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2014-11-17 08:54:16 +0200 asked a question All Ideals of Ring

For given group G, by G.subgroups(), we can list all subgroups. now my question is :

Is there something for subgroups() for finding all left ideals of a given ring. For instance, k = GF(5); M = MatrixSpace(k,2,2) How can I have all left ideals?

2014-01-15 15:09:25 +0200 commented answer Subgroups of Linear Groups

It is not working on mu SAGE. I have following error: Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_26.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RyA9IFNMKDIsR0YoMykpCmEgPSBHLmdlbnMoKVswXSA7IGEKSCA9IEcuc3ViZ3JvdXAoW2FdKSA7IEg="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpYB4kTc/___code___.py", line 5, in <module> exec compile(u'H = G.subgroup([a]) ; H File "", line 1, in <module> File "parent.pyx", line 620, in sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:5943) File "misc

2014-01-15 10:37:38 +0200 asked a question Subgroups of Linear Groups

I want to find the subgroup which is generated by two elements.

G = SL(2,GF(3))

D = G.subgroup([G[1],G[2]])

Why do I have this error:

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_50.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + >_support_.preparse_worksheet_cell(base64.b64decode("RyA9IFNMKDIsR0YoMykpCkQgPSBH>LnN1Ymdyb3VwKFtCWzFdLEJbMl1dKQ=="),globals())+"\n"); >execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpGFGoqT/___code___.py", line 4, in <module> exec compile(u'D = G.subgroup([B[_sage_const_1 ],B[_sage_const_2 ]]) File "", line 1, in <module>

File "parent.pyx", line 620, in sage.structure.parent.Parent.__getattr__ >(sage/structure/parent.c:5943) File "misc.pyx", line 200, in sage.structure.misc.getattr_from_other_class >(sage/structure/misc.c:1427) AttributeError: 'SpecialLinearGroup_finite_field_with_category' object has no >attribute 'subgroup'

2014-01-02 02:26:09 +0200 commented question Error with Automorphism group

@kcrisman If order() replace with Order(), then the error eliminates.

2014-01-01 13:46:23 +0200 received badge  Student (source)
2014-01-01 13:00:14 +0200 asked a question Error with Automorphism group

I use this for computing automorphism group:

G = SymmetricGroup(3)

H = libgap(G).AutomorphismGroup()

but when I want to compute order of automorphism group, I cant compute and I have this error:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_20.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RyA9IFN5bW1ldHJpY0dyb3VwKDMpCkggPSBsaWJnYXAoRykuQXV0b21vcnBoaXNtR3JvdXAoKQpILm9yZGVyKCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>

  File "/tmp/tmpm9uLkv/___code___.py", line 5, in <module>
    exec compile(u'H.order()
  File "", line 1, in <module>

  File "element.pyx", line 1867, in sage.structure.element.RingElement.order (sage/structure/element.c:15911)
  File "element.pyx", line 1873, in sage.structure.element.RingElement.additive_order (sage/structure/element.c:15968)
NotImplementedError
2013-12-29 02:19:04 +0200 commented question Automorphism Group of a Group

@kcrisman we need automorphism group, as our research continues in graph theory and we use graph tools of sage and GAP doesnt have such tools.

2013-12-28 04:59:48 +0200 asked a question Automorphism Group of a Group

I used to find the automorphism group of a group with GAP. Now, I would like to know that Is the way which I can compute automorphism group of a group with SAGE without using GAP?

2013-04-21 16:54:11 +0200 commented question affine variety

in che soali akhe?

2013-02-17 01:47:54 +0200 commented answer Locally-Dihedral 2-group

I check but I can't find any thing.

2013-02-14 15:09:54 +0200 asked a question Locally-Dihedral 2-group

Let $Z_{2^{\infty}}$ be 2-prufer group. I want to define $G=Z_{2^{\infty}}$semi-direct $ b$ =$<$$a$$,b|b^2=1,b^{-1}ab=a^{-1} $, for $a$ $\in A>$ in sage. I think this is possible in GAP but I don't know how to define?

2013-02-06 14:58:23 +0200 marked best answer One-dimension subspace

You need to take care of the zero element of the subspace. for x in i will iterate over all the vectors including the zero vector.

2013-02-05 07:34:43 +0200 commented answer One-dimension subspace

how can I take care of the zero element?

2013-02-05 03:33:19 +0200 asked a question One-dimension subspace

I am looking for one-dimension subspace $x$ such that for every $v\in$$\langle x\rangle$ we have $v.v=0$.

I try this:

V = VectorSpace(GF(5),2)

for i in V.subspaces(1):

    for x in i:
       if (x*x==0):
          print(i)

but I have trouble with it:

sage gives me subspace "Vector space of degree 2 and dimension 1 over Finite Field of size 5 Basis matrix: [1 0]" this subspace is not satisfied my condition

2013-01-27 07:29:16 +0200 asked a question permutation representation

Dear all

Does sage support groups such as Frobenius groups or general affine group. How can I find the permutation representation of an arbitrary group.

Best regrad

2013-01-19 13:41:45 +0200 received badge  Scholar (source)
2013-01-19 13:41:45 +0200 marked best answer Product of Elements in Group

Use D(x)*D(y) instead of D(x*y):

sage: D = SymmetricGroup(4)
sage: H=D.subgroups()
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[6])
sage: print(A)
{(1,4,3,2), (), (1,3,4), (2,4), (1,3,2,4), (1,2,3), (1,4,2,3), (1,2)(3,4)}
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[26])
sage: print(A)
{(1,4), (1,3)(2,4), (1,3,4,2), (2,3), (3,4), (1,4,2,3), (), (2,3,4), (1,3,2,4), (1,4)(2,3), (1,4,3), (1,2,4), (1,2), (1,2)(3,4), (1,3,2), (1,2,4,3)}
2013-01-19 01:34:05 +0200 asked a question Product of Elements in Group

I have problem with product of two elements. it runs for H[18] and H[6] and it has no error but it doesn't run for H[18] and H[26]. I can't figure out this problem.

I was wondering if you could help me.

D = SymmetricGroup(4)

H=D.subgroups()

A=Set(D(x*y) for x in H[18] for y in H[6])

print(A)


{(1,4,3,2), (), (1,3,4), (2,4), (1,3,2,4), (1,2,3), (1,4,2,3), (1,2)(3,4)}
//



D = SymmetricGroup(4)

H=D.subgroups()

A=Set(D(x*y) for x in H[18] for y in H[26])

print(A)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_54.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RCA9IFN5bW1ldHJpY0dyb3VwKDQpCkg9RC5zdWJncm91cHMoKQpBPVNldChEKHgqeSkgZm9yIHggaW4gSFsxOF0gZm9yIHkgaW4gSFsyNl0pCnByaW50KEEp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>

  File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpcoW8YW/___code___.py", line 5, in <module>
    A=Set(D(x*y) for x in H[_sage_const_18 ] for y in H[_sage_const_26 ])
  File "/Applications/sage/local/lib/python2.7/site-packages/sage/sets/set.py", line 129, in Set
    return Set_object_enumerated(list(X))
  File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpcoW8YW/___code___.py", line 5, in <genexpr>
    A=Set(D(x*y) for x in H[_sage_const_18 ] for y in H[_sage_const_26 ])
  File "element.pyx", line 1388, in sage.structure.element.MonoidElement.__mul__ (sage/structure/element.c:11883)
  File "element.pyx", line 1382, in sage.structure.element.MonoidElement.__mul__ (sage/structure/element.c:11742)
  File "coerce.pyx", line 797, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7672)
TypeError: unsupported operand parent(s) for '*': 'Permutation Group with generators [(1,2)(3,4), (1,3,2,4)]' and 'Permutation Group with generators [(1,2)(3,4), (1,3)(2,4), (1,4)]'
2012-10-30 16:33:45 +0200 received badge  Editor (source)
2012-10-30 16:32:49 +0200 asked a question Finding subgroup summand

Hi everyone, Let (G,.) be group with two subgroup H and K, I want to know when HK=G? $HK={h.k | h\in H ,k\in K}$ I try this

  D= CyclicPermutationGroup(9)
  H=D.subgroups()
  for i in H:
   for j in H:
     i*j=K
   if(K==G)

I have no idea how define " * "

2012-10-17 12:17:15 +0200 asked a question Create graph

I want define new graph in sage. Let G be finite group. The graph's vertices are subgroup and two vertices are adjacent if and only if sum of two subgroup is G.

I have trouble with define this graph in sage. Any suggestion? I have idea in gap but I don't have idea what can I change in sage?

Summands := function(G) 

local n, i, sgl, l, A, B, D;

obtain a list of all subgroups

sgl := List(LatticeSubgroups(G)!.conjugacyClassesSubgroups, Representative);

n is the number of divisors of |G|

n := Size(DivisorsInt(Size(G)));

D := [];

if IsOddInt(n) then l := QuoInt(n + 1, 2);
           else l := QuoInt(n, 2);
fi;

for i in [1..l] do
  for A in Filtered(sgl, function(g) return Size(g) = DivisorsInt(Size(G))[i]; end) do
    for B in Filtered(sgl, function(g) return Size(g) = DivisorsInt(Size(G))[n+1-i]; end) do
        Add(D, [A, B]);
    od;
  od;
od;

return D;
end;