Miscellaneous

class sage.combinat.misc.DoublyLinkedList(l)

A doubly linked list class that provides constant time hiding and unhiding of entries.

Note that this list’s indexing is 1-based.

EXAMPLES:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3]); dll
Doubly linked list of [1, 2, 3]: [1, 2, 3]
sage: dll.hide(1); dll
Doubly linked list of [1, 2, 3]: [2, 3]
sage: dll.unhide(1); dll
Doubly linked list of [1, 2, 3]: [1, 2, 3]
sage: dll.hide(2); dll
Doubly linked list of [1, 2, 3]: [1, 3]
sage: dll.unhide(2); dll
Doubly linked list of [1, 2, 3]: [1, 2, 3]
head()

TESTS:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3])
sage: dll.head()
1
sage: dll.hide(1)
sage: dll.head()
2
hide(i)

TESTS:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3])
sage: dll.hide(1)
sage: list(dll)
[2, 3]
next(j)

TESTS:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3])
sage: dll.next(1)
2
sage: dll.hide(2)
sage: dll.next(1)
3
prev(j)

TESTS:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3])
sage: dll.prev(3)
2
sage: dll.hide(2)
sage: dll.prev(3)
1
unhide(i)

TESTS:

sage: dll = sage.combinat.misc.DoublyLinkedList([1,2,3])
sage: dll.hide(1); dll.unhide(1)
sage: list(dll)
[1, 2, 3]
class sage.combinat.misc.IterableFunctionCall(f, *args, **kwargs)

This class wraps functions with a yield statement (generators) by an object that can be iterated over. For example,

EXAMPLES:

sage: def f(): yield 'a'; yield 'b'

This does not work:

sage: for z in f: print z
Traceback (most recent call last):
...
TypeError: 'function' object is not iterable

Use IterableFunctionCall if you want something like the above to work:

sage: from sage.combinat.misc import IterableFunctionCall
sage: g = IterableFunctionCall(f)
sage: for z in g: print z
a
b

If your function takes arguments, just put them after the function name. You needn’t enclose them in a tuple or anything, just put them there:

sage: def f(n, m): yield 'a' * n; yield 'b' * m; yield 'foo'
sage: g = IterableFunctionCall(f, 2, 3)
sage: for z in g: print z
aa
bbb
foo
sage.combinat.misc.check_integer_list_constraints(l, **kwargs)

EXAMPLES:

sage: from sage.combinat.misc import check_integer_list_constraints
sage: cilc = check_integer_list_constraints
sage: l = [[2,1,3],[1,2],[3,3],[4,1,1]]
sage: cilc(l, min_part=2)
[[3, 3]]
sage: cilc(l, max_part=2)
[[1, 2]]
sage: cilc(l, length=2)
[[1, 2], [3, 3]]
sage: cilc(l, max_length=2)
[[1, 2], [3, 3]]
sage: cilc(l, min_length=3)
[[2, 1, 3], [4, 1, 1]]
sage: cilc(l, max_slope=0)
[[3, 3], [4, 1, 1]]
sage: cilc(l, min_slope=1)
[[1, 2]]
sage: cilc(l, outer=[2,2])
[[1, 2]]
sage: cilc(l, inner=[2,2])
[[3, 3]]
sage: cilc([1,2,3], length=3, singleton=True)
[1, 2, 3]
sage: cilc([1,2,3], length=2, singleton=True) is None
True
sage.combinat.misc.umbral_operation(poly)

Returns the umbral operation \(\downarrow\) applied to poly.

The umbral operation replaces each instance of \(x_i^{a_i}\) with \(x_i*(x_i - 1)*\cdots*(x_i - a_i + 1)\).

EXAMPLES:

sage: P = PolynomialRing(QQ, 2, 'x')
sage: x = P.gens()
sage: from sage.combinat.misc import umbral_operation
sage: umbral_operation(x[0]^3) == x[0]*(x[0]-1)*(x[0]-2)
True
sage: umbral_operation(x[0]*x[1])
x0*x1
sage: umbral_operation(x[0]+x[1])
x0 + x1
sage: umbral_operation(x[0]^2*x[1]^2) == x[0]*(x[0]-1)*x[1]*(x[1]-1)
True

Previous topic

Pointwise addition of dictionaries

Next topic

Combinatorial maps

This Page