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[推荐]ecc 和群论工具GAP4.0
发表于: 2011-2-5 15:15 5629

[推荐]ecc 和群论工具GAP4.0

lilianjie 活跃值
1
2011-2-5 15:15
5629
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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lilianjie
雪    币： 433
活跃值： (45)
能力值： ( LV4，RANK：50 )
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2 楼
CHAR=2的

brk_12> Factors(x^(2^7)-x^5+1);
[ x^10+x^8+x^4+x^3+x^2+x+Z(2)^0,
  x^13+x^12+x^10+x^9+x^8+x^7+x^6+x^4+x^2+x+Z(2)^0,
  x^34+x^26+x^24+x^23+x^18+x^16+x^13+x^12+x^10+x^6+x^5+x^2+Z(2)^0,
  x^71+x^70+x^68+x^65+x^64+x^61+x^58+x^57+x^56+x^55+x^52+x^50+x^48+x^46+x^45+x\
^42+x^41+x^40+x^39+x^38+x^36+x^35+x^30+x^29+x^26+x^23+x^22+x^18+x^13+x^11+x^10\
+x^9+x^7+x^6+x^4+x^3+Z(2)^0 ]

CHAR=3的

brk_12> Factors(x^(3^4)-x^5+1);
[ x^3-x^2+x+Z(3)^0, x^6+x^5+x^3+x^2+Z(3)^0, x^10-x^9+x^7-x^6+x^5-x^3-Z(3)^0,
  x^22+x^21-x^20-x^19-x^18+x^16-x^14+x^13-x^12-x^11-x^10+x^9+x^7+x^6-x^5-x^4-x\
^3-Z(3)^0,
  x^40-x^38-x^37-x^35-x^34+x^33+x^31-x^29-x^28-x^26-x^25+x^24+x^23+x^22+x^21-x\
^20-x^19-x^17+x^16-x^13-x^12-x^10+x^8-x^7-x^6-x^5-x^4+x^2-x+Z(3)^0 ]

CHAR=5的

brk_12> Factors(x^5+6*x^4+x+1);
[ x-Z(3)^0, x-Z(3)^0, x^3-x^2+Z(3)^0 ]
2011-2-5 15:30
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lilianjie
雪    币： 433
活跃值： (45)
能力值： ( LV4，RANK：50 )
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接着学！
2011-4-2 11:30
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