学模和向量空间了，看看区别

cjsh

[这个贴子最后由cjsh在 2011/06/29 03:34pm 第 1 次编辑]

R:=ResidueClassRing(3) ;
R;
RS:=RSpace(R, 2);
RS;
M := RModule(R, 2);
M;
RM:=RMatrixSpace(R, 2, 2);
RM;
F:=FiniteField(3);
F;
FF:=FiniteField(3, 2);
FF;
FFF:=FiniteField(3, 4);
FFF;
Set(F) ;
Set(FF) ;
Set(FFF) ;
RSpace(F, 5);
RSpace(FF, 5);
RSpace(FFF, 5);
VectorSpace(FF, F);
VectorSpace(FFF, F);
VectorSpace(FFF, FF);
Degree(F);
Degree(FF);
Degree(FF);
Degree(F, F);
Degree(FF, F);
Degree(FFF, F);
Degree(FFF, FF);
Generator(FF, F) ;
Generator(FFF, FF) ;
Generator(FFF, F) ;
PrimitiveElement(F);
PrimitiveElement(FF);
PrimitiveElement(FFF);
NormalElement(F);
NormalElement(FF);
NormalElement(FFF);
NormalElement(FF, F);
NormalElement(FFF, F);
NormalElement(FFF, FF);
MatrixAlgebra(FF, F);
MatrixAlgebra(FFF, F);
MatrixAlgebra(FFF, FF);
Set(R) ;
Set(RS) ;
Set(RM) ;
M . 1;
M . 2;
Generators(RM);
CoefficientRing(RM) ;
Zero(RM) ;
Random(RM);
Degree(RS);
Basis(RM);
Rank(RM) ;

Residue class ring of integers modulo 3
Full Vector space of degree 2 over IntegerRing(3)
RModule(IntegerRing(3), 2)
Full KMatrixSpace of 2 by 2 matrices over IntegerRing(3)
Finite field of size 3
Finite field of size 3^2
Finite field of size 3^4
{ 0, 1, 2 }
{ 1, FF.1, FF.1^2, FF.1^3, 2, FF.1^5, FF.1^6, FF.1^7, 0 }
{ 1, FFF.1, FFF.1^2, FFF.1^3, FFF.1^4, FFF.1^5, FFF.1^6, FFF.1^7, FFF.1^8,
FFF.1^9, FFF.1^10, FFF.1^11, FFF.1^12, FFF.1^13, FFF.1^14, FFF.1^15, FFF.1^16,
FFF.1^17, FFF.1^18, FFF.1^19, FFF.1^20, FFF.1^21, FFF.1^22, FFF.1^23, FFF.1^24,
FFF.1^25, FFF.1^26, FFF.1^27, FFF.1^28, FFF.1^29, FFF.1^30, FFF.1^31, FFF.1^32,
FFF.1^33, FFF.1^34, FFF.1^35, FFF.1^36, FFF.1^37, FFF.1^38, FFF.1^39, 2,
FFF.1^41, FFF.1^42, FFF.1^43, FFF.1^44, FFF.1^45, FFF.1^46, FFF.1^47, FFF.1^48,
FFF.1^49, FFF.1^50, FFF.1^51, FFF.1^52, FFF.1^53, FFF.1^54, FFF.1^55, FFF.1^56,
FFF.1^57, FFF.1^58, FFF.1^59, FFF.1^60, FFF.1^61, FFF.1^62, FFF.1^63, FFF.1^64,
FFF.1^65, FFF.1^66, FFF.1^67, FFF.1^68, FFF.1^69, FFF.1^70, FFF.1^71, FFF.1^72,
FFF.1^73, FFF.1^74, FFF.1^75, FFF.1^76, FFF.1^77, FFF.1^78, FFF.1^79, 0 }
Full Vector space of degree 5 over GF(3)
Full Vector space of degree 5 over GF(3^2)
Full Vector space of degree 5 over GF(3^4)
Full Vector space of degree 2 over GF(3)
Mapping from: FldFin: FF to Full Vector space of degree 2 over GF(3)
Full Vector space of degree 4 over GF(3)
Mapping from: FldFin: FFF to Full Vector space of degree 4 over GF(3)
Full Vector space of degree 2 over GF(3^2)
Mapping from: FldFin: FFF to Full Vector space of degree 2 over GF(3^2)
1
2
2
1
2
4
2
FF.1
FFF.1
FFF.1
2
FF.1
FFF.1
1
FF.1
FFF.1
FF.1
FFF.1
FFF.1
Matrix Algebra of degree 2 and dimension 2 with 1 generator over GF(3)
Mapping from: FldFin: FF to Matrix Algebra of degree 2 and dimension 2 with 1
generator over GF(3)
Matrix Algebra of degree 4 and dimension 4 with 1 generator over GF(3)
Mapping from: FldFin: FFF to Matrix Algebra of degree 4 and dimension 4 with 1
generator over GF(3)
Matrix Algebra of degree 2 and dimension 2 with 1 generator over GF(3^2)
Mapping from: FldFin: FFF to Matrix Algebra of degree 2 and dimension 2 with 1
generator over GF(3^2)
{ 0, 1, 2 }
{
    (1 2),
    (0 2),
    (1 0),
    (0 0),
    (2 2),
    (1 1),
    (0 1),
    (2 0),
    (2 1)
}
{
    [0 1]
    [1 1],
    [1 1]
    [1 1],
    [0 0]
    [0 1],
    [2 2]
    [0 1],
    [0 2]
    [2 1],
    [1 0]
    [0 1],
    [2 1]
    [1 0],
    [1 2]
    [2 1],
    [1 2]
    [0 2],
    [1 1]
    [0 1],
    [2 0]
    [0 0],
    [0 0]
    [2 0],
    [2 2]
    [2 0],
    [2 0]
    [2 2],
    [0 1]
    [2 0],
    [2 1]
    [0 0],
    [2 1]
    [2 2],
    [1 1]
    [2 0],
    [2 0]
    [1 1],
    [1 2]
    [1 0],
    [1 0]
    [1 2],
    [2 1]
    [1 1],
    [2 0]
    [0 1],
    [0 0]
    [2 1],
    [2 2]
    [2 1],
    [1 0]
    [2 1],
    [2 0]
    [2 0],
    [0 2]
    [0 2],
    [0 1]
    [0 1],
    [1 0]
    [1 0],
    [0 2]
    [1 0],
    [0 0]
    [1 2],
    [2 2]
    [1 2],
    [0 1]
    [1 2],
    [1 1]
    [1 2],
    [0 2]
    [0 0],
    [0 0]
    [0 2],
    [2 2]
    [0 2],
    [0 2]
    [2 2],
    [1 2]
    [0 0],
    [1 0]
    [0 2],
    [1 2]
    [2 2],
    [2 1]
    [0 1],
    [0 1]
    [2 1],
    [1 1]
    [2 1],
    [0 2]
    [1 1],
    [1 1]
    [0 2],
    [1 2]
    [1 1],
    [2 1]
    [2 0],
    [0 0]
    [1 0],
    [2 2]
    [1 0],
    [2 0]
    [1 2],
    [0 1]
    [1 0],
    [1 2]
    [0 1],
    [2 1]
    [1 2],
    [1 1]
    [1 0],
    [2 0]
    [2 1],
    [0 2]
    [2 0],
    [2 2]
    [0 0],
    [0 0]
    [0 0],
    [2 0]
    [0 2],
    [0 0]
    [2 2],
    [2 2]
    [2 2],
    [1 0]
    [0 0],
    [1 2]
    [2 0],
    [1 0]
    [2 2],
    [2 1]
    [2 1],
    [1 0]
    [1 1],
    [0 1]
    [0 2],
    [2 0]
    [1 0],
    [0 2]
    [0 1],
    [1 0]
    [2 0],
    [0 1]
    [0 0],
    [2 1]
    [0 2],
    [0 1]
    [2 2],
    [1 1]
    [0 0],
    [2 2]
    [1 1],
    [0 0]
    [1 1],
    [1 1]
    [2 2],
    [0 2]
    [1 2],
    [1 2]
    [1 2]
}
M: (1 0)
M: (0 1)
{
    [1 0]
    [0 0],
    [0 0]
    [0 1],
    [0 0]
    [1 0],
    [0 1]
    [0 0]
}
Residue class ring of integers modulo 3
[0 0]
[0 0]
[2 1]
[1 1]
2
[
    [1 0]
    [0 0],
    [0 1]
    [0 0],
    [0 0]
    [1 0],
    [0 0]
    [0 1]
]
4