学格了：

cjsh

[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] ]