of attribute values.

```python
def __get__(self, instance, instance_type=None):
        if instance is not None:
            return tuple([getattr(instance, field_name)
                          for field_name in self.field_names])
        return self
```

--------------------------------

### Initialize Link from periodic lines

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/spacecurves/link.html

Creates a Link instance by unwrapping lines through periodic boundaries. Optionally perturbs the knot to avoid lattice issues.

```python
link = cls(lines)
        if perturb:
            link.translate(n.array([0.00123, 0.00231, 0.00321]))
            link.rotate()
```

--------------------------------

### Get Last Insert ID from Cursor

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the ID of the last inserted row from a database cursor.

```python
def last_insert_id(self, cursor, query_type=None):
    return cursor.lastrowid
```

--------------------------------

### Applying Ordering and Limits in Peewee Queries

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Applies ordering, limit, and offset clauses to the SQL context. It handles cases where limit or offset might be None or use a default maximum limit.

```python
def _apply_ordering(self, ctx):
        if self._order_by:
            (ctx
             .literal(' ORDER BY ')
             .sql(CommaNodeList(self._order_by)))
        if self._limit is not None or (self._offset is not None and
                                       ctx.state.limit_max):
            ctx.literal(' LIMIT ').sql(self._limit or ctx.state.limit_max)
        if self._offset is not None:
            ctx.literal(' OFFSET ').sql(self._offset)
        return ctx
```

--------------------------------

### Get Table Object

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the Table object associated with the model's metadata. Creates it if it doesn't exist.

```python
@property
    def table(self):
        if self._table is None:
            self._table = Table(
                self.table_name,
                [field.column_name for field in self.sorted_fields],
                schema=self.schema,
                alias=self.table_alias,
                _model=self.model,
                _database=self.database)
        return self._table
```

--------------------------------

### Get MySQL Binary Type

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the MySQL-specific binary type object. Used for handling binary data.

```python
def get_binary_type(self):
        return mysql.Binary
```

--------------------------------

### VirtualField Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a VirtualField, optionally accepting a specific field class. It stores an instance of the field if provided.

```python
class VirtualField(MetaField):
    field_class = None

    def __init__(self, field_class=None, *args, **kwargs):
        Field = field_class if field_class is not None else self.field_class
        self.field_instance = Field() if Field is not None else None
        super(VirtualField, self).__init__(*args, **kwargs)
```

--------------------------------

### Get MySQL Column Metadata

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves metadata for columns of a given MySQL table. Queries the 'information_schema.columns' table.

```python
def get_columns(self, table, schema=None):
        sql = """
            SELECT column_name, is_nullable, data_type, column_default
            FROM information_schema.columns
            WHERE table_name = %s AND table_schema = DATABASE()"""
        cursor = self.execute_sql(sql, (table,))
        pks = set(self.get_primary_keys(table))
        return [ColumnMetadata(name, dt, null == 'YES', name in pks, table, df)
                for name, null, dt, df in cursor.fetchall()]
```

--------------------------------

### Get Peewee Columns Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Placeholder method to retrieve column information for a table. Raises NotImplementedError if not implemented.

```python
def get_columns(self, table, schema=None):
    raise NotImplementedError
```

--------------------------------

### Get Peewee Indexes Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Placeholder method to retrieve index information for a table. Raises NotImplementedError if not implemented.

```python
def get_indexes(self, table, schema=None):
    raise NotImplementedError
```

--------------------------------

### Handle Simple INSERT

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Generates the SQL for a simple INSERT statement with provided data.

```python
def _simple_insert(self, ctx):
        if not self._insert:
            raise self.DefaultValuesException('Error: no data to insert.')
        return self._generate_insert((self._insert,), ctx)
```

--------------------------------

### Model Metadata Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes model metadata, including table name, indexes, constraints, and relationships. Handles table name generation if not explicitly provided.

```python
self.name = model.__name__.lower()
        self.table_function = table_function
        if not table_name:
            table_name = (self.table_function(model)
                          if self.table_function
                          else re.sub('[^\\w]+', '_', self.name))
        self.table_name = table_name
        self._table = None

        self.indexes = list(indexes) if indexes else []
        self.constraints = constraints
        self._schema = schema
        self.primary_key = primary_key
        self.composite_key = self.auto_increment = None
        self.only_save_dirty = only_save_dirty
        self.table_alias = table_alias
        self.depends_on = depends_on
        self.without_rowid = without_rowid

        self.refs = {}
        self.backrefs = {}
        self.model_refs = collections.defaultdict(list)
        self.model_backrefs = collections.defaultdict(list)
        self.manytomany = {}

        self.options = options or {}
        for key, value in kwargs.items():
            setattr(self, key, value)
        self._additional_keys = set(kwargs.keys())
```

--------------------------------

### Get Rows Affected from Cursor

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the number of rows affected by the last executed query from a database cursor.

```python
def rows_affected(self, cursor):
    return cursor.rowcount
```

--------------------------------

### Column Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a Column object with its source and name.

```python
class Column(ColumnBase):
    def __init__(self, source, name):
        self.source = source
        self.name = name
```

--------------------------------

### close

Source: https://pyknotid.readthedocs.io/en/latest/sources/spacecurves/spacecurve.html

Modifies the SpaceCurve in-place by adding the starting point to the end of the curve, ensuring it forms a closed loop.

```APIDOC
## close

### Description
Adds the starting point to the end of the curve, so that it ends exactly where it began.
```

--------------------------------

### State Call Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Creates a new State instance, inheriting most settings from the current state but allowing overrides for scope, parentheses, subquery, and other settings.

```python
    def __call__(self, scope=None, parentheses=None, subquery=None, **kwargs):
        # All state is "inherited" except parentheses.
        scope = self.scope if scope is None else scope
        subquery = self.subquery if subquery is None else subquery

        # Try to avoid unnecessary dict copying.
        if kwargs and self.settings:
            settings = self.settings.copy()  # Copy original settings dict.
            settings.update(kwargs)  # Update copy with overrides.
        elif kwargs:
            settings = kwargs
        else:
            settings = self.settings
        return State(scope, parentheses, subquery, **settings)
```

--------------------------------

### Enter Peewee Manual Commit Mode

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns a context manager for manual transaction commit control.

```python
def manual_commit(self):
    return _manual(self)
```

--------------------------------

### Download Database

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/catalogue/getdb.html

Downloads the knots database to the target directory. It creates the directory if it doesn't exist and raises an IOError if the file already exists. Uses requests and tqdm for downloading and progress display.

```python
from pyknotid.catalogue.getdb import download_database

try:
    download_database()
    print('Database downloaded successfully.')
except IOError as e:
    print(f'Error: {e}')
```

--------------------------------

### Peewee FieldAccessor

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Base class for accessing model fields. Handles getting and setting field values on model instances.

```python
class FieldAccessor(object):
    def __init__(self, model, field, name):
        self.model = model
        self.field = field
        self.name = name

    def __get__(self, instance, instance_type=None):
        if instance is not None:
            return instance.__data__.get(self.name)
        return self.field

    def __set__(self, instance, value):
        instance.__data__[self.name] = value
        instance._dirty.add(self.name)
```

--------------------------------

### Get MySQL Foreign Keys

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves metadata for foreign key constraints on a given MySQL table. Queries 'information_schema.key_column_usage'.

```python
def get_foreign_keys(self, table, schema=None):
        query = """
            SELECT column_name, referenced_table_name, referenced_column_name
            FROM information_schema.key_column_usage
            WHERE table_name = %s
                AND table_schema = DATABASE()
                AND referenced_table_name IS NOT NULL
                AND referenced_column_name IS NOT NULL"""
        cursor = self.execute_sql(query, (table,))
        return [
            ForeignKeyMetadata(column, dest_table, dest_column, table)
            for column, dest_table, dest_column in cursor.fetchall()]
```

--------------------------------

### Peewee Index Class SQL Generation

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

This snippet demonstrates the SQL generation for creating indexes, including unique, safe (IF NOT EXISTS), and USING clauses.

```python
def __sql__(self, ctx):
        statement = 'CREATE UNIQUE INDEX ' if self._unique else 'CREATE INDEX ' 
        with ctx.scope_values(subquery=True):
            ctx.literal(statement)
            if self._safe:
                ctx.literal('IF NOT EXISTS ')
            (ctx
             .sql(Entity(self._name))
             .literal(' ON ')
             .sql(self._table)
             .literal(' '))
            if self._using is not None:
                ctx.literal('USING %s ' % self._using)
```

--------------------------------

### Get MySQL Index Metadata

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves metadata for indexes on a given MySQL table. Parses the output of 'SHOW INDEX FROM'.

```python
def get_indexes(self, table, schema=None):
        cursor = self.execute_sql('SHOW INDEX FROM `%s`' % table)
        unique = set()
        indexes = {}
        for row in cursor.fetchall():
            if not row[1]:
                unique.add(row[2])
            indexes.setdefault(row[2], [])
            indexes[row[2]].append(row[4])
        return [IndexMetadata(name, None, indexes[name], name in unique, table)
                for name in indexes]
```

--------------------------------

### Enter Peewee Savepoint

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns a context manager for managing database savepoints.

```python
def savepoint(self):
    return _savepoint(self)
```

--------------------------------

### Peewee Select Query Building

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Demonstrates the internal methods used to construct a SQL SELECT query in Peewee, including handling joins, grouping, filtering, and ordering.

```Python
    @Node.copy
    def join(self, dest, join_type='INNER', on=None):
        if not self._from_list:
            raise ValueError('No sources to join on.')
        item = self._from_list.pop()
        self._from_list.append(Join(item, dest, join_type, on))

    @Node.copy
    def group_by(self, *columns):
        grouping = []
        for column in columns:
            if isinstance(column, Table):
                if not column._columns:
                    raise ValueError('Cannot pass a table to group_by() that '
                                     'does not have columns explicitly '
                                     'declared.')
                grouping.extend([getattr(column, col_name)
                                 for col_name in column._columns])
            else:
                grouping.append(column)
        self._group_by = grouping

    @Node.copy
    def group_by_extend(self, *values):
        group_by = tuple(self._group_by or ()) + values
        return self.group_by(*group_by)

    @Node.copy
    def having(self, *expressions):
        if self._having is not None:
            expressions = (self._having,) + expressions
        self._having = reduce(operator.and_, expressions)

    @Node.copy
    def distinct(self, *columns):
        if len(columns) == 1 and (columns[0] is True or columns[0] is False):
            self._simple_distinct = columns[0]
        else:
            self._simple_distinct = False
            self._distinct = columns

    @Node.copy
    def window(self, *windows):
        self._windows = windows if windows else None

    @Node.copy
    def for_update(self, for_update=True):
        self._for_update = 'FOR UPDATE' if for_update is True else for_update

    def _get_query_key(self):
        return self._alias

    def __sql_selection__(self, ctx, is_subquery=False):
        return ctx.sql(CommaNodeList(self._returning))

    def __sql__(self, ctx):
        super(Select, self).__sql__(ctx)
        if ctx.scope == SCOPE_COLUMN:
            return self.apply_column(ctx)

        is_subquery = ctx.subquery
        state = {
            'converter': None,
            'in_function': False,
            'parentheses': is_subquery or (ctx.scope == SCOPE_SOURCE),
            'subquery': True,
        }
        if ctx.state.in_function:
            state['parentheses'] = False

        with ctx.scope_normal(**state):
            ctx.literal('SELECT ')
            if self._simple_distinct or self._distinct is not None:
                ctx.literal('DISTINCT ')
                if self._distinct:
                    (ctx
                     .literal('ON ')
                     .sql(EnclosedNodeList(self._distinct))
                     .literal(' '))

            with ctx.scope_source():
                ctx = self.__sql_selection__(ctx, is_subquery)

            if self._from_list:
                with ctx.scope_source(parentheses=False):
                    ctx.literal(' FROM ').sql(CommaNodeList(self._from_list))

            if self._where is not None:
                ctx.literal(' WHERE ').sql(self._where)

            if self._group_by:
                ctx.literal(' GROUP BY ').sql(CommaNodeList(self._group_by))

            if self._having is not None:
                ctx.literal(' HAVING ').sql(self._having)

            if self._windows is not None:
                ctx.literal(' WINDOW ')
                ctx.sql(CommaNodeList(self._windows))

            # Apply ORDER BY, LIMIT, OFFSET.
            self._apply_ordering(ctx)

            if self._for_update:
                if not ctx.state.for_update:
                    raise ValueError('FOR UPDATE specified but not supported '
                                     'by database.')
                ctx.literal(' ')
                ctx.sql(SQL(self._for_update))

        if not ctx.state.in_function:
            ctx = self.apply_alias(ctx)
        return ctx
```

--------------------------------

### Get Top Peewee Transaction

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns the most recent transaction object from the stack without removing it, or None if no transactions are active.

```python
def top_transaction(self):
    if self._state.transactions:
        return self._state.transactions[-1]
```

--------------------------------

### Sorted Field List Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes an empty list for storing sorted fields.

```python
def __init__(self):
        self._keys = []
        self._items = []
```

--------------------------------

### AliasManager Get Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Retrieves the alias for a given source. If any_depth is True, it searches through all mapping scopes from the most recent to the oldest.

```python
    def get(self, source, any_depth=False):
        if any_depth:
            for idx in reversed(range(self._current_index)):
                if source in self._mapping[idx]:
                    return self._mapping[idx][source]
        return self.add(source)
```

--------------------------------

### Download Knot Database

Source: https://pyknotid.readthedocs.io/en/latest/sources/catalogue/index.html

Downloads the pre-built knot database. This is necessary for explicit knot identification and direct database queries. The download may take a few seconds.

```python
from pyknotid.catalogue.getdb import download_database
download_database()
```

--------------------------------

### PlanarDiagram as Extended NetworkX Graph

Source: https://pyknotid.readthedocs.io/en/latest/sources/representations/planardiagram.html

Internal use method to get a NetworkX graph along with additional crossing information.

```python
as_networkx_extended() -> (Graph, dict)
```

--------------------------------

### ValuesList Class Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a ValuesList object with a list of values and optional column names.

```python
class ValuesList(BaseTable):
    def __init__(self, values, columns=None, alias=None):
        super(ValuesList, self).__init__(alias=alias)
        self._values = values
        self._columns = columns
```

--------------------------------

### Peewee ModelInsert Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a ModelInsert query. If a RETURNING clause is not specified and the database supports it, it defaults to returning primary keys.

```python
def __init__(self, *args, **kwargs):
        super(ModelInsert, self).__init__(*args, **kwargs)
        if self._returning is None and self.model._meta.database is not None:
            if self.model._meta.database.returning_clause:
                self._returning = self.model._meta.get_primary_keys()
                self._row_type = ROW.TUPLE
```

--------------------------------

### SpaceCurve.plot_projection

Source: https://pyknotid.readthedocs.io/en/latest/sources/spacecurves/spacecurve.html

Plots a 2D diagram of the knot projected along the current z-axis, with options to mark crossings and the start point.

```APIDOC
## SpaceCurve.plot_projection

### Description
Plots a 2D diagram of the knot projected along the current z-axis. The crossings, and start point of the curve, can optionally be marked.

### Method
Instance Method

### Parameters
#### Path Parameters
None

#### Query Parameters
- **with_crossings** (bool) - Optional - If True, marks the location of each self-intersection in projection. Defaults to True.
- **mark_start** (bool) - Optional - If True, marks the first point of the curve. Defaults to False.
- **fig_ax** (tuple) - Optional - A 2-tuple of the matplotlib (fig, ax) to use, or None to create a new pair.
- **show** (bool) - Optional - If True, opens a new window showing the drawing. Defaults to True.

#### Request Body
None

### Returns
A 2-tuple of the matplotlib (fig, ax) used for the drawing.
```

--------------------------------

### Loading SQLite Functions

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Registers custom scalar functions with the SQLite connection. This method is called internally during connection setup.

```python
def _load_functions(self, conn):
        for name, (fn, num_params) in self._functions.items():
            conn.create_function(name, num_params, fn)
```

--------------------------------

### Loading SQLite Collations

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Registers custom collation sequences with the SQLite connection. This method is called internally during connection setup.

```python
def _load_collations(self, conn):
        for name, fn in self._collations.items():
            conn.create_collation(name, fn)
```

--------------------------------

### Schema Manager Context Creation

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Creates and returns an SQL context for the associated database with the specified options.

```python
def _create_context(self):
        return self.database.get_sql_context(**self.context_options)
```

--------------------------------

### Context Enter Method (Parentheses)

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Enters the context manager. If parentheses are enabled in the current state, it appends a literal '(' to the SQL.

```python
    def __enter__(self):
        if self.parentheses:
            self.literal('(')
        return self
```

--------------------------------

### Loading SQLite Aggregates

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Registers custom aggregate functions with the SQLite connection. This method is called internally during connection setup.

```python
def _load_aggregates(self, conn):
        for name, (klass, num_params) in self._aggregates.items():
            conn.create_aggregate(name, num_params, klass)
```

--------------------------------

### ManyToManyField Get Models Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Returns a list of the two models involved in the many-to-many relationship, ordered by whether they are the back reference.

```python
def get_models(self):
        return [model for _, model in sorted((
            (self._is_backref, self.model),
            (not self._is_backref, self.rel_model)))]
```

--------------------------------

### Peewee Ordering __sql__ Method

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Generates SQL for ordering clauses, including direction, collation, and NULLS handling.

```python
def __sql__(self, ctx):
        ctx.sql(self.node).literal(' %s' % self.direction)
        if self.collation:
            ctx.literal(' COLLATE %s' % self.collation)
        if self.nulls:
            ctx.literal(' NULLS %s' % self.nulls)
        return ctx
```

--------------------------------

### Insert from a Query

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Prepares an operation to insert data into the model's table from the results of another query. Requires the query and a list of fields to map the results to.

```python
@classmethod
    def insert_from(cls, query, fields):
        columns = [getattr(cls, field) if isinstance(field, basestring)
                   else field for field in fields]
        return ModelInsert(cls, insert=query, columns=columns)
```

--------------------------------

### Get Peewee Primary Keys Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Placeholder method to retrieve primary key information for a table. Raises NotImplementedError if not implemented.

```python
def get_primary_keys(self, table, schema=None):
    raise NotImplementedError
```

--------------------------------

### Initialize Update Query

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes an UPDATE query with the table to update and the fields to set.

```python
def __init__(self, table, update=None, **kwargs):
        super(Update, self).__init__(table, **kwargs)
        self._update = update
        self._from = None
```

--------------------------------

### Access Knot Property Directly

Source: https://pyknotid.readthedocs.io/en/latest/sources/catalogue/index.html

Accesses a specific property of a knot object directly as an attribute. This example retrieves the determinant of a knot.

```python
k.determinant  # 7
```

--------------------------------

### PostgreSQL Database Connection

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Establishes a connection to the PostgreSQL database using `psycopg2`. Handles Unicode type registration and client encoding if specified during initialization.

```python
def _connect(self):
        if psycopg2 is None:
            raise ImproperlyConfigured('Postgres driver not installed!')
        conn = psycopg2.connect(database=self.database, **self.connect_params)
        if self._register_unicode:
            pg_extensions.register_type(pg_extensions.UNICODE, conn)
            pg_extensions.register_type(pg_extensions.UNICODEARRAY, conn)
        if self._encoding:
            conn.set_client_encoding(self._encoding)
        if self._need_server_version:
            self.set_server_version(conn.server_version)
            self._need_server_version = False
        return conn
```

--------------------------------

### PrimaryKeyField Deprecation Warning

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Handles initialization for PrimaryKeyField, which is now an alias for AutoField. Includes a deprecation warning to guide users to update their code.

```python
class PrimaryKeyField(AutoField):
    def __init__(self, *args, **kwargs):
        __deprecated__('"PrimaryKeyField" has been renamed to "AutoField". ')
        super(PrimaryKeyField, self).__init__(*args, **kwargs)
```

--------------------------------

### download_target_dir

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/catalogue/getdb.html

Returns the directory to which the knots database will be downloaded.

```APIDOC
## download_target_dir

### Description
Returns the directory to which the knots database will be downloaded.

### Method
GET

### Endpoint
/download_target_dir

### Parameters
None

### Response
#### Success Response
- **string** - The path to the download directory.

#### Response Example
```
/path/to/user/data/pyknotid
```
```

--------------------------------

### Cursor Wrapper Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a wrapper around a database cursor to manage query results. It includes attributes for tracking row count, index, and caching.

```python
class CursorWrapper(object):
    def __init__(self, cursor):
        self.cursor = cursor
        self.count = 0
        self.index = 0
        self.initialized = False
        self.populated = False
        self.row_cache = []
```

--------------------------------

### Populate Instance with Prefetched Data

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Populates a model instance with data from a prefetch query. It uses an ID map to efficiently link related objects to the primary instance based on whether it's a backreference or a forward relationship.

```python
def populate_instance(self, instance, id_map):
        if self.is_backref:
            for field in self.fields:
                identifier = instance.__data__[field.name]
                key = (field, identifier)
                if key in id_map:
                    setattr(instance, field.name, id_map[key])
        else:
            for field, attname in self.field_to_name:
                identifier = instance.__data__[field.rel_field.name]
                key = (field, identifier)
                rel_instances = id_map.get(key, [])
                for inst in rel_instances:
                    setattr(inst, attname, instance)
                setattr(instance, field.backref, rel_instances)
```

--------------------------------

### Parsing Matrix String with cypari

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/invariants.html

Converts the constructed matrix string into a cypari polynomial representation. Requires the 'cypari' library to be installed and imported.

```python
from cypari.gen import pari
    return pari(''.join(outstrs))
```

--------------------------------

### Table Class Initialization

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Initializes a Table object, setting up its name, columns, primary key, schema, and model associations. It also dynamically creates column attributes if columns are provided.

```python
class Table(_HashableSource, BaseTable):
    def __init__(self, name, columns=None, primary_key=None, schema=None,
                 alias=None, _model=None, _database=None):
        self.__name__ = name
        self._columns = columns
        self._primary_key = primary_key
        self._schema = schema
        self._path = (schema, name) if schema else (name,)
        self._model = _model
        self._database = _database
        super(Table, self).__init__(alias=alias)

        # Allow tables to restrict what columns are available.
        if columns is not None:
            self.c = _ExplicitColumn()
            for column in columns:
                setattr(self, column, Column(self, column))

        if primary_key:
            col_src = self if self._columns else self.c
            self.primary_key = getattr(col_src, primary_key)
        else:
            self.primary_key = None
```

--------------------------------

### Plotting Function Dispatcher

Source: https://pyknotid.readthedocs.io/en/latest/_modules/pyknotid/visualise.html

Selects the appropriate plotting backend based on the 'mode' parameter. Ensure the required backend (mayavi or vispy) is installed.

```python
if mode == 'mayavi':
    plot_cell_mayavi(lines, **kwargs)
elif mode == 'vispy':
    plot_cell_vispy(lines, zero_centroid=False, **kwargs)
else:
    raise ValueError('invalid toolkit/mode')
```

--------------------------------

### Schema Manager Database Property

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Gets or sets the database associated with the schema manager. Defaults to the model's database if not explicitly set.

```python
@property
def database(self):
        return self._database or self.model._meta.database

    @database.setter
def database(self, value):
        self._database = value
```

--------------------------------

### Cursor Wrapper Initialization Placeholder

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

A placeholder method for initialization logic within the CursorWrapper. It is intended to be overridden or extended by subclasses.

```python
    def initialize(self):
        pass
```

--------------------------------

### Create Peewee Tables

Source: https://pyknotid.readthedocs.io/en/latest/_modules/peewee.html

Creates database tables for a list of Peewee models, ensuring they are processed in the correct order.

```python
def create_tables(self, models, **options):
    for model in sort_models(models):
        model.create_table(**options)
```