Miscellaneous#
- class sage.combinat.misc.DoublyLinkedList(l)#
Bases:
object
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()#
- hide(i)#
- next(j)#
- prev(j)#
- unhide(i)#
- class sage.combinat.misc.IterableFunctionCall(f, *args, **kwargs)#
Bases:
object
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