FAQ

Changes

What happened to getDBconnection()?

The getDBconnection() method has been replaced by an object that provides an abstraction layer over the raw database connection. You can access this object from Python by importing it: from lmfdb import db.
What's an overview of the changes?

There is a new folder, lmfdb/backend/, containing the main components of the new interface to the Postgres database. Postgres is a mature, open-source implementation of SQL. One of the main differences is that Postgres is a strongly-typed relational database, meaning that every table has a schema with types for each column. In contrast, Mongo allows you to insert arbitrary documents into a collection. This flexibility can be useful, but it also causes performance headaches as the size of the database grows.

Postgres enables queries that weren't possible before, especially around subsets (for example, searching for number fields with specified ramification is now feasible). Moreover, SQL allows for queries across tables that weren't possible in Mongo, though this isn't supported by the LMFDB website.

For the most part, the front-end experience will be very similar. One change that you will see is some queries will now report a total of "at least 1000". This results from a limitation in the postgres storage mechanism that can make getting exact counts for queries much slower than retrieving the first 50 rows. If you care about the number of results, you can click on "at least 1000" and it will compute the count for you.

The implementation of search functions across various parts of the lmfdb has also been standardized, and some common features have been refactored into a common codebase.
Why did the databases/collections get renamed?

Postgres doesn't have the same notion of databases and collections that Mongo does, so some renaming was required. We decided to take advantage of this restructuring to add some consistency to the naming scheme.
Why do I still see messages about mongo when I start the LMFDB?

Classical modular forms are still using mongo. We're working on revising them to use postgres, but in the mean time we're still connecting to a mongo database.

Database Interface

How do I interact with the database as a developer?

There are three main objects in the database interface: the overall database interface (db, of type PostgresDatabase) which contains tables (e.g. db.nf_fields of type PostgresTable), each of which has a statistics object (e.g. db.nf_fields.stats of type PostgresStatsTable).

Each section of the lmfdb will generally rely on one (or perhaps a few) table, and most of the methods of interest are on the table objects.
How do I find the names of all of the tables?

The list db.tablenames is a list of the tables (with the exception of knowls, users, and meta tables).

How do I determine what columns are in a table?

Each table has a col_type dictionary, whose keys are column names and values are column types. For example,

sage: from lmfdb import db
sage: db.fq_fields.col_type
{u'characteristic': u'bigint',
 u'conway': u'smallint',
 u'degree': u'integer',
 u'id': u'bigint',
 u'polynomial': u'jsonb'}

How do I search for entries in a table?

Use the search method on a table. For example,
```
sage: from lmfdb import db
sage: nf = db.nf_fields
sage: info = {}
sage: nf.search({'degree':int(6)}, projection=['label','class_number','galt'], limit=4, info=info)
[{'class_number': 1, 'galt': 5, 'label': u'6.0.9747.1'},
 {'class_number': 1, 'galt': 11, 'label': u'6.0.10051.1'},
 {'class_number': 1, 'galt': 11, 'label': u'6.0.10571.1'},
 {'class_number': 1, 'galt': 5, 'label': u'6.0.10816.1'}]
sage: info['number'], info['exact_count']
(5522600, True)
```
The first argument is a dictionary specifying the query (in a style similar to what you're used to from MongoDB, but with custom operators like $contains that are translated to Postgres expressions). You can project in order to obtain only a certain set of columns, and provide limits, offsets and custom sort orders. Note that if you specify the projection as a string (instead of a list), you will get just the values in that column, rather than dictionaries.

The info argument is a dictionary that will be updated with various data that is commonly needed by templates populated by the search functions. For more details, see the documentation in the folder lmfdb/backend.
What if I only want a single entry, for example with a specified label?

Use either the lucky method or the lookup method. The first is more general, allowing you to specify a query that produces a single result (if you're sure it produces only one result, specifying sort=[] may improve performance). The lookup method is a specific case that takes just a label and returns the row with that label.
What other methods are of interest in querying the database?

You can use exists to determine whether there are any matches for a query.

The random method produces a random label or row.

The max method finds the maximum value attained by a specified column.

The distinct method returns the distinct values taken by a specified column.

The count method returns the total number of rows matching a given query.

The _parse_projection method controls how you can specify output columns.

The _parse_special method defines the keys that allow more complicated queries, such as containment, inequalities and disjunctions.
How can I execute other kinds of SQL commands?

You have three options: use the _execute method of the db object, run commands from a psql prompt, or use the pgAdmin4 interface (not yet supported).

If use db._execute, make sure to wrap your statements in the SQL class from psycopg2.sql (you can also import it from lmfdb.backend). You can see lots of examples of this paradigm in lmfdb/backend/.
```
sage: from lmfdb.backend import db, SQL
sage: cur = db._execute(SQL("SELECT label, dim, cm_discs, rm_discs from mf_newforms WHERE projective_image = %s AND cm_discs @> %s LIMIT 2"), ['D2', [-19]])
sage: cur.rowcount
2
sage: list(cur)
[(u'95.1.d.a', 1, [-19, -95], [5]), (u'171.1.c.a', 1, [-3, -19], [57])]
```
If you do this within lmfdb code (rather than just at the command line), make sure you properly escpae literals and identifiers to prevent SQL injection attacks. This means wrapping any table or column name that might have come from an untrusted source in Identifier, and using either the %s construction shown above or the Literal or Placeholder objects when passing constants into your query. More documentation on these constructions can be found in the psycopg2.sql module.

If you want to use SQL from a command prompt, you should log into legendre.mit.edu (ask Edgar Costa or David Roe if you need an account) and then run the following from bash:

psql -d lmfdb and then give the lmfdb password. This will give you read-only access to the database.

If you want write access, type psql -U editor -d lmfdb and then give the editor password.

Either way, you will get a prompt where you can type SQL commands. Don't forget ending semicolons, which are not required when executing commands from python.

Developer configuration

Where do I put my passwords?

When you run sage -python start-lmfdb.py for the first time, it will create a configuration file config.ini in the lmfdb root directory. In the postgresql section it will add the default username lmfdb, password lmfdb, host devmirror.lmfdb.xyz, and port 5432 which altogether allows for read access to the database.

In order to get write access to the database, you need to connect to the PostgreSQL server running at legendre.mit.edu, which only accepts internal connections. For this we recommend to ssh into legendre.mit.edu, change the user field to editor, the password field to the editor password, and the host to localhost. Instead, if you prefer to work from your own machine, you may use the ssh connection to forward a local port to 5432, and use that port on your config.ini file.

Adding and modifying data

Note that you need editor priviledges to add, delete or modify data.

How do I create a new table?

If you want to add a new table to the lmfdb, see the create_table method. You will need to provide a name (try to follow the naming conventions, where the first few characters indicate the general area of your table, separated by an underscore from the main name, which is often a single word). You then give a dictionary whose keys are postgres types and values are lists of columns with that type. The next argument is the column which should be used in the lookup method. You should provide a default sort order if your table will be the primary table behind a section of the website (auxiliary tables may not need a sort order). The id_ordered argument specifies whether the id column should match your sort order (which can make indexes smaller and simpler but updating data more time-consuming). You can give columns for an extra table (see the question two prior), using the same format as the second argument. Finally, you can specify the order of columns, which will be used in copy_from and copy_to by default.
```
db.create_table(name='halfmf_forms',
                search_columns={'smallint': ['dim', 'weight', 'level', 'dimtheta'],
                                'text': ['label'],
                                'jsonb': ['thetas', 'newpart'],
                                'numeric': ['character']},
                label_col='label',
                sort=['level', 'label'],
                id_ordered=False,
                search_order=['dim', 'weight', 'thetas', 'level', 'character',
                              'label', 'dimtheta', 'newpart'])
```
Once this table exists, you can access it via the object db.halfmf_forms, which is of type PostgresTable.

Conversely, to remove a table from the LMFDB you can use drop_table.
How do I see the type of a column?

You can access the type of a column using the col_type attribute.
```
sage: db.test_table.col_type['dim']
'integer'
```
How do I add a column?

If you want to add a column to an existing table, use the add_column method.
```
sage: db.test_table.add_column("bad_primes", 'jsonb', description = 'The primes of bad reduction.')
```
This column will be NULL for existing rows.
How do I delete a column?

If you want to delete a column to an existing table, use the drop_column method.
```
sage: db.test_table.drop_column("bad_primes")
```
How do I insert new data?

There are two main methods for adding data to a table. The first is the insert_many method, which takes a list of dictionaries with the data to insert.
```
sage: L = [{'dim':1, 'discriminant':12, 'label':'1.12.A', 'bad_primes':[2,3]},
           {'dim':2, 'discriminant':30, 'label':'2.30.A', 'bad_primes':[2,3,5]}]
sage: db.test_table.insert_many(L)
```
The second is copy_from, which takes a file with one line per row to be inserted, with tabs separating the data on each line. For large numbers of rows, this method will be faster.
```
sage: db.test_table.copy_from('test.txt', sep='|'])
```
Example contents of test.txt:
```
dim|discriminant|label|bad_primes
smallint|numeric|text|jsonb

1|12|1.12.A|[2,3]
2|30|2.30.A|[2,3,5]
```
Note that very few (if any) LMFDB tables currently enforce uniqueness on any of their columns, so be careful that you do not insert duplicate rows.

You can also export your data using copy_to, add rows to the resulting file, then use reload to load the result back into postgres. Use copy_to_example if you want an example of the file format for your table.
How do I update data?

There are a number of methods for updating data. We present them in rough order of ease of use, and roughly reverse order in terms of speed.

The first option is upsert, which takes a query and dictionary containing values to be set and updates a single row satisfying the query. If no row satisfies the query, a new row will be added. If multiple rows satisfy the query, an error will be raised. Note that columns not contained in the specified data will be left unchanged.
```
sage: db.test_table.upsert({'discriminant': 12}, {'label':'1.12.B'})
sage: db.test_table.upsert({'discriminant': 20, 'dim': 2}, {'label':'2.20.B', 'bad_primes':[2,5]})
```
Since upsert only modifies one row at a time, it will be slow if many rows need to be changed. Another option is the rewrite method. The first argument is a function that processes an existing row and outputs a dictionary giving the changes to be made. The second is an optional query allowing you to filter rows from being processed. Further keywords are documented in the docstring for the function.
```
sage: def func(D):
....:     D['dim'] += 1
....:     old_label = D['label']
....:     D['label'] = str(D['dim']) + old_label[:old_label.find('.')]
....:     return D
sage: db.test_table.rewrite(func, {'discriminant':{'$le':25}})
```
Sometimes the new data cannot be derived from existing data. In this case the update_from_file function can be used, which allows you to specify new values for any subset of columns and of rows. For example:
```
sage: db.test_table.update_from_file("test.txt", label_col="label", sep=":")
```
Example contents of test.txt:
```
label:discriminant:bar
text:numeric:text

1.12.A:33:hello
2.30.A:90:world
```
Under the hood, the rewrite function uses reload, which is also available for use directly. It takes as input files containing the desired data for the table (for basic usage, you can just give one file; others are available if your table has an attached extra table, or you want to update the stats with the same command).
```
sage: db.test_table.reload("test.txt", includes_ids=False)
```
Example contents of test.txt:
```
2    12      2.12.B  [2,3]
3    30      3.30.A  [2,3,5]
3    20      3.20.B  [2,5]
```
The reload method supports arbitrary changes to the data, but requires you to produce an appropriate file.
What if I change my mind and want to revert to the old version of a table, from before a reload?

You can use the reload_revert method to switch back to the old version. Note that this will also work for the rewrite method, since it relies on reload, and for the update_from_file method (unless inplace=True was used). If you want to undo a reload_all, see the reload_all_revert method on db.

There is no built-in way to undo direct additions to tables via copy_from, upsert, or insert_many.
What is an extra_table?

A few large tables (e.g. nf_fields) have been split in two. The columns in the search table can be used in queries, while the columns in the extra table cannot. Moreover, you should refrain from projecting onto columns in the extra table in queries that contain more than a few results (in particular, queries without a LIMIT clause). The columns in the extra table are intended to be accessed by the lookup and lucky methods that only return a single row.

The benefit of having an extra table is that it drastically shrinks the size of the table on which queries are actually being performed. For both elliptic curves and number fields, the search table is about a seventh the size of the extra table. Keeping the search table small means that if we need to resort to a sequential scan it will be faster.

If you use the public interface, the distinction between search and extra tables should be mostly invisible. But if you are working with a large table it may be worth splitting it in a similar way; see the create_extra_table method.
What should I know about sorting?

Every search table has an id column, which is a 64-bit integer. One purpose is to link rows in search tables with corresponding rows in the extra table. Another is to simplify sorting for tables that have multiple columns defining their sort order (which is most of them).

Since tables in the LMFDB are updated rarely, and they have a standard sort order (based on the order results are displayed on the website), it's feasible to have a column that mirrors this sort order in integers. For tables with the _id_ordered attribute (also stored in the meta_tables table), the id column serves this purpose. As a consequence, indexes can contain this column, rather than all of the columns that define the sort order. The id column is added as a primary key, and because its used for sorting, many queries will actually use this primary key in searches (see the next section on analyze).

The actual sort order for each table is specified at creation time, but it can be changed using the set_sort method. The sort order is stored in meta_tables and in the _sort attribute on each table, as a string. It is this default sort order that is used when you don't specify a sort in a search query.

Actually, the id column will be used as the sort order (if _id_ordered is True, _out_of_order is False and the query does not contain the first column of the true sort order). This last point is important because the query planner does not know that the id column is correlated with the columns that define it.

If the sort order is broken (either by changing the columns that define it or by modifying or adding rows), you can use the resort method to reset it (changing the id column to match the correct order). Many of the methods that modify tables include an option to resort afterward.
What other methods should I be aware of for modifying data?

The delete method will delete rows from a table that satisfy a given query (if you want to delete all rows, use the empty query {}).

The drop_column method allows you to drop a column from a table.

Performance and indexes

If my queries are running slowly, what can I do about it?

Once you have a substantial number of rows in your table (e.g. hundreds of thousands or more), you will start needing to worry about performance. The main tool we have to improve performance is the creation of indexes.
How do I create an index, and what types are available?

In order to create an index on your table, use the create_index method. There are two main index types used in the lmfdb (though postgres supports others). The btree type is the main one, which allows for ordering and searching. If you want to test set containment you can use the gin type on a jsonb column. For most of our applications we use the jsonb_path_ops option (which is the default in the lmfdb interface if you specify a gin index); be aware that it only supports the containment operator @>, not <@.

If you decide you don't need an index, you can drop it with the drop_index method.
If my queries are still slow, what should I do?

Use the analyze method to determine what query plan postgres is choosing. Sometimes it may not be taking advantage of your index. One possible source of problems is the interaction between sort orders and LIMIT clauses and your search terms. Another is that different columns can be correlated in ways that cause the query planner to misestimate the number of results, causing it to choose a poor query plan. The second issue can be alleviated to some extent by using Postgres' extended statistics objects, though we have not yet done so in the LMFDB. More details on query optimization is beyond the scope of this document; search online or ask on the LMFDB mailing list.

Statistics

What are statistics used for in the LMFDB?

One purpose of statistics is to inform viewers of the website of the extent of the data. Many sections of the lmfdb have statistics pages for this purpose (e.g. number field statistics). Each table has an attached statistics object (e.g. db.nf_fields.stats) with methods to support the collection of and access to statistics on the table.

Of course, one of the mathematical aims of the lmfdb is to use databases to understand statistical trends in the objects that we study. There is still much that should be done to make statistics more sophisticated than counts and averages available for study.

Another purpose of statistics is to record counts of queries so that fewer common queries will result in the "at least 1000 results" message. While aggregated statistics such as maximums, minimums and averages are stored in tables like nf_fields_stats, counts of the number of rows with a given set of values taken on by specific columns are recorded in tables such as nf_fields_counts.

Finally, statistics are used by the query planner when searching for rows. These statistics are stored internally within postgres using postgres' ANALYZE and CREATE STATISTICS functions, and are not easily accesssible to developers.
How do I access statistics?

There are two methods to determine a count of the number of results for a given query: quick_count (which returns None if the query is not recorded in the _counts table) and count (which will actually count the number of rows if not recorded, and store the answer in the _counts table by default). The max method will return the maximum value attained by a column.

In addition, the display_data method is designed to provide a dictionary for use in creating statistics webpages. See lmfdb/genus2_curves/main.py for an example of it in use. Some tables are still using statistics created in Mongo (see create_oldstats and get_oldstat) but they should be transitioned to the new statistics functionality in order to more easily update.
How do I add statistics for a set of columns?

See the add_stats method. It allows you to specify a set of columns, and then will compute counts of the rows with a given set of values taken on by those columns. You can also add a threshold, in which case the function will only compute counts of at least the threshold. You can also specify a dictionary of constraints (in fact, an arbitrary search query), in which case only rows satsifying the query will be considered.

For example, consider the following data.
```
A B
1 0
1 0
1 1
2 0
2 1
2 2
2 2
3 0
4 1
5 0
5 1
8 2
```
If you added stats for column A, it would record that there are four instances of 2, three of 1, two of 5 and one each of 3, 4, and 8. It would also record the minimum value (1), the maximum value (6), the average (3), and the total (12 rows).

If you specified a threshold of 3, it would only record that there are four instances of 2 and three of 1. Now the minimum and maximum values would be 1 and 2 (resp.), the average would be 1.57 and the total number of rows 7.

If you instead specified a constraint that B be at most 1, it would throw out the rows with B=2, producing three instances of 1, two of 2, two of 5 and one each of 3 and 4, with the corresponding statistics.

If you want to group values into buckets (for example, class numbers of number fields split into ranges like 1 < h <= 10 and 10 < h <= 100 and 100 < h <= 1000), you can use the add_bucketed_counts method.

If you want to add counts for many sets of columns (in order to provide counts for common queries that have a large number of results), add_stats_auto may be useful.
How can I easily add a statistics page?

Create a statistics object inheriting from StatsDisplay in lmfdb/display_stats.py. It should have attributes
- short_summary (which can be displayed at the top of your browse page),
- summary (which will be displayed at the top of the statistics page),
- table (the postgres table on which statistics are computed),
- baseurl_func (the function giving your browse page, e.g. '.index'),
- stat_list (a list of dictionaries giving the statistics to be displayed;
- 'cols', 'row_title' and 'knowl' are required arguments,
- and other optional arguments allow you to adjust the default behavior)
Once you've created such an object, you can call its setup() method from a sage prompt (with editor privileges) in order to collect the relevant statistics. You should also create a view using the display_stats.html template, passing your object in as the info parameter. Note that DisplayStats inherits from Sage's `UniqueRepresentation, so it will only be created once.
How do I display statistics from multiple tables on one page?

You can use the 'table' and 'query_formatter' keys. See classical modular forms for an example.
How do I make dynamic statistics work?

Once you create a statistics object inheriting from StatsDisplay and populate it appropriately, enabling dynamic statistics is fairly easy. Just add a view using the dynamic_stats.html template, and call the dynamic_setup method of your stats object with info as an argument. See classical modular forms for an examaple.
If I change the data in a table, how can I update the statistics on the table?

If you use a function like reload or update_from_file, they should refresh the statistics by default (if you don't want this behavior you can use the keyword restat=False). But if there seems to be something wrong with the statistics on a table, you can refresh them manually using, for example, db.g2c_curves.stats.refresh_statistics(). Sometimes this isn't sufficient (if there are extra stats that shouldn't be present for example). A more drastic option is to call db.g2c_curves._clear_stats_counts(). If you do this, make sure to visit the relevant statistics page while logged in as editor, in order to regenerate the statistics used there.

Data Validation

How can I add consistency checks for data in the LMFDB?

One option is to add constraints to your table. To do so, use the create_constraint method in database.py. You can see the current constraints using list_constraints.

There are three supported types of constraints. The simplest is not null, which checks that a specified column is filled in for every row in the table. The second is unique, which checks that a column or set of columns is unique across all rows of a table. The final options is check, which runs an arbitrary SQL function on a set of rows. We are building up a library of SQL functions for use in this way; you can see them in backend/utils.psql. Once written, these functions need to be added to postgres, at which point they can be used in checks.

Note that constraints are checked whenever a row is added or updated, so if they are complicated it will impose a speed penalty when changing data.
What if I do not want to use a constraint, or if I want to add checks that cross multiple tables?

You can use the lmfdb.verify module. Create a python file in the lmfdb/verify folder with the same name as your postgres table, and a class in that file that inherits from TableChecker in lmdfb.verify.verification. You can then add tests, which should be decorated with one of the four speed types imported from lmfdb.verify.verification.

The fastest option is to write an SQL query that searches for violations of your condition. The TableChecker class has various utilities for writing such queries, such as check_values, check_iff, check_count. You can also write the query directly and use _run_query. If you want to run queries that check consistency accross multiple tables, see the check_crosstable utility functions. For fast queries you can use the @overall decorator; if your query takes longer than about a minute, you may want to use the @overall_long decorator instead.

@fast and @slow tests are run by iterating over rows in the table. They take a dictionary representing a row as input, and should return either True (if the test passes) or False. You can provide keyword arguments to the decorator: ratio controls the fraction of rows in your table on which the test is run, projection controls which columns of the table are present in the record, and constraint provides a constraint on rows on which the test is run. The difference between fast and slow tests is just a matter of convention: fast tests are run by default on every row of the table and should take about a minute each to run, while slow tests are run by default on 10% of the rows of a table and can take longer.

You must run verification tests manually from a Sage prompt. First, run from lmfdb.verify import db. This will give you a version of the database with verification enabled (it is not enabled by default since the verification checks are vulnerable to SQL injection and should not be available when the website is running). Then use, for example, db.mf_newforms.verify().

You can specify a paricular speedtype to run (e.g. speedtype="slow" or speedtype="overall"), a specific check (e.g. check="check_cmrm_discs"), or a specific object (e.g. label="24.37.h.c"). You can also run tests on multiple tables in parallel using db.verify().

The tests will write output to a log folder (defaulting to LMFDB_ROOT/logs/verification), and will also print the output sent to this folder to your terminal. You can control which output you see using the follow option.
How can I see what verification functions are written for a given table?

You can use the list_verifications() method. With details=False it will show a list of verification functions; if details=True it will also print their docstrings and configuration options that differ from the defaults.

SQL Tips

Sometimes the interface isn't enough, and you need to do something directly with SQL. Note that some of these operations will require you to be logged in as editor.

How can I change the type of a column from jsonb to an array?

When we first switched to postgres, we planned to use jsonb for everything. But we have since learned that there are some advantages to using Postgres arrays. If you want to convert from jsonb to an array (of numerics) for example, you could do the following. We first check to see if this column is being used in any indexes or constraints. If it were, you would need to update meta_indexes or meta_constraints.

lmfdb=> SELECT * FROM meta_indexes WHERE columns @> '["heights"]'::jsonb;
 index_name | table_name | type | columns | modifiers | storage_params
------------+------------+------+---------+-----------+----------------
(0 rows)
lmfdb=> SELECT * FROM meta_constraints WHERE columns @> '["heights"]'::jsonb;
 constraint_name | table_name | type | columns | check_func
-----------------+------------+------+---------+------------
(0 rows)
lmfdb=> ALTER TABLE ec_nfcurves ADD COLUMN new_heights numeric[];
ALTER TABLE
lmfdb=> SELECT label, heights, (SELECT array_agg(value::numeric) FROM jsonb_array_elements_text(heights)) AS new_heights FROM ec_nfcurves WHERE jsonb_array_len(heights) > 1 LIMIT 3;
        label        |                  heights                  |               new_heights
---------------------+-------------------------------------------+------------------------------------------
 2.2.8.1-2066.2-e1   | [0.2026108605260589, 0.1517386576969303]  | {0.2026108605260589,0.1517386576969303}
 3.1.23.1-15857.3-A2 | [0.06782294138768774, 0.6525410927449266] | {0.06782294138768774,0.6525410927449266}
 3.1.23.1-18509.3-A1 | [0.1658028623327324, 0.2297502250210176]  | {0.1658028623327324,0.2297502250210176}
(3 rows)
lmfdb=> UPDATE ec_nfcurves SET new_heights = (SELECT array_agg(value::numeric) FROM jsonb_array_elements_text(heights));
UPDATE 661073
lmfdb=> ALTER TABLE ec_nfcurves RENAME COLUMN heights TO old_heights;
ALTER TABLE
lmfdb=> ALTER TABLE ec_nfcurves RENAME COLUMN new_heights TO heights;
ALTER TABLE

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Postgres_FAQ.md

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