Ivo Hedtke's profile - activity

(first try) what you want might be the following

sage: G = SymmetricGroup(3)
sage: p = G.cycle_index()
sage: p.expand(2)
x0^3 + x0^2*x1 + x0*x1^2 + x1^3 + x0^2*x2 + x0*x1*x2 + x1^2*x2 + x0*x2^2 + x1*x2^2 + x2^3

It is not x,y,z but x0,x1,x2.

(second try) In order to obtain the same polynomial as in GAP, you may define a morphism from symmetric functions to the polynomial ring in x,y,z. Hopefully, it is not that hard as you only need to define it on the basis.

The following defines the polynomial ring as well as a function that given a partition returns the associated monomial in R

R.<x,y,z> = PolynomialRing(QQ,'x,y,z')
def partition_to_xyz(p):
    e = p.to_exp_dict()
    return x^e.get(1,0) * y^e.get(2,0) * z^e.get(3,0)

you can check

sage: partition_to_xyz(Partition([3]))
z
sage: partition_to_xyz(Partition([1,1,1]))
x^3

then to define the morphism, simply do

sage: Sym = SymmetricFunctions(QQ).power()
sage: phi = Sym.module_morphism(on_basis=partition_to_xyz, codomain=R)

and then

sage: G = SymmetricGroup(3)
sage: p = G.cycle_index()
sage: phi(p)
1/6*x^3 + 1/2*x*y + 1/3*z

You may have a look at the documentation of symmetric functions.

But I don't want to do it by hand. I would like to have the result of GAP, but as an element of PolynomialRing(QQ,3,"xyz").

But `gap.CycleIndex(G)` tells me something different.

How do I get the cycle_index of a group as an element of PolynomialRing(QQ,...)? For example I tried

G=SymmetricGroup(3)
p=G.cycle_index()

But I want p as an element of PolynomialRing(QQ,3,"xyz").

Hi,

we installed sage-5.9 on a server (Ubuntu 12.04) of our working group. We would like to open the port, such that all members of the team can access the notebook without a ssh tunnel. Is it possible to secure the access with htaccess or something like that?

Or to ask it in an other direction: Is a notebook secure enough without restricting the access? The users are not allowed to create new users. But could this be a security issue for our server?

Thanks.