You just need to git Trac try the branch, there are examples in the
docstring of PermutationGroup
On Tuesday, 3 May 2022 at 15:27:06 UTC+2 David Joyner wrote:
> On Tue, May 3, 2022 at 7:12 AM 'Martin R' via sage-devel
> <sage-...@googlegroups.com> wrote:
> >
> > I implemented (well, the implementation is trivial) the following, and
> I'd like feedback. I am not completely sure whether the interface for the
> second variant, where the generators of the acting group are required, is
> ideal, but I think it looks useable.
> >
> > A more serious problem is that orbits are currently computed twice: once
> when creating the generators of the permutation group, and another time,
> when asking for them.
> >
> > Martin
> >
>
> Hi Martin:
>
> Thanks for programming this. I'd like to test it's functionality but
> don't know your function's syntax. Something like
>
> def PermutationGroup2(gens=None, gap_group=None, domain=None,
> canonicalize=True, category=None, action=None):
>
> maybe?
>
> - David
>
>
> > """
> > ...
> > We can create a permutation group from a group action::
> >
> > sage: A = lambda x: (2*x) % 6
> > sage: X = [0,1,2,3,4,5]
> > sage: G = PermutationGroup(action=A, domain=X)
> > sage: G.orbits()
> > [[0], [1, 2, 4], [3], [5]]
> >
> > sage: A = lambda g, x: vector(g*x, immutable=True)
> > sage: X = [vector(x, immutable=True) for x in GF(3)^2]
> > sage: G = SL(2,3); G.gens()
> > (
> > [1 1] [0 1]
> > [0 1], [2 0]
> > )
> > sage: H = PermutationGroup(G.gens(), action=A, domain=X)
> > sage: H.orbits()
> > [[(0, 0)], [(1, 0), (0, 2), (2, 2), (2, 0), (1, 2), (2, 1), (0, 1), (1,
> 1)]]
> > sage: H.gens()
> > [((0,1),(1,1),(2,1))((0,2),(2,2),(1,2)),
> > ((1,0),(0,2),(2,0),(0,1))((1,1),(1,2),(2,2),(2,1))]
> > ...
> > """
> > if not is_ExpectElement(gens) and hasattr(gens, '_permgroup_'):
> > return gens._permgroup_()
> > if gens is not None and not isinstance(gens, (tuple, list, GapElement)):
> > raise TypeError("gens must be a tuple, list, or GapElement")
> > gap_group = kwds.get("gap_group", None)
> > domain = kwds.get("domain", None)
> > canonicalize = kwds.get("canonicalize", True)
> > category = kwds.get("category", None)
> > action = kwds.get("action", None)
> > if action is not None:
> > if domain is None:
> > raise ValueError("you must specify the domain for an action")
> > from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
> > if gap_group is not None:
> > raise ValueError("gap_group is not supported with action")
> > if gens is None and gap_group is None:
> > gens = [tuple(o) for o in orbit_decomposition(domain, action)]
> > else:
> > gens = [[tuple(o) for o in orbit_decomposition(domain, lambda x:
> action(g, x))]
> > for g in gens]
> > if args:
> > from sage.misc.superseded import deprecation
> > deprecation(31510, "gap_group, domain, canonicalize, category will
> become keyword only")
> > if len(args) > 4:
> > raise ValueError("invalid input")
> > args = list(args)
> > gap_group = args.pop(0)
> > if args:
> > domain = args.pop(0)
> > if args:
> > canonicalize = args.pop(0)
> > if args:
> > category = args.pop(0)
> > return PermutationGroup_generic(gens=gens, gap_group=gap_group,
> domain=domain,
> > canonicalize=canonicalize, category=category)
> >
> >
> > On Monday, 2 May 2022 at 23:01:42 UTC+2 David Joyner wrote:
> >>
> >> On Mon, May 2, 2022 at 11:24 AM 'Martin R' via sage-devel
> >> <sage-...@googlegroups.com> wrote:
> >> >
> >> > I am actually not sure anymore, which methods or functionality this
> class should provide.
> >> >
> >> > Would it possibly be better to enhance PermutationGroup with an
> additional optional "from_action" and "from_cyclic_action" argument? Eg.:
> >> >
> >> > PermutationGroup(domain = X, cyclic_action = lambda x: f(x))
> >> >
> >> > PermutationGroup(domain = X, group_action = (G, lambda g, x: f(g, x)))
> >> >
> >>
> >> I like this idea!
> >>
> >> > Martin
> >> > On Monday, 2 May 2022 at 14:20:57 UTC+2 kcrisman wrote:
> >> >>
> >> >> On Sunday, May 1, 2022 at 7:32:01 PM UTC-4 Travis Scrimshaw wrote:
> >> >>>>>
> >> >>>>> Sorry, I don't know an easy way. I've always just defined them by
> hand
> >> >>>>> whenever needed.
> >> >>>>> However, I agree with you that a better way is needed.
> >> >>>>
> >> >>>>
> >> >>>> I would love for there to be some standard way to define a group
> action on a set - preferably maintaining other algebraic properties of the
> set, such as addition! But I don't know if there is even close to a
> standard way to do this either.
> >> >>>
> >> >>>
> >> >>> - There is a standard way to do this, but not a generic
> method/class for it IIRC. You can do this by implementing an _act_on_()
> method on a wrapper class. Yet, this requires some manual input.
> >> >>> - For cyclic actions, there is the DiscreteDynamicalSystem class
> introduced in https://trac.sagemath.org/ticket/24128.
> >> >>> - There is also the Representation class in
> modules/with_basis/representation.py if you want to want to extend the
> action on the set to the module with a basis given by that set.
> >> >>>
> >> >>> Likely we will want to implement a class SetWithAction that
> automates a collects the orbit_decomposition functions and similar together
> as methods as a single global entry point.
> >> >>>
> >> >>
> >> >> Hmm, maybe a tutorial is needed for this. I would imagine that a lot
> of people who aren't familiar with how to create a new wrapper class would
> be the ones who need this. Of course, the FiniteGroupAction suggestion
> sounds quite welcome, too, though really having both options would be best.
> >> >
> >> > --
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