Coverage for local/lib/python2.7/site-packages/sage/categories/tutorial.py : 100%

r""" 

Implementing a new parent: a (draft of) tutorial 

The easiest approach for implementing a new parent is to start from a 

close example in sage.categories.examples. Here, we will get through 

the process of implementing a new finite semigroup, taking as starting 

point the provided example:: 

sage: S = FiniteSemigroups().example() 

sage: S 

An example of a finite semigroup: the left regular band generated by ('a', 'b', 'c', 'd') 

You may lookup the implementation of this example with:: 

sage: S?? # not tested 

Or by browsing the source code of 

:class:`sage.categories.examples.finite_semigroups.LeftRegularBand`. 

Copy-paste this code into, say, a cell of the notebook, and replace 

every occurrence of ``FiniteSemigroups().example(...)`` in the 

documentation by ``LeftRegularBand``. This will be equivalent to:: 

sage: from sage.categories.examples.finite_semigroups import LeftRegularBand 

Now, try:: 

sage: S = LeftRegularBand(); S 

An example of a finite semigroup: the left regular band generated by ('a', 'b', 'c', 'd') 

and play around with the examples in the documentation of ``S`` and of 

:class:`FiniteSemigroups`. 

Rename the class to ``ShiftSemigroup``, and modify the product to 

implement the semigroup generated by the given alphabet such that `au 

= u` for any `u` of length `3`. 

Use ``TestSuite`` to test the newly implemented semigroup; draw its 

Cayley graph. 

Add another option to the constructor to generalize the construction 

to any u of length `k`. 

Lookup the Sloane for the sequence of the sizes of those semigroups. 

Now implement the commutative monoid of subsets of `\{1,\dots,n\}` 

endowed with union as product. What is its category? What are the 

extra functionalities available there? Implement iteration and 

cardinality. 

TODO: the tutorial should explain there how to reuse the enumerated 

set of subsets, and endow it with more structure. 

"""