6.执行辗转相除法第六步
F 5 = Q 6 × F 6 + F 7 deg ( F 5 ) = 3 deg ( F 6 ) = 2 deg ( F 7 ) = 1 F_{5} = Q_{6} \times F_{6} + F_{7}\ \ \ \ \ \ \ \ \ \ \deg\left( F_{5} \right) = 3\ \ \ \ \ \ \deg\left( F_{6} \right) = 2\ \ \ \ \ \ \deg\left( F_{7} \right) = 1 F5=Q6×F6+F7 deg(F5)=3 deg(F6)=2 deg(F7)=1
∣ S ′ ∣ = F 1 F 1 F 2 F 2 F 3 F 3 F 4 F 4 F 5 F 5 F 6 F 6 F 6 F 5 F 5 ∣ b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 ∣ = F 1 F 1 F 2 F 2 F 3 F 3 F 4 F 4 F 5 F 5 F 6 F 6 F 6 F 7 F 7 ∣ b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 h 1 h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h 1 h 0 ∣ \left| S^{'} \right| = \begin{matrix} \begin{matrix} F_{1} \\ F_{1} \\ F_{2} \\ F_{2} \\ F_{3} \\ F_{3} \\ F_{4} \\ F_{4} \\ F_{5} \\ F_{5} \\ F_{6} \\ F_{6} \\ F_{6} \\ F_{5} \\ F_{5} \end{matrix} & \left| \begin{matrix} b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} \end{matrix} \right| = \end{matrix}\begin{matrix} \begin{matrix} F_{1} \\ F_{1} \\ F_{2} \\ F_{2} \\ F_{3} \\ F_{3} \\ F_{4} \\ F_{4} \\ F_{5} \\ F_{5} \\ F_{6} \\ F_{6} \\ F_{6} \\ F_{7} \\ F_{7} \end{matrix} & \left| \begin{matrix} b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & h_{1} & h_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & h_{1} & h_{0} \end{matrix} \right| \end{matrix} S′ =F1F1F2F2F3F3F4F4F5F5F6F6F6F5F5 b700000000000000b6b70000000000000b5b6c6000000000000b4b5c5c600000000000b3b4c4c5d50000000000b2b3c3c4d4d5000000000b1b2c2c3d3d4e400000000b0b1c1c2d2d3e3e400000000b0c0c1d1d2e2e3f3000000000c0d0d1e1e2f2f30000000000d0e0e1f1f2g200f300000000e0f0f1g1g20f2f3000000000f0g0g1g2f1f200000000000g0g1f0f1000000000000g00f0 =F1F1F2F2F3F3F4F4F5F5F6F6F6F7F7 b700000000000000b6b70000000000000b5b6c6000000000000b4b5c5c600000000000b3b4c4c5d50000000000b2b3c3c4d4d5000000000b1b2c2c3d3d4e400000000b0b1c1c2d2d3e3e400000000b0c0c1d1d2e2e3f3000000000c0d0d1e1e2f2f30000000000d0e0e1f1f2g200000000000e0f0f1g1g2000000000000f0g0g1g2h1000000000000g0g1h0h1000000000000g00h0
对应子结式 S 1 S_{1} S1：
S 1 = ( − 1 ) ( m − 1 ) ( l − 1 ) d e t p o l ( F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 0 F 0 F 0 F 0 F 0 F 0 ( b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 0 0 0 0 0 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 0 0 0 0 0 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 0 0 0 0 0 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 0 0 0 0 0 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 0 0 0 0 0 0 a 8 a 7 a 6 a 5 a 4 a 3 a 2 a 1 a 0 ) ) = ( − 1 ) ( m − 1 ) ( l − 1 ) d e t p o l ( F 1 F 1 F 2 F 2 F 3 F 3 F 4 F 4 F 5 F 5 F 6 F 6 F 7 ∣ b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 c 6 c 5 c 4 c 3 c 2 c 1 c 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 d 5 d 4 d 3 d 2 d 1 d 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 e 4 e 3 e 2 e 1 e 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 f 3 f 2 f 1 f 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 g 2 g 1 g 0 0 0 0 0 0 0 0 0 0 0 0 0 h 1 h 0 ∣ ) S_{1} = ( - 1)^{(m - 1)(l - 1)}detpol\begin{pmatrix} \begin{matrix} F_{1} \\ F_{1} \\ F_{1} \\ F_{1} \\ F_{1} \\ F_{1} \\ F_{1} \\ F_{0} \\ F_{0} \\ F_{0} \\ F_{0} \\ F_{0} \\ F_{0} \end{matrix} & \begin{pmatrix} b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} \\ a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & a_{8} & a_{7} & a_{6} & a_{5} & a_{4} & a_{3} & a_{2} & a_{1} & a_{0} \end{pmatrix} \end{pmatrix} = ( - 1)^{(m - 1)(l - 1)}detpol\begin{pmatrix} \begin{matrix} F_{1} \\ F_{1} \\ F_{2} \\ F_{2} \\ F_{3} \\ F_{3} \\ F_{4} \\ F_{4} \\ F_{5} \\ F_{5} \\ F_{6} \\ F_{6} \\ F_{7} \end{matrix} & \left| \begin{matrix} b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & b_{7} & b_{6} & b_{5} & b_{4} & b_{3} & b_{2} & b_{1} & b_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & c_{6} & c_{5} & c_{4} & c_{3} & c_{2} & c_{1} & c_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & d_{5} & d_{4} & d_{3} & d_{2} & d_{1} & d_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & e_{4} & e_{3} & e_{2} & e_{1} & e_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & f_{3} & f_{2} & f_{1} & f_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & g_{2} & g_{1} & g_{0} \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0& 0 & h_{1} & h_{0} \end{matrix} \right| \end{pmatrix} S1=(−1)(m−1)(l−1)detpol F1F1F1F1F1F1F1F0F0F0F0F0F0 b7000000a800000b6b700000a7a80000b5b6b70000a6a7a8000b4b5b6b7000a5a6a7a800b3b4b5b6b700a4a5a6a7a80b2b3b4b5b6b70a3a4a5a6a7a8b1b2b3b4b5b6b7a2a3a4a5a6a7b0b1b2b3b4b5b6a1a2a3a4a5a60b0b1b2b3b4b5a0a1a2a3a4a500b0b1b2b3b40a0a1a2a3a4000b0b1b2b300a0a1a2a30000b0b1b2000a0a1a200000b0b10000a0a1000000b000000a0 =(−1)(m−1)(l−1)detpol F1F1F2F2F3F3F4F4F5F5F6F6F7 b7000000000000b6b700000000000b5b6c60000000000b4b5c5c6000000000b3b4c4c5d500000000b2b3c3c4d4d50000000b1b2c2c3d3d4e4000000b0b1c1c2d2d3e3e4000000b0c0c1d1d2e2e3f30000000c0d0d1e1e2f2f300000000d0e0e1f1f2g2000000000e0f0f1g1g20000000000f0g0g1h100000000000g0h0