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[这个贴子最后由cjsh在 2011/06/30 00:21pm 第 1 次编辑]
G := MatrixGroup<4, IntegerRing() |
[ -1, 0, 1, 0, 0, -1, 1, -3, -1, 0, 0, 0, 0, 0, 0, 1 ],
[ -1, 0, 0, 0, -3, 2, 0, 3, 0, 0, -1, 0, 1, -1, 0, -1 ] >;
G;
L:=Lattice(G) ;
L;
IsGLattice(L);
Group(L) ;
NumberOfActionGenerators(L);
Nagens(L) ;
ActionGenerator(L, 1);
ActionGenerator(L, 2);
NaturalGroup(L);
NaturalActionGenerator(L, 1);
NaturalActionGenerator(L, 2);
InvariantForms(L);
InvariantForms(L, 1) ;
InvariantForms(L, 2) ;
InvariantForms(L, 3) ;
InvariantForms(L, 0) ;
SymmetricForms(L) ;
SymmetricForms(L, 1);
SymmetricForms(L, 2);
SymmetricForms(L, 0);
AntisymmetricForms(L);
AntisymmetricForms(L, 1) ;
AntisymmetricForms(L, 0) ;
NumberOfInvariantForms(L);
NumberOfSymmetricForms(L);
NumberOfAntisymmetricForms(L);
PositiveDefiniteForm(L) ;
E := EndomorphismRing(G);
E;
Endomorphisms(L, 1) ;
Endomorphisms(L, 2) ;
Endomorphisms(L, 3) ;
DimensionOfEndomorphismRing(L) ;
DimensionOfCentreOfEndomorphismRing(L);
CentreOfEndomorphismRing(L) ;
CentralEndomorphisms(L, 1);
CentreOfEndomorphismRing(L) ;
CentralEndomorphisms(L, 1);
CentralEndomorphisms(L, 2);
CentralEndomorphisms(L, 3);
MatrixGroup(4, Integer Ring)
Generators:
[-1 0 1 0]
[ 0 -1 1 -3]
[-1 0 0 0]
[ 0 0 0 1]
[-1 0 0 0]
[-3 2 0 3]
[ 0 0 -1 0]
[ 1 -1 0 -1]
Standard G-Lattice of rank 4 and degree 4
true
MatrixGroup(4, Integer Ring)
Generators:
[-1 0 1 0]
[ 0 -1 1 -3]
[-1 0 0 0]
[ 0 0 0 1]
[-1 0 0 0]
[-3 2 0 3]
[ 0 0 -1 0]
[ 1 -1 0 -1]
2
2
[-1 0 1 0]
[ 0 -1 1 -3]
[-1 0 0 0]
[ 0 0 0 1]
[-1 0 0 0]
[-3 2 0 3]
[ 0 0 -1 0]
[ 1 -1 0 -1]
MatrixGroup(4, Integer Ring)
Generators:
[-1 0 1 0]
[ 0 -1 1 -3]
[-1 0 0 0]
[ 0 0 0 1]
[-1 0 0 0]
[-3 2 0 3]
[ 0 0 -1 0]
[ 1 -1 0 -1]
[-1 0 1 0]
[ 0 -1 1 -3]
[-1 0 0 0]
[ 0 0 0 1]
[-1 0 0 0]
[-3 2 0 3]
[ 0 0 -1 0]
[ 1 -1 0 -1]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10],
[ 14 14 7 0]
[ 14 176 7 -81]
[ 7 7 14 0]
[ 0 -81 0 54],
[ 0 0 -1 0]
[ 0 0 -1 0]
[ 1 1 0 0]
[ 0 0 0 0]
]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10]
]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10],
[ 14 14 7 0]
[ 14 176 7 -81]
[ 7 7 14 0]
[ 0 -81 0 54]
]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10],
[ 14 14 7 0]
[ 14 176 7 -81]
[ 7 7 14 0]
[ 0 -81 0 54],
[ 0 0 -1 0]
[ 0 0 -1 0]
[ 1 1 0 0]
[ 0 0 0 0]
]
[]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10],
[ 14 14 7 0]
[ 14 176 7 -81]
[ 7 7 14 0]
[ 0 -81 0 54]
]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10]
]
[
[ 4 4 2 0]
[ 4 34 2 -15]
[ 2 2 4 0]
[ 0 -15 0 10],
[ 14 14 7 0]
[ 14 176 7 -81]
[ 7 7 14 0]
[ 0 -81 0 54]
]
[]
[
[ 0 0 -1 0]
[ 0 0 -1 0]
[ 1 1 0 0]
[ 0 0 0 0]
]
[
[ 0 0 -1 0]
[ 0 0 -1 0]
[ 1 1 0 0]
[ 0 0 0 0]
]
[]
3
2
1
>> PositiveDefiniteForm(L) ;
^
Runtime error in ' ositiveDefiniteForm';: Bad argument types
Argument types given: Lat
Matrix Algebra of degree 4 and dimension 3 over Integer Ring
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
]
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1],
[ 2 0 2 0]
[ 5 -3 2 0]
[-2 0 4 0]
[ 0 0 0 -3]
]
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1],
[ -2 0 10 0]
[ -5 3 10 0]
[-10 0 8 0]
[ 0 0 0 3],
[ -96 0 60 0]
[-105 9 60 0]
[ -60 0 -36 0]
[ 0 0 0 9]
]
3
3
Matrix Algebra of degree 4 and dimension 3 over Integer Ring
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
]
Matrix Algebra of degree 4 and dimension 3 over Integer Ring
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
]
[
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1],
[-2 0 0 0]
[-3 1 0 0]
[ 0 0 -2 0]
[ 0 0 0 1]
]
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