Rankers#

sage.combinat.ranker.from_list(l)#

Returns a ranker from the list l.

INPUT:

l - a list

OUTPUT:

[rank, unrank] - functions

EXAMPLES:

sage: import sage.combinat.ranker as ranker
sage: l = [1,2,3]
sage: r,u = ranker.from_list(l)
sage: r(1)
0
sage: r(3)
2
sage: u(2)
3
sage: u(0)
1

sage.combinat.ranker.on_fly()#

Returns a pair of enumeration functions rank / unrank.

rank assigns on the fly an integer, starting from 0, to any object passed as argument. The object should be hashable. unrank is the inverse function; it returns None for indices that have not yet been assigned.

EXAMPLES:

sage: [rank, unrank] = sage.combinat.ranker.on_fly()
sage: rank('a')
0
sage: rank('b')
1
sage: rank('c')
2
sage: rank('a')
0
sage: unrank(2)
'c'
sage: unrank(3)
sage: rank('d')
3
sage: unrank(3)
'd'

Todo

add tests as in combinat::rankers

sage.combinat.ranker.rank_from_list(l)#

Return a rank function for the elements of l.

INPUT:

l – a duplicate free list (or iterable) of hashable objects

OUTPUT:

a function from the elements of l to 0,...,len(l)

EXAMPLES:

sage: import sage.combinat.ranker as ranker
sage: l = ['a', 'b', 'c']
sage: r = ranker.rank_from_list(l)
sage: r('a')
0
sage: r('c')
2

For non elements a ValueError is raised, as with the usual index method of lists:

sage: r('blah')
Traceback (most recent call last):
...
ValueError: 'blah' is not in dict

Currently, the rank function is a CallableDict; but this is an implementation detail:

sage: type(r)
<class 'sage.misc.callable_dict.CallableDict'>
sage: r
{'a': 0, 'b': 1, 'c': 2}

With the current implementation, no error is issued in case of duplicate value in l. Instead, the rank function returns the position of some of the duplicates:

sage: r = ranker.rank_from_list(['a', 'b', 'a', 'c'])
sage: r('a')
2

Constructing the rank function itself is of complexity O(len(l)). Then, each call to the rank function consists of an essentially constant time dictionary lookup.

sage.combinat.ranker.unrank(L, i)#

Return the \(i\)-th element of \(L\).

INPUT:

L – a list, tuple, finite enumerated set, …
i – an int or Integer

The purpose of this utility is to give a uniform idiom to recover the \(i\)-th element of an object L, whether L is a list, tuple (or more generally a collections.abc.Sequence), an enumerated set, some old parent of Sage still implementing unranking in the method __getitem__, or an iterable (see collections.abc.Iterable). See trac ticket #15919.

EXAMPLES:

Lists, tuples, and other sequences:

sage: from sage.combinat.ranker import unrank
sage: unrank(['a','b','c'], 2)
'c'
sage: unrank(('a','b','c'), 1)
'b'
sage: unrank(range(3,13,2), 1)
5

Enumerated sets:

sage: unrank(GF(7), 2)
2
sage: unrank(IntegerModRing(29), 10)
10

An iterable:

sage: unrank(NN,4)
4

An iterator:

sage: unrank(('a{}'.format(i) for i in range(20)), 0)
'a0'
sage: unrank(('a{}'.format(i) for i in range(20)), 2)
'a2'

Warning

When unranking an iterator, it returns the i-th element beyond where it is currently at:

sage: from sage.combinat.ranker import unrank
sage: it = iter(range(20))
sage: unrank(it, 2)
2
sage: unrank(it, 2)
5

sage.combinat.ranker.unrank_from_list(l)#

Returns an unrank function from a list.

EXAMPLES:

sage: import sage.combinat.ranker as ranker
sage: l = [1,2,3]
sage: u = ranker.unrank_from_list(l)
sage: u(2)
3
sage: u(0)
1