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A python package for all things schemata related

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schematax is a simple Python package to do all things related to schemata.

A schema is word made using an extra symbol, ‘*’, called the wild card symbol. For example the schema over the binary aplhapbet ‘1*0’, represents the set of strings. {‘100’,’110’}’.

Schema have properties. For example, for a schema s, the order of s is the number of symbols in s which are not the wild card symbols (called fixed symbols). The defining length of s is the distance between the first and last fixed symbol.

Given a set of words of the same length S, the schematic completion of S returns all schema which make subsets of the words in S. Whats more given the partial ordering over schemata, the schematic completion of S forms a Complete Lattice.


This package runs under Python 2.7, use pip to install:

$ pip install schematax

This will also install the graphviz package from PyPI as required dependencies.

Important: Drawing the the schematic lattice uses Graphviz software. Make sure it is installed and dot executable is on your systems’ path.


The file gives a good overview of how to use the package.

Basic schema operations:

>>> import schematax

>>> s = schematax.schema('10*1') #makes a schema

>>> s

>>> s.get_order()

>>> s.get_defining_length()

>>> s2 = schematax.schema('1**1') #makes another schema

>>> s <= s2

>>> s < s2

>>> s == s2


>>> schematax.join(s,s2)

>>> s3 = schematax.schema('00*1')

>>> schematax.supremum([s,s2,s3])

>>> schematax.infimum([s,s2,s3])
e                               #e stands for the empty schema

Schematic completion and drawing the schematic lattice:

>>> import schematax

>>> xs = ['111', '011', '001']

>>> ss = schematax.complete(xs) #performing schematic completion

>>> ss
[111, 011, 001, *11, **1, 0*1, e] #e stands for the empty schema

>>> schematax.draw(ss,'my_lattice') #draws the schematic lattice of ss and saves it as my_lattice.pdf

The image produced here:

Further reading

See also

The implementation is based on these Python packages:

  • graphviz – Simple Python interface for Graphviz


Schemata is distributed under the MIT license.

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schematax-0.1.6.tar.gz (39.5 kB view hashes)

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