可分解环的表示

Posted 2022-12-03 华仔Ivan

D:\\MathTool\\gaptool>FiniteRing
R4_1×R4_1=R16_107
R4_1×R4_2=R16_116
R4_1×R4_3=R16_112
R4_1×R4_4=R16_206
R4_1×R4_5=R16_207
R4_1×R4_6=R16_208
R4_1×R4_7=R16_209
R4_1×R4_8=R16_255
R4_1×R4_9=R16_210
R4_1×R4_10=R16_224
R4_1×R4_11=R16_211
R4_2×R4_2=R16_103
R4_2×R4_3=R16_113
R4_2×R4_4=R16_212
R4_2×R4_5=R16_213
R4_2×R4_6=R16_214
R4_2×R4_7=R16_215
R4_2×R4_8=R16_256
R4_2×R4_9=R16_216
R4_2×R4_10=R16_217
R4_2×R4_11=R16_218
R4_3×R4_3=R16_104
R4_3×R4_4=R16_219
R4_3×R4_5=R16_220
R4_3×R4_6=R16_221
R4_3×R4_7=R16_222
R4_3×R4_8=R16_223
R4_3×R4_9=R16_225
R4_3×R4_10=R16_226
R4_3×R4_11=R16_227
R4_4×R4_4=R16_301
R4_4×R4_5=R16_303
R4_4×R4_6=R16_305
R4_4×R4_7=R16_308
R4_4×R4_8=R16_354
R4_4×R4_9=R16_314
R4_4×R4_10=R16_307
R4_4×R4_11=R16_324
R4_5×R4_5=R16_304
R4_5×R4_6=R16_306
R4_5×R4_7=R16_309
R4_5×R4_8=R16_355
R4_5×R4_9=R16_315
R4_5×R4_10=R16_319
R4_5×R4_11=R16_325
R4_6×R4_6=R16_307
R4_6×R4_7=R16_310
R4_6×R4_8=R16_356
R4_6×R4_9=R16_316
R4_6×R4_10=R16_320
R4_6×R4_11=R16_326
R4_7×R4_7=R16_311
R4_7×R4_8=R16_312
R4_7×R4_9=R16_317
R4_7×R4_10=R16_321
R4_7×R4_11=R16_327
R4_8×R4_8=R16_313
R4_8×R4_9=R16_318
R4_8×R4_10=R16_322
R4_8×R4_11=R16_328
R4_9×R4_9=R16_384
R4_9×R4_10=R16_323
R4_9×R4_11=R16_302
R4_10×R4_10=R16_386
R4_10×R4_11=R16_387
R4_11×R4_11=R16_389
D:\\MathTool\\gaptool>IRing
R16_312 g_i=0
cnt1=1:R16_312->i=6,j=12=>[[1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,0]],[[0,1,0,0],[0,0,0,0],[0,0,1,0],[0,0,1,0]]
R16_312
R16_312 g_i=0
cnt1=1:R8_41->i=1,j=8=>[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]],[[1,1,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,0]]
cnt1=2:R8_29->i=1,j=14=>[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]],[[1,1,0,0],[0,0,0,0],[0,0,0,0],[0,0,1,0]]
cnt1=3:R8_47->i=3,j=7=>[[0,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,0]],[[1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,1,0]]
cnt1=4:R8_34->i=3,j=12=>[[0,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,0]],[[0,1,0,0],[0,0,0,0],[0,0,1,0],[0,0,1,0]]
cnt1=5:R8_36->i=6,j=9=>[[1,0,0,0],[0,0,0,0],[0,0,1,0],[0,0,0,0]],[[1,1,0,0],[0,0,0,0],[0,0,1,0],[0,0,1,0]]
R16_312
cnt1=1:R16_312/R2_1=R8_47->i=0,j=5
cnt1=2:R16_312/R2_1=R8_41->i=0,j=10 
else if(ID==312)     //R4_7×R4_8=R16_312，A,B是R4_7的2阶矩阵表示生成元，C,D是R4_8的2阶矩阵表示生成元，那么A,B,C,D是R4_7×R4_8的4阶矩阵表示生成元
        m_r=new ZmodnZ(1,2);    
        m_n=4;           
        MATRIXi8 A(4,vector<TElem>(4,0));
        MATRIXi8 B(4,vector<TElem>(4,0));
        MATRIXi8 C(4,vector<TElem>(4,0));
        MATRIXi8 D(4,vector<TElem>(4,0));        
        A[0][0]=1;
        A[0][1]=0;
        A[1][0]=0;
        A[1][1]=0;
        B[0][0]=1;
        B[0][1]=1;
        B[1][0]=0;
        B[1][1]=0; 
        C[2][2]=1;
        C[2][3]=0;
        C[3][2]=0;
        C[3][3]=0;
        D[2][2]=1;
        D[2][3]=0;
        D[3][2]=1;
        D[3][3]=0;         
        gen.push_back(A);
        gen.push_back(B);
        gen.push_back(C);
        gen.push_back(D);