2021-04-13 22:27:34 +0200 received badge ● Notable Question (source) 2016-04-10 16:42:54 +0200 received badge ● Popular Question (source) 2015-10-20 11:54:11 +0200 received badge ● Taxonomist 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 "", line 1, in File "_sage_input_26.py", line 10, in 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 File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpYB4kTc/___code___.py", line 5, in exec compile(u'H = G.subgroup([a]) ; H File "", line 1, in 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 "", line 1, in File "_sage_input_50.py", line 10, in 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 File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpGFGoqT/___code___.py", line 4, in exec compile(u'D = G.subgroup([B[_sage_const_1 ],B[_sage_const_2 ]]) File "", line 1, in 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 "", line 1, in File "_sage_input_20.py", line 10, in 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 File "/tmp/tmpm9uLkv/___code___.py", line 5, in exec compile(u'H.order() File "", line 1, in 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 "", line 1, in File "_sage_input_54.py", line 10, in 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 File "/private/var/folders/rp/rpRaJRnOEQyzp4ftzijESU+++TI/-Tmp-/tmpcoW8YW/___code___.py", line 5, in 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 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;