• 2022-07-23
    设 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 与 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 是互素的正整数. 证明存在环同构: [tex=7.286x1.571]kp4OZVfysTZ/a63vpI0xvXe1jY0uv3BxxuOPz11hsBit5LMamPkMSKpFO7Gu7uLNeA++d4X8SFyfgab5AyCPdNhe7H4Yq6C/GxR/gqv6cpI=[/tex] 
  • 证明  令[p=align:center][tex=10.071x1.214]Qx7oRdRIbZZS4cD//815j1d11eycLCluTOEe/sFxEkFqX9zgex1ZSt/gjpxqD0W+ARxxgotkMg/+O41K/8624S95a6DMjdkEjYMTxv0tdW+i5zMhZ8+q6qXCci3AAxBO[/tex][p=align:center][tex=5.143x1.357]dNpJb9ZdtLwPUwcoeuDIXkFFPHL8h4bZaHbpVkaUf3t3rkFNpqASc2JkN7W625pU[/tex](1) 如果[tex=2.143x1.071]jcdyMlEAbQpDG+hjvS5DmtQDVlkNVWZj7Cx7zeIylxU=[/tex]则 [tex=4.429x1.357]8x67N4ybH2Ls9lP5OhPosQ==[/tex] 于是 [tex=8.0x1.357]UTEOYglMt66PM3wHOaPR46u/zrZcBCvBeI4Qg7cfM7s=[/tex]所以 [tex=5.643x1.357]CUSX85vyvN4N/ph+GAjVt/9DwSjajukzF3ieF92H3NWCUhHuczSBhaIKKwXbJSO6[/tex]因此 [tex=0.643x1.214]4ssBDc1re7hhNB3dpzYmRg==[/tex] 为[tex=1.786x1.214]OjBr4Tm1YnNvv06UUiIxRJ5vGVFKBUWPKbG75emFhSY=[/tex] 到[tex=3.714x1.214]HKAeg2qzVt8ikAes+zpf0COcRTJW5dTtGn11L8uZPbHba3Qvj30Hl/Y43VcVGtqV[/tex]的映射.(2) 设 [tex=4.214x1.214]M85TtvnUWUvJ8/vnE+rp1/lowvybKVkM5HLYk7V5q/moOzmFy7YZsh9uU2w2NzP0[/tex]如果[tex=4.929x1.357]8qmvWE9ZQrRKM207Bvc9ZB12PXY8XtG+MTv/lIENCnE=[/tex] 即[tex=5.643x1.357]CUSX85vyvN4N/ph+GAjVt/9DwSjajukzF3ieF92H3NWCUhHuczSBhaIKKwXbJSO6[/tex]则[tex=8.0x1.357]UTEOYglMt66PM3wHOaPR46u/zrZcBCvBeI4Qg7cfM7s=[/tex]由于 [tex=4.143x1.357]UcAN0AoWl/LgcJvUyg7qcg==[/tex] 因此 [tex=5.214x1.357]N0DrwJq8XAUM5i2fL9Ef4/7qgddwuEZr2IV/p6cSWcY=[/tex]从而 [tex=4.571x1.214]jcdyMlEAbQpDG+hjvS5DmjFyvuOnbVIPTusgQ1mbCFXjvRAB85b15pNwh7w8qKeK[/tex] 这说明 [tex=0.643x1.214]4ssBDc1re7hhNB3dpzYmRg==[/tex] 是[tex=1.786x1.214]OjBr4Tm1YnNvv06UUiIxRJ5vGVFKBUWPKbG75emFhSY=[/tex]到[tex=3.714x1.214]HKAeg2qzVt8ikAes+zpf0COcRTJW5dTtGn11L8uZPbHba3Qvj30Hl/Y43VcVGtqV[/tex]的单映射. 又因为 [tex=10.357x1.357]zLwP6Tvhyaj/I5HF8W8xE8fczDJtn23N/sEOd5XENqDwOSyRgo7BWojchJb9IBR7DWBwfHbODlx4oAvLVYLgzrc4+yntUTwe3uQhdFmiMakhjd5oZN+0nzcAQPopqGlP[/tex] 所以 [tex=8.214x1.357]vhLyAcVxNM1poGIOkuamPkXYAieo6oBCTs5x34rtJFCYzXeKx13+7xU7uuyPdcGgAC/9djcmlxDOxizbrS13CvBf5NaNnk9VQTRRXvFhqRQ=[/tex] 因此[tex=0.643x1.214]4ssBDc1re7hhNB3dpzYmRg==[/tex] 也是[tex=1.786x1.214]OjBr4Tm1YnNvv06UUiIxRJ5vGVFKBUWPKbG75emFhSY=[/tex] 到 [tex=3.714x1.214]HKAeg2qzVt8ikAes+zpf0COcRTJW5dTtGn11L8uZPbHba3Qvj30Hl/Y43VcVGtqV[/tex]的满映射.(3) 对任意的 [tex=4.214x1.214]M85TtvnUWUvJ8/vnE+rp1/lowvybKVkM5HLYk7V5q/moOzmFy7YZsh9uU2w2NzP0[/tex] 有[p=align:center][tex=24.429x2.786]KSS/Uj9pWxUMUjtnRF7HtXTFD/l0YdrQWY8jZSBfzhbklZE4Pz2bPmzwkBEY6OgUOwJi4ZDtnvBELnuf+Q2uYnSrDzO5OtLQvPBFeS9Jank0jctHob9l0UbTaDqnKuRfRtBGMCy7FZTa1FQWVinrt42HSLh4+Huxs/rBZ2aSi3Jxh5ghlklMoAIEu8m++CUoO5VNO6E8Sbi2c2Suf4f+EpXrT9k+Ab3JPp37/iZlo9G7K4m3pkzXNrZeGCJJiPXE5G+NrYtkqMuBWEjQ1vM8ZjxW4JIrcSEkH6LE18zuFElTnZuRn7q5JNGKcVOJGFOPsF+yUiwIGegEWiJTXRsHuhFa1IlOyoOKWLb79LwKMeilDU9Odsmy1TReWmZlf+6osQh1T/VQqL5xlNIlzOMeotUJ2hObOb7oM52DLqOC5/g=[/tex]所以 [tex=0.643x1.214]4ssBDc1re7hhNB3dpzYmRg==[/tex] 为 [tex=1.786x1.214]OjBr4Tm1YnNvv06UUiIxRJ5vGVFKBUWPKbG75emFhSY=[/tex]到 [tex=3.714x1.214]HKAeg2qzVt8ikAes+zpf0COcRTJW5dTtGn11L8uZPbHba3Qvj30Hl/Y43VcVGtqV[/tex]环满同态. 因此 [tex=0.643x1.214]4ssBDc1re7hhNB3dpzYmRg==[/tex] 是 [tex=1.786x1.214]OjBr4Tm1YnNvv06UUiIxRJ5vGVFKBUWPKbG75emFhSY=[/tex] 到 [tex=3.714x1.214]HKAeg2qzVt8ikAes+zpf0COcRTJW5dTtGn11L8uZPbHba3Qvj30Hl/Y43VcVGtqV[/tex] 的同构映射[p=align:center][tex=9.357x1.571]X4E8QtTAYA/5MqIQX8qzLHoUu8DmQNR8rGOyDg2ZWKElmVV7SgFUERD11DYFPjVGiBtrBOUJ/uKpYfLTYGF9sQPyhBnwH8C0ezeROUgQCN0=[/tex]

    内容

    • 0

      采用基2时间抽取FFT算法流图计算8点序列的DFT,第一级的数据顺序为 A: x[0],x[2],x[4],x[6],x[1],x[3],x[5],x[7] B: x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7] C: x[0],x[4],x[2],x[6],x[1],x[5],x[3],x[7] D: x[0],x[2],x[1],x[3],x[4],x[6],x[5],x[7]

    • 1

       证明如果 [tex=0.929x0.786]VF0GLe2VBE/4VKNzpyOfFg==[/tex] 与 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 是不同的正整数, 则环 [tex=1.643x1.0]/YsKT7S2YH+eMKhH6BVb3g==[/tex]与 [tex=1.357x1.0]8jytUXDN0JoJDKzPCmdDnA==[/tex]不同构. 

    • 2

      设DES加密算法中的一个S盒为: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 15 12 8 2 4 9 1 7 5 11 A: 1010 B: 0001 C: 1011 D: 0111

    • 3

      下面是图的拓扑排序的是?(多选)[img=340x240]1802faef6ebcc2a.png[/img] A: 2 8 0 7 1 3 5 6 4 9 10 11 12 B: 2 8 7 0 6 9 11 12 10 1 3 5 4 C: 8 2 7 3 0 6 1 5 4 9 10 11 12 D: 8 2 7 0 6 9 10 11 12 1 3 5 4

    • 4

      下面语句的输出结果是?range(len('HelloWorld')) A: [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11] B: 11 C: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] D: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]