f(x)=x^5-a1*x^4+a2*x^3-a3*x^2+a4*x-a5 は既約で可解な有理数係数の方程式とします． θa=r1*r4+r2*r3, θb=(r1*r4-r2*r3)^2, θc=l1+l2+l3+l4, θd=(l1+l4-l2-l3)^2 とします. このとき， [1] θa=2 a1^2-5 a2 [2]θb,θc,θd は各々 fb=0,fc=0,fd=0の（重複度が1または 6 の) 有理数解 fb=15625*a2^12 - 250000*a1*a2^10*a3 + 1500000*a1^2*a2^8*a3^2 + 500000*a2^9*a3^2 - 4000000*a1^3*a2^6*a3^3 - 6000000*a1*a2^7*a3^3 + 4000000*a1^4*a2^4*a3^4 + 24000000*a1^2*a2^5*a3^4 + 6000000*a2^6*a3^4 - 32000000*a1^3*a2^3*a3^5 - 48000000*a1*a2^4*a3^5 + 96000000*a1^2*a2^2*a3^6 + 32000000*a2^3*a3^6 - 128000000*a1*a2*a3^7 + 64000000*a3^8 + 500000*a1^2*a2^9*a4 - 875000*a2^10*a4 - 6000000*a1^3*a2^7*a3*a4 + 10500000*a1*a2^8*a3*a4 + 24000000*a1^4*a2^5*a3^2*a4 - 30000000*a1^2*a2^6*a3^2*a4 - 21000000*a2^7*a3^2*a4 - 32000000*a1^5*a2^3*a3^3*a4 - 40000000*a1^3*a2^4*a3^3*a4 + 168000000*a1*a2^5*a3^3*a4 + 192000000*a1^4*a2^2*a3^4*a4 - 240000000*a1^2*a2^3*a3^4*a4 - 168000000*a2^4*a3^4*a4 - 384000000*a1^3*a2*a3^5*a4 + 672000000*a1*a2^2*a3^5*a4 + 256000000*a1^2*a3^6*a4 - 448000000*a2*a3^6*a4 + 6000000*a1^4*a2^6*a4^2 - 21000000*a1^2*a2^7*a4^2 + 17750000*a2^8*a4^2 - 48000000*a1^5*a2^4*a3*a4^2 + 168000000*a1^3*a2^5*a3*a4^2 - 140000000*a1*a2^6*a3*a4^2 + 96000000*a1^6*a2^2*a3^2*a4^2 - 240000000*a1^4*a2^3*a3^2*a4^2 - 68000000*a1^2*a2^4*a3^2*a4^2 + 284000000*a2^5*a3^2*a4^2 - 384000000*a1^5*a2*a3^3*a4^2 + 1376000000*a1^3*a2^2*a3^3*a4^2 - 1104000000*a1*a2^3*a3^3*a4^2 + 384000000*a1^4*a3^4*a4^2 - 1472000000*a1^2*a2*a3^4*a4^2 + 1136000000*a2^2*a3^4*a4^2 + 128000000*a1*a3^5*a4^2 + 32000000*a1^6*a2^3*a4^3 - 168000000*a1^4*a2^4*a4^3 + 284000000*a1^2*a2^5*a4^3 - 164000000*a2^6*a4^3 - 128000000*a1^7*a2*a3*a4^3 + 672000000*a1^5*a2^2*a3*a4^3 - 1104000000*a1^3*a2^3*a3*a4^3 + 640000000*a1*a2^4*a3*a4^3 + 256000000*a1^6*a3^2*a4^3 - 1472000000*a1^4*a2*a3^2*a4^3 + 2336000000*a1^2*a2^2*a3^2*a4^3 - 1392000000*a2^3*a3^2*a4^3 + 256000000*a1^3*a3^3*a4^3 + 192000000*a1*a2*a3^3*a4^3 - 640000000*a3^4*a4^3 + 64000000*a1^8*a4^4 - 448000000*a1^6*a2*a4^4 + 1136000000*a1^4*a2^2*a4^4 - 1392000000*a1^2*a2^3*a4^4 + 764000000*a2^4*a4^4 + 128000000*a1^5*a3*a4^4 + 192000000*a1^3*a2*a3*a4^4 - 768000000*a1*a2^2*a3*a4^4 - 1216000000*a1^2*a3^2*a4^4 + 2240000000*a2*a3^2*a4^4 - 640000000*a1^4*a4^5 + 2240000000*a1^2*a2*a4^5 - 1760000000*a2^2*a4^5 - 640000000*a1*a3*a4^5 + 1600000000*a4^6 - 1500000*a1*a2^9*a5 + 18000000*a1^2*a2^7*a3*a5 + 2500000*a2^8*a3*a5 - 72000000*a1^3*a2^5*a3^2*a5 - 64000000*a1*a2^6*a3^2*a5 + 96000000*a1^4*a2^3*a3^3*a5 + 392000000*a1^2*a2^4*a3^3*a5 + 40000000*a2^5*a3^3*a5 - 704000000*a1^3*a2^2*a3^4*a5 - 576000000*a1*a2^3*a3^4*a5 + 1664000000*a1^2*a2*a3^5*a5 + 160000000*a2^2*a3^5*a5 - 1280000000*a1*a3^6*a5 - 36000000*a1^3*a2^6*a4*a5 + 62000000*a1*a2^7*a4*a5 + 288000000*a1^4*a2^4*a3*a4*a5 - 456000000*a1^2*a2^5*a3*a4*a5 - 20000000*a2^6*a3*a4*a5 - 576000000*a1^5*a2^2*a3^2*a4*a5 + 128000000*a1^3*a2^3*a3^2*a4*a5 + 1096000000*a1*a2^4*a3^2*a4*a5 + 2816000000*a1^4*a2*a3^3*a4*a5 - 3744000000*a1^2*a2^2*a3^3*a4*a5 + 240000000*a2^3*a3^3*a4*a5 - 3328000000*a1^3*a3^4*a4*a5 + 2560000000*a1*a2*a3^4*a4*a5 + 3200000000*a3^5*a4*a5 - 288000000*a1^5*a2^3*a4^2*a5 + 992000000*a1^3*a2^4*a4^2*a5 - 824000000*a1*a2^5*a4^2*a5 + 1152000000*a1^6*a2*a3*a4^2*a5 - 3808000000*a1^4*a2^2*a3*a4^2*a5 + 3440000000*a1^2*a2^3*a3*a4^2*a5 - 960000000*a2^4*a3*a4^2*a5 - 2816000000*a1^5*a3^2*a4^2*a5 + 6912000000*a1^3*a2*a3^2*a4^2*a5 - 2240000000*a1*a2^2*a3^2*a4^2*a5 + 5120000000*a1^2*a3^3*a4^2*a5 - 11200000000*a2*a3^3*a4^2*a5 - 768000000*a1^7*a4^3*a5 + 3968000000*a1^5*a2*a4^3*a5 - 6592000000*a1^3*a2^2*a4^3*a5 + 4000000000*a1*a2^3*a4^3*a5 + 2432000000*a1^4*a3*a4^3*a5 - 11840000000*a1^2*a2*a3*a4^3*a5 + 8000000000*a2^2*a3*a4^3*a5 + 9600000000*a1*a3^2*a4^3*a5 + 3840000000*a1^3*a4^4*a5 - 6400000000*a1*a2*a4^4*a5 - 16000000000*a3*a4^4*a5 + 86000000*a1^2*a2^6*a5^2 - 125000000*a2^7*a5^2 - 688000000*a1^3*a2^4*a3*a5^2 + 880000000*a1*a2^5*a3*a5^2 + 1376000000*a1^4*a2^2*a3^2*a5^2 + 240000000*a1^2*a2^3*a3^2*a5^2 - 1900000000*a2^4*a3^2*a5^2 - 7040000000*a1^3*a2*a3^3*a5^2 + 6400000000*a1*a2^2*a3^3*a5^2 + 9600000000*a1^2*a3^4*a5^2 - 8000000000*a2*a3^4*a5^2 + 1376000000*a1^4*a2^3*a4*a5^2 - 4360000000*a1^2*a2^4*a4*a5^2 + 3500000000*a2^5*a4*a5^2 - 5504000000*a1^5*a2*a3*a4*a5^2 + 16480000000*a1^3*a2^2*a3*a4*a5^2 - 14800000000*a1*a2^3*a3*a4*a5^2 + 14080000000*a1^4*a3^2*a4*a5^2 - 30400000000*a1^2*a2*a3^2*a4*a5^2 + 32000000000*a2^2*a3^2*a4*a5^2 - 32000000000*a1*a3^3*a4*a5^2 + 5504000000*a1^6*a4^2*a5^2 - 26880000000*a1^4*a2*a4^2*a5^2 + 43200000000*a1^2*a2^2*a4^2*a5^2 - 22000000000*a2^3*a4^2*a5^2 - 16000000000*a1^3*a3*a4^2*a5^2 + 24000000000*a1*a2*a3*a4^2*a5^2 + 40000000000*a3^2*a4^2*a5^2 - 16000000000*a1^2*a4^3*a5^2 + 40000000000*a2*a4^3*a5^2 - 2400000000*a1^3*a2^3*a5^3 + 6000000000*a1*a2^4*a5^3 + 9600000000*a1^4*a2*a3*a5^3 - 20000000000*a1^2*a2^2*a3*a5^3 - 10000000000*a2^3*a3*a5^3 - 32000000000*a1^3*a3^2*a5^3 + 80000000000*a1*a2*a3^2*a5^3 - 19200000000*a1^5*a4*a5^3 + 80000000000*a1^3*a2*a4*a5^3 - 80000000000*a1*a2^2*a4*a5^3 + 80000000000*a1^2*a3*a4*a5^3 - 200000000000*a2*a3*a4*a5^3 + 40000000000*a1^4*a5^4 - 200000000000*a1^2*a2*a5^4 + 250000000000*a2^2*a5^4 - (18750*a2^10 - 250000*a1*a2^8*a3 + 1200000*a1^2*a2^6*a3^2 + 400000*a2^7*a3^2 - 2400000*a1^3*a2^4*a3^3 - 3600000*a1*a2^5*a3^3 + 1600000*a1^4*a2^2*a3^4 + 9600000*a1^2*a2^3*a3^4 + 2800000*a2^4*a3^4 - 6400000*a1^3*a2*a3^5 - 12800000*a1*a2^2*a3^5 + 6400000*a1^2*a3^6 + 6400000*a2*a3^6 + 400000*a1^2*a2^7*a4 - 575000*a2^8*a4 - 3600000*a1^3*a2^5*a3*a4 + 4600000*a1*a2^6*a3*a4 + 9600000*a1^4*a2^3*a3^2*a4 - 3600000*a1^2*a2^4*a3^2*a4 - 7800000*a2^5*a3^2*a4 - 6400000*a1^5*a2*a3^3*a4 - 25600000*a1^3*a2^2*a3^3*a4 + 25600000*a1*a2^3*a3^3*a4 + 12800000*a1^4*a3^4*a4 + 41600000*a1^2*a2*a3^4*a4 - 25600000*a2^2*a3^4*a4 - 44800000*a1*a3^5*a4 + 2800000*a1^4*a2^4*a4^2 - 7800000*a1^2*a2^5*a4^2 + 6200000*a2^6*a4^2 - 12800000*a1^5*a2^2*a3*a4^2 + 25600000*a1^3*a2^3*a3*a4^2 - 14400000*a1*a2^4*a3*a4^2 + 6400000*a1^6*a3^2*a4^2 + 41600000*a1^4*a2*a3^2*a4^2 - 91200000*a1^2*a2^2*a3^2*a4^2 + 40000000*a2^3*a3^2*a4^2 - 96000000*a1^3*a3^3*a4^2 + 124800000*a1*a2*a3^3*a4^2 + 9600000*a3^4*a4^2 + 6400000*a1^6*a2*a4^3 - 25600000*a1^4*a2^2*a4^3 + 40000000*a1^2*a2^3*a4^3 - 5600000*a2^4*a4^3 - 44800000*a1^5*a3*a4^3 + 124800000*a1^3*a2*a3*a4^3 - 182400000*a1*a2^2*a3*a4^3 + 96000000*a1^2*a3^2*a4^3 + 92800000*a2*a3^2*a4^3 + 9600000*a1^4*a4^4 + 92800000*a1^2*a2*a4^4 - 129600000*a2^2*a4^4 - 294400000*a1*a3*a4^4 + 339200000*a4^5 - 400000*a1^3*a2^6*a5 + 600000*a1*a2^7*a5 + 3200000*a1^4*a2^4*a3*a5 - 3600000*a1^2*a2^5*a3*a5 - 1000000*a2^6*a3*a5 - 6400000*a1^5*a2^2*a3^2*a5 - 6400000*a1^3*a2^3*a3^2*a5 + 19200000*a1*a2^4*a3^2*a5 + 44800000*a1^4*a2*a3^3*a5 - 57600000*a1^2*a2^2*a3^3*a5 + 19200000*a2^3*a3^3*a5 - 38400000*a1^3*a3^4*a5 - 38400000*a1*a2*a3^4*a5 + 185600000*a3^5*a5 - 6400000*a1^5*a2^3*a4*a5 + 23200000*a1^3*a2^4*a4*a5 - 27600000*a1*a2^5*a4*a5 + 25600000*a1^6*a2*a3*a4*a5 - 83200000*a1^4*a2^2*a3*a4*a5 + 153600000*a1^2*a2^3*a3*a4*a5 - 134400000*a2^4*a3*a4*a5 - 89600000*a1^5*a3^2*a4*a5 + 12800000*a1^3*a2*a3^2*a4*a5 + 403200000*a1*a2^2*a3^2*a4*a5 + 364800000*a1^2*a3^3*a4*a5 - 1296000000*a2*a3^3*a4*a5 - 25600000*a1^7*a4^2*a5 + 147200000*a1^5*a2*a4^2*a5 - 342400000*a1^3*a2^2*a4^2*a5 + 236800000*a1*a2^3*a4^2*a5 + 544000000*a1^4*a3*a4^2*a5 - 1731200000*a1^2*a2*a3*a4^2*a5 + 1392000000*a2^2*a3*a4^2*a5 + 1024000000*a1*a3^2*a4^2*a5 - 563200000*a1^3*a4^3*a5 + 992000000*a1*a2*a4^3*a5 - 1920000000*a3*a4^3*a5 + 19200000*a1^4*a2^3*a5^2 - 128400000*a1^2*a2^4*a5^2 + 270600000*a2^5*a5^2 - 76800000*a1^5*a2*a3*a5^2 + 556800000*a1^3*a2^2*a3*a5^2 - 1376000000*a1*a2^3*a3*a5^2 + 6400000*a1^4*a3^2*a5^2 + 112000000*a1^2*a2*a3^2*a5^2 + 2040000000*a2^2*a3^2*a5^2 - 1280000000*a1*a3^3*a5^2 + 153600000*a1^6*a4*a5^2 - 1286400000*a1^4*a2*a4*a5^2 + 3744000000*a1^2*a2^2*a4*a5^2 - 2680000000*a2^3*a4*a5^2 - 288000000*a1^3*a3*a4*a5^2 - 2960000000*a1*a2*a3*a4*a5^2 + 3200000000*a3^2*a4*a5^2 + 2240000000*a1^2*a4^2*a5^2 + 400000000*a2*a4^2*a5^2 + 179200000*a1^5*a5^3 - 1120000000*a1^3*a2*a5^3 + 1200000000*a1*a2^2*a5^3 + 2400000000*a1^2*a3*a5^3 - 2000000000*a2*a3*a5^3 - 8000000000*a1*a4*a5^3 + 10000000000*a5^4)*x + (9375*a2^8 - 100000*a1*a2^6*a3 + 360000*a1^2*a2^4*a3^2 + 120000*a2^5*a3^2 - 480000*a1^3*a2^2*a3^3 - 720000*a1*a2^3*a3^3 + 160000*a1^4*a3^4 + 960000*a1^2*a2*a3^4 + 400000*a2^2*a3^4 - 640000*a1*a3^5 + 120000*a1^2*a2^5*a4 - 110000*a2^6*a4 - 720000*a1^3*a2^3*a3*a4 + 240000*a1*a2^4*a3*a4 + 960000*a1^4*a2*a3^2*a4 + 2160000*a1^2*a2^2*a3^2*a4 - 600000*a2^3*a3^2*a4 - 3520000*a1^3*a3^3*a4 - 1600000*a1*a2*a3^3*a4 + 1600000*a3^4*a4 + 400000*a1^4*a2^2*a4^2 - 600000*a1^2*a2^3*a4^2 + 900000*a2^4*a4^2 - 640000*a1^5*a3*a4^2 - 1600000*a1^3*a2*a3*a4^2 - 2400000*a1*a2^2*a3*a4^2 + 15200000*a1^2*a3^2*a4^2 - 800000*a2*a3^2*a4^2 + 1600000*a1^4*a4^3 - 800000*a1^2*a2*a4^3 + 800000*a2^2*a4^3 - 28800000*a1*a3*a4^3 + 28000000*a4^4 - 240000*a1^3*a2^4*a5 + 720000*a1*a2^5*a5 + 1280000*a1^4*a2^2*a3*a5 - 3600000*a1^2*a2^3*a3*a5 - 1200000*a2^4*a3*a5 - 1280000*a1^5*a3^2*a5 + 1600000*a1^3*a2*a3^2*a5 + 9600000*a1*a2^2*a3^2*a5 - 1600000*a1^2*a3^3*a5 - 8000000*a2*a3^3*a5 - 1280000*a1^5*a2*a4*a5 + 4000000*a1^3*a2^2*a4*a5 - 1200000*a1*a2^3*a4*a5 + 12800000*a1^4*a3*a4*a5 - 43200000*a1^2*a2*a3*a4*a5 + 12000000*a2^2*a3*a4*a5 + 24000000*a1*a3^2*a4*a5 - 28800000*a1^3*a4^2*a5 + 88000000*a1*a2*a4^2*a5 - 80000000*a3*a4^2*a5 + 2560000*a1^6*a5^2 - 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