才把PATH搞对,刚在WINDOWS 装上
http://www.gap-system.org,SAGE里的好麻烦
gap> s3 := SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> l := List(s3, p-> Permuted(words, p));
[ [ "LI", "LIAN", "JIE" ], [ "JIE", "LIAN", "LI" ], [ "JIE", "LI", "LIAN" ],
[ "LI", "JIE", "LIAN" ], [ "LIAN", "JIE", "LI" ], [ "LIAN", "LI", "JIE" ] ]
Sym( [ 1 .. 6 ] )
brk_12> r:= (1,3,4,5,6);
(1,3,4,5,6)
brk_12> s:= (1,3,2);
Syntax error: warning: unbound global variable in *errin* line 4
s:= (1,3,2);
^
(1,3,2)
brk_12> K:= Subgroup(G,[r,s]);
Syntax error: warning: unbound global variable in *errin* line 5
K:= Subgroup(G,[r,s]);
^
Group([ (1,3,4,5,6), (1,3,2) ])
brk_12> Elements(K);
[ (), (4,5,6), (4,6,5), (3,4)(5,6), (3,4,5), (3,4,6), (3,5,4), (3,5,6),
(3,5)(4,6), (3,6,4), (3,6,5), (3,6)(4,5), (2,3)(5,6), (2,3)(4,5),
(2,3)(4,6), (2,3,4), (2,3,4,5,6), (2,3,4,6,5), (2,3,5,6,4), (2,3,5),
(2,3,5,4,6), (2,3,6,5,4), (2,3,6), (2,3,6,4,5), (2,4,3), (2,4,5,6,3),
(2,4,6,5,3), (2,4)(5,6), (2,4,5), (2,4,6), (2,4)(3,5), (2,4,3,5,6),
(2,4,6,3,5), (2,4)(3,6), (2,4,3,6,5), (2,4,5,3,6), (2,5,6,4,3), (2,5,3),
(2,5,4,6,3), (2,5,4), (2,5,6), (2,5)(4,6), (2,5,6,3,4), (2,5)(3,4),
(2,5,3,4,6), (2,5,3,6,4), (2,5,4,3,6), (2,5)(3,6), (2,6,5,4,3), (2,6,3),
(2,6,4,5,3), (2,6,4), (2,6,5), (2,6)(4,5), (2,6,5,3,4), (2,6)(3,4),
(2,6,3,4,5), (2,6,3,5,4), (2,6,4,3,5), (2,6)(3,5), (1,2)(5,6), (1,2)(4,5),
(1,2)(4,6), (1,2)(3,4), (1,2)(3,4,5,6), (1,2)(3,4,6,5), (1,2)(3,5,6,4),
(1,2)(3,5), (1,2)(3,5,4,6), (1,2)(3,6,5,4), (1,2)(3,6), (1,2)(3,6,4,5),
(1,2,3), (1,2,3)(4,5,6), (1,2,3)(4,6,5), (1,2,3,4)(5,6), (1,2,3,4,5),
(1,2,3,4,6), (1,2,3,5,4), (1,2,3,5,6), (1,2,3,5)(4,6), (1,2,3,6,4),
(1,2,3,6,5), (1,2,3,6)(4,5), (1,2,4,3)(5,6), (1,2,4,5,3), (1,2,4,6,3),
(1,2,4), (1,2,4,5,6), (1,2,4,6,5), (1,2,4)(3,5,6), (1,2,4,3,5),
(1,2,4,6)(3,5), (1,2,4)(3,6,5), (1,2,4,3,6), (1,2,4,5)(3,6), (1,2,5,4,3),
(1,2,5,6,3), (1,2,5,3)(4,6), (1,2,5,6,4), (1,2,5), (1,2,5,4,6),
(1,2,5,3,4), (1,2,5,6)(3,4), (1,2,5)(3,4,6), (1,2,5,4)(3,6),
(1,2,5)(3,6,4), (1,2,5,3,6), (1,2,6,4,3), (1,2,6,5,3), (1,2,6,3)(4,5),
(1,2,6,5,4), (1,2,6), (1,2,6,4,5), (1,2,6,3,4), (1,2,6,5)(3,4),
(1,2,6)(3,4,5), (1,2,6,4)(3,5), (1,2,6)(3,5,4), (1,2,6,3,5), (1,3,2),
(1,3,2)(4,5,6), (1,3,2)(4,6,5), (1,3,4,2)(5,6), (1,3,4,5,2), (1,3,4,6,2),
(1,3,5,4,2), (1,3,5,6,2), (1,3,5,2)(4,6), (1,3,6,4,2), (1,3,6,5,2),
(1,3,6,2)(4,5), (1,3)(5,6), (1,3)(4,5), (1,3)(4,6), (1,3,4), (1,3,4,5,6),
(1,3,4,6,5), (1,3,5,6,4), (1,3,5), (1,3,5,4,6), (1,3,6,5,4), (1,3,6),
(1,3,6,4,5), (1,3)(2,4), (1,3)(2,4,5,6), (1,3)(2,4,6,5), (1,3,2,4)(5,6),
(1,3,2,4,5), (1,3,2,4,6), (1,3,5,2,4), (1,3,5,6)(2,4), (1,3,5)(2,4,6),
(1,3,6,2,4), (1,3,6,5)(2,4), (1,3,6)(2,4,5), (1,3)(2,5,6,4), (1,3)(2,5),
(1,3)(2,5,4,6), (1,3,2,5,4), (1,3,2,5,6), (1,3,2,5)(4,6), (1,3,4)(2,5,6),
(1,3,4,2,5), (1,3,4,6)(2,5), (1,3,6,4)(2,5), (1,3,6)(2,5,4), (1,3,6,2,5),
(1,3)(2,6,5,4), (1,3)(2,6), (1,3)(2,6,4,5), (1,3,2,6,4), (1,3,2,6,5),
(1,3,2,6)(4,5), (1,3,4)(2,6,5), (1,3,4,2,6), (1,3,4,5)(2,6),
(1,3,5,4)(2,6), (1,3,5)(2,6,4), (1,3,5,2,6), (1,4,3,2)(5,6), (1,4,5,3,2),
(1,4,6,3,2), (1,4,2), (1,4,5,6,2), (1,4,6,5,2), (1,4,2)(3,5,6),
(1,4,3,5,2), (1,4,6,2)(3,5), (1,4,2)(3,6,5), (1,4,3,6,2), (1,4,5,2)(3,6),
(1,4,3), (1,4,5,6,3), (1,4,6,5,3), (1,4)(5,6), (1,4,5), (1,4,6),
(1,4)(3,5), (1,4,3,5,6), (1,4,6,3,5), (1,4)(3,6), (1,4,3,6,5), (1,4,5,3,6),
(1,4,2,3)(5,6), (1,4,5,2,3), (1,4,6,2,3), (1,4)(2,3), (1,4,5,6)(2,3),
(1,4,6,5)(2,3), (1,4)(2,3,5,6), (1,4,2,3,5), (1,4,6)(2,3,5),
(1,4)(2,3,6,5), (1,4,2,3,6), (1,4,5)(2,3,6), (1,4,2,5,3), (1,4,3)(2,5,6),
(1,4,6,3)(2,5), (1,4)(2,5,6,3), (1,4,3,2,5), (1,4,6)(2,5,3), (1,4)(2,5),
(1,4,2,5,6), (1,4,6,2,5), (1,4)(2,5,3,6), (1,4,2,5)(3,6), (1,4,3,6)(2,5),
(1,4,2,6,3), (1,4,3)(2,6,5), (1,4,5,3)(2,6), (1,4)(2,6,5,3), (1,4,3,2,6),
(1,4,5)(2,6,3), (1,4)(2,6), (1,4,2,6,5), (1,4,5,2,6), (1,4)(2,6,3,5),
(1,4,2,6)(3,5), (1,4,3,5)(2,6), (1,5,4,3,2), (1,5,6,3,2), (1,5,3,2)(4,6),
(1,5,6,4,2), (1,5,2), (1,5,4,6,2), (1,5,3,4,2), (1,5,6,2)(3,4),
(1,5,2)(3,4,6), (1,5,4,2)(3,6), (1,5,2)(3,6,4), (1,5,3,6,2), (1,5,6,4,3),
(1,5,3), (1,5,4,6,3), (1,5,4), (1,5,6), (1,5)(4,6), (1,5,6,3,4),
(1,5)(3,4), (1,5,3,4,6), (1,5,3,6,4), (1,5,4,3,6), (1,5)(3,6), (1,5,4,2,3),
(1,5,6,2,3), (1,5,2,3)(4,6), (1,5,6,4)(2,3), (1,5)(2,3), (1,5,4,6)(2,3),
(1,5,2,3,4), (1,5,6)(2,3,4), (1,5)(2,3,4,6), (1,5,4)(2,3,6),
(1,5)(2,3,6,4), (1,5,2,3,6), (1,5,6,3)(2,4), (1,5,2,4,3), (1,5,3)(2,4,6),
(1,5,3,2,4), (1,5,6)(2,4,3), (1,5)(2,4,6,3), (1,5,6,2,4), (1,5)(2,4),
(1,5,2,4,6), (1,5,2,4)(3,6), (1,5,3,6)(2,4), (1,5)(2,4,3,6),
(1,5,3)(2,6,4), (1,5,4,3)(2,6), (1,5,2,6,3), (1,5,4)(2,6,3),
(1,5)(2,6,4,3), (1,5,3,2,6), (1,5,2,6,4), (1,5,4,2,6), (1,5)(2,6),
(1,5,3,4)(2,6), (1,5)(2,6,3,4), (1,5,2,6)(3,4), (1,6,4,3,2), (1,6,5,3,2),
(1,6,3,2)(4,5), (1,6,5,4,2), (1,6,2), (1,6,4,5,2), (1,6,3,4,2),
(1,6,5,2)(3,4), (1,6,2)(3,4,5), (1,6,4,2)(3,5), (1,6,2)(3,5,4),
(1,6,3,5,2), (1,6,5,4,3), (1,6,3), (1,6,4,5,3), (1,6,4), (1,6,5),
(1,6)(4,5), (1,6,5,3,4), (1,6)(3,4), (1,6,3,4,5), (1,6,3,5,4), (1,6,4,3,5),
(1,6)(3,5), (1,6,4,2,3), (1,6,5,2,3), (1,6,2,3)(4,5), (1,6,5,4)(2,3),
(1,6)(2,3), (1,6,4,5)(2,3), (1,6,2,3,4), (1,6,5)(2,3,4), (1,6)(2,3,4,5),
(1,6,4)(2,3,5), (1,6)(2,3,5,4), (1,6,2,3,5), (1,6,5,3)(2,4), (1,6,2,4,3),
(1,6,3)(2,4,5), (1,6,3,2,4), (1,6,5)(2,4,3), (1,6)(2,4,5,3), (1,6,5,2,4),
(1,6)(2,4), (1,6,2,4,5), (1,6,2,4)(3,5), (1,6,3,5)(2,4), (1,6)(2,4,3,5),
(1,6,3)(2,5,4), (1,6,4,3)(2,5), (1,6,2,5,3), (1,6,4)(2,5,3),
(1,6)(2,5,4,3), (1,6,3,2,5), (1,6,2,5,4), (1,6,4,2,5), (1,6)(2,5),
(1,6,3,4)(2,5), (1,6)(2,5,3,4), (1,6,2,5)(3,4) ]
brk_12> Factorization(K,(2,3,4));
x1^-1*x2*x1
brk_12> Factorization(K,(4,5,6));
x1*x2^-1*x1^-1*x2^-1*x1
brk_12> Factorization(K,(3,4));
fail
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