diff --git a/sage/categories/finite_posets.py b/sage/categories/finite_posets.py
--- a/sage/categories/finite_posets.py
+++ b/sage/categories/finite_posets.py
@@ -340,7 +340,7 @@ class FinitePosets(Category):
ideal `C`, where `C` is the (set-theoretic) complement of
the order filter of `P` generated by `A`.
- ``panyushev_complement`` is an alias for this method.
+ :meth:`panyushev_complement` is an alias for this method.
Panyushev complementation is related (actually, isomorphic)
to rowmotion (:meth:`rowmotion`).
@@ -354,10 +354,9 @@ class FinitePosets(Category):
OUTPUT:
- - the complement order filter (resp. order ideal) of the
- order ideal (resp. order filter) generated by the
- antichain ``antichain``, represented by its generating
- antichain
+ - the generating antichain of the complement order filter
+ (resp. order ideal) of the order ideal (resp. order filter)
+ generated by the antichain ``antichain``
EXAMPLES::
@@ -542,6 +541,16 @@ class FinitePosets(Category):
in this order.
See :meth:`order_ideal_toggle` for a definition of toggling.
+
+ .. WARNING::
+
+ The orbits are those under the composition of toggles,
+ *not* under the single toggles themselves. Thus, for
+ example, if ``vs == [1,2]``, then the orbits have the
+ form `(I, T_2 T_1 I, T_2 T_1 T_2 T_1 I, \ldots)`
+ (where `I` denotes an order ideal and `T_i` means
+ toggling at `i`) rather than
+ `(I, T_1 I, T_2 T_1 I, T_1 T_2 T_1 I, \ldots)`.
INPUT:
@@ -777,6 +786,16 @@ class FinitePosets(Category):
See :meth:`order_ideal_toggle` for a definition of toggling.
+ .. WARNING::
+
+ The orbit is that under the composition of toggles,
+ *not* under the single toggles themselves. Thus, for
+ example, if ``vs == [1,2]``, then the orbit has the
+ form `(I, T_2 T_1 I, T_2 T_1 T_2 T_1 I, \ldots)`
+ (where `I` denotes ``oideal`` and `T_i` means
+ toggling at `i`) rather than
+ `(I, T_1 I, T_2 T_1 I, T_1 T_2 T_1 I, \ldots)`.
+
INPUT:
- ``vs``: a list (or other iterable) of elements of ``self``