Re: Two starting programming questions re alternating groups and EulerPhi LCM numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg37926] Re: [mg37912] Two starting programming questions re alternating groups and EulerPhi LCM numbers
- From: Tomas Garza <tgarza01 at prodigy.net.mx>
- Date: Tue, 19 Nov 2002 20:58:54 -0500 (EST)
- References: <200211190851.DAA15960@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I'm sure you'll enjoy playing around with Mathematica. Just to give you a
taste of what to expect, I take Program1A and Program 2:
1A:
In[1]:=
<<DiscreteMath`Combinatorica`
In[2]:=
Table[NthPermutation[2 j,{1,2,3,4,5}],{j,0,59}]
2:
In[1]:=
EulerPhi[10]
Out[1]= 4
In[2]:=
Select[Range[10],GCD[#1,10]==1&]
Out[2]=
{1,3,7,9}
Tomas Garza
Mexico City
----- Original Message -----
From: "Diana" <diana53 at earthlink.net>
To: mathgroup at smc.vnet.net
Subject: [mg37926] [mg37912] Two starting programming questions re alternating groups
and EulerPhi LCM numbers
> Mathematica junkies...
>
> I have ordered Mathematica Student, and am excited about starting to
> program with it.
>
> I was wondering if someone with experience could help me with two
> (easy?) programs to get started.
>
> Program 1:
>
> A. I want to first list the elements of A_5. These would be the even
> permutations of S_5, such as:
>
> (1, 2, 3, 4, 5)
> (1, 2, 4, 3 5), etc. There are 60 of these.
>
> B. Secondly, I want to figure out how to compute the order of each of
> the elements.
>
> C. Last, I want to create a Cayley table of 60 x 60 elements, i.e.,
> (1, 2, 3, 4, 5) * (1, 2, 4, 3, 5). This would be the answer you get to
> first permuting a 5-tuple by (1, 2, 3, 4, 5), and then permuting it by
> (1, 2, 4, 3, 5).
>
> I have done all of this with an Excel spreadsheet, and am not turning
> this in or getting credit for it. Just want to know how to do it.
>
> Program 2
>
> I understand that Mathematica has the EulerPhi function in it. Does
> anyone know how to get the program to list the elements which are less
> than and relatively prime to any given "n"?
>
> Thanks,
>
> Diana
>
>
- References:
- Two starting programming questions re alternating groups and EulerPhi LCM numbers
- From: diana53@earthlink.net (Diana)
- Two starting programming questions re alternating groups and EulerPhi LCM numbers