On 23/04/2022 12.43, Avi Gross wrote:
Given what you added, Michael, your function is part of a larger collection of
functions and being compatible with the others is a valid consideration.
Whatever you decide, would ideally be done consistently with all or most of
them.
And, of course, it others in the collection also can handle multiple ways to
specify a permutation, it may be simpler to have each call something like
as.permutation() that handlesmultiple forms and converts to the one easiest for
you to use.
I am not sure that is needed as I suspect the simplest storage is something
like a list: [0,3,2,4,5,6,7,1,9,8] but could also be shown with each cycle as
a sub-list or something like anumpy vector or a customized class.
Since you ask, I'm using dictionaries as the internal representation.
If you think about it, a python dictionary *is* a function from one
finite set to another, mathematically. And a (finite) permutation is
a bijection from a (finite) set to itself.
For convenience, the module provides two methods of defining a permutation
other than just entering a dictionary:
>>> import PermGroups as pg
>>> a = {'1':'2', '2':'1', '3':'3'}
>>> b = pg.ParsePerm( '(12)(3)' )
>>> c = pg.ParseDomImg( '123', '213' )
>>> a==b
True
>>> b==c
True
>>>
All of the other functions work on these dictionaries.
I had thought about defining a permutation object, but the conceptual
match between "dict" and "permutation" was too good to discard.
Clearly if you control the package and how it is used, errors from bad data may
not be a concern.
An invalidly-constructed permutation will cause an exception, so
the function won't return.
>>> d = {'1':'2', '2':'2', '3':'3'}
>>> pg.ValidateDict(d)
False
>>>
If I was to do it over, I would have named this function something
like IsValidPermutation(), hiding the internal representation as
well as making the function's Boolean nature explicit.
--
Michael F. Stemper
No animals were harmed in the composition of this message.
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