| 1 | dribbling to file "colored-poly-tests.output"
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| 2 |
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| 3 | Warning: Test 1
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| 4 | ------------------- CASE 1 -------------------
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| 5 | Condition:
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| 6 | Green list: [ ]
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| 7 | Red list: [ ]
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| 8 | Basis: [ (4) * X + (5) * Y, ( - 10) * Y^2 ]
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| 9 | Warning: Test 2 - Enneper
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| 10 | ------------------- CASE 1 -------------------
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| 11 | Condition:
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| 12 | Green list: [ ]
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| 13 | Red list: [ ]
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| 14 | Basis: [ ( - 3) * U^2 + (3) * V^2 + (1) * Z, (2) * V^3 + (1) * V * Z + (3) * V + ( - 1) * Y, ( - 6) * U * V^2 + (1) * U * Z + ( - 9) * U + (3) * X, (4) * U * V * Z + ( - 3) * U * Y + (3) * V * X, (9) * U * V * Y + ( - 2) * U * Z^2 + (18) * U * Z + ( - 9) * V^2 * X + ( - 6) * X * Z, ( - 27) * U * Y^2 + (8) * U * Z^3 + ( - 72) * U * Z^2 + (36) * V^2 * X * Z + (27) * V * X * Y + (24) * X * Z^2, (34992) * V^2 * X^2 + ( - 34992) * V^2 * Y^2 + ( - 186624) * V^2 * Z + ( - 15552) * V * Y * Z^2 + (46656) * V * Y * Z + (15552) * X^2 * Z + (93312) * X^2 + (19440) * Y^2 * Z + ( - 93312) * Y^2 + ( - 576) * Z^4 + (6912) * Z^3 + (15552) * Z^2 + ( - 279936) * Z, (139968) * U * X + (93312) * V^2 * Z + ( - 139968) * V * Y + (15552) * Z^2 + ( - 139968) * Z, (105815808) * V^2 * Y * Z + (52907904) * V * X^2 + ( - 52907904) * V * Y^2 + (15676416) * V * Z^3 + (141087744) * V * Z^2 + ( - 17635968) * Y * Z^2 + ( - 52907904) * Y * Z, (31104) * V^2 * Z^2 + (93312) * V^2 * Z + ( - 93312) * V * Y * Z + ( - 46656) * X^2 + (46656) * Y^2 + (1728) * Z^3 + ( - 31104) * Z^2 + (139968) * Z, (8817984) * V * X^2 * Z + (26453952) * V * X^2 + (44089920) * V * Y^2 * Z + ( - 26453952) * V * Y^2 + (2612736) * V * Z^4 + (31352832) * V * Z^3 + (70543872) * V * Z^2 + (26453952) * X^2 * Y + ( - 26453952) * Y^3 + ( - 3919104) * Y * Z^3 + ( - 105815808) * Y * Z, ( - 158723712) * V * X^2 * Y + ( - 317447424) * V * Y^3 * Z + (158723712) * V * Y^3 + ( - 23514624) * V * Y * Z^4 + ( - 188116992) * V * Y * Z^3 + ( - 634894848) * V * Y * Z^2 + (26453952) * X^4 + ( - 211631616) * X^2 * Y^2 + (6858432) * X^2 * Z^3 + (88179840) * X^2 * Z^2 + ( - 79361856) * X^2 * Z + (185177664) * Y^4 + (34292160) * Y^2 * Z^3 + ( - 35271936) * Y^2 * Z^2 + (714256704) * Y^2 * Z + ( - 290304) * Z^6 + (2612736) * Z^5 + (23514624) * Z^4 + ( - 211631616) * Z^3, ( - 317447424) * V * Y^3 * Z^2 + ( - 23514624) * V * Y * Z^5 + ( - 211631616) * V * Y * Z^4 + ( - 634894848) * V * Y * Z^3 + ( - 634894848) * V * Y * Z^2 + (26453952) * X^4 * Z + (79361856) * X^4 + ( - 211631616) * X^2 * Y^2 * Z + ( - 158723712) * X^2 * Y^2 + (6858432) * X^2 * Z^4 + (108755136) * X^2 * Z^3 + (185177664) * X^2 * Z^2 + ( - 238085568) * X^2 * Z + (185177664) * Y^4 * Z + (79361856) * Y^4 + (34292160) * Y^2 * Z^4 + ( - 2939328) * Y^2 * Z^3 + (608440896) * Y^2 * Z^2 + (238085568) * Y^2 * Z + ( - 290304) * Z^7 + (1741824) * Z^6 + (31352832) * Z^5 + ( - 141087744) * Z^4 + ( - 634894848) * Z^3, (79361856) * V * X^4 + (2539579392) * V * X^2 + (317447424) * V * Y^4 * Z + ( - 79361856) * V * Y^4 + (23514624) * V * Y^2 * Z^4 + (117573120) * V * Y^2 * Z^3 + ( - 423263232) * V * Y^2 * Z^2 + (5079158784) * V * Y^2 * Z + ( - 2539579392) * V * Y^2 + ( - 6967296) * V * Z^6 + ( - 125411328) * V * Z^5 + ( - 564350976) * V * Z^4 + (752467968) * V * Z^3 + (6772211712) * V * Z^2 + ( - 26453952) * X^4 * Y + (211631616) * X^2 * Y^3 + ( - 6858432) * X^2 * Y * Z^3 + ( - 255721536) * X^2 * Y * Z^2 + ( - 846526464) * X^2 * Y * Z + (2539579392) * X^2 * Y + ( - 185177664) * Y^5 + ( - 34292160) * Y^3 * Z^3 + (44089920) * Y^3 * Z^2 + (211631616) * Y^3 * Z + ( - 2539579392) * Y^3 + (290304) * Y * Z^6 + (10450944) * Y * Z^5 + (7838208) * Y * Z^4 + (188116992) * Y * Z^3 + (3386105856) * Y * Z^2 + ( - 10158317568) * Y * Z, ( - 714256704) * X^6 + (2142770112) * X^4 * Y^2 + ( - 396809280) * X^4 * Z^3 + ( - 4285540224) * X^4 * Z^2 + (2142770112) * X^4 * Z + ( - 2142770112) * X^2 * Y^4 + ( - 2063408256) * X^2 * Y^2 * Z^3 + ( - 4285540224) * X^2 * Y^2 * Z + ( - 47029248) * X^2 * Z^6 + ( - 1269789696) * X^2 * Z^5 + ( - 6348948480) * X^2 * Z^4 + (11428107264) * X^2 * Z^3 + (714256704) * Y^6 + ( - 396809280) * Y^4 * Z^3 + (4285540224) * Y^4 * Z^2 + (2142770112) * Y^4 * Z + (47029248) * Y^2 * Z^6 + ( - 1269789696) * Y^2 * Z^5 + (6348948480) * Y^2 * Z^4 + (11428107264) * Y^2 * Z^3 + (2322432) * Z^9 + ( - 376233984) * Z^7 + (15237476352) * Z^5 ]
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| 15 | Args:[ U^3 - 3 * U * V^2 - 3 * U + X, - 3 * U^2 * V + V^3 - 3 * V + Y, - 3 * U^2 + 3 * V^2 + Z ]
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| 16 | [ 2187 * V * X^4 + 69984 * V * X^2 + 8748 * V * Y^4 * Z - 2187 * V * Y^4 + 648 * V * Y^2 * Z^4 + 3240 * V * Y^2 * Z^3 - 11664 * V * Y^2 * Z^2 + 139968 * V * Y^2 * Z - 69984 * V * Y^2 - 192 * V * Z^6 - 3456 * V * Z^5 - 15552 * V * Z^4 + 20736 * V * Z^3 + 186624 * V * Z^2 - 729 * X^4 * Y + 5832 * X^2 * Y^3 - 189 * X^2 * Y * Z^3 - 7047 * X^2 * Y * Z^2 - 23328 * X^2 * Y * Z + 69984 * X^2 * Y - 5103 * Y^5 - 945 * Y^3 * Z^3 + 1215 * Y^3 * Z^2 + 5832 * Y^3 * Z - 69984 * Y^3 + 8 * Y * Z^6 + 288 * Y * Z^5 + 216 * Y * Z^4 + 5184 * Y * Z^3 + 93312 * Y * Z^2 - 279936 * Y * Z, 54 * V^2 * Y * Z + 27 * V * X^2 - 27 * V * Y^2 + 8 * V * Z^3 + 72 * V * Z^2 - 9 * Y * Z^2 - 27 * Y * Z, 9 * U * X + 6 * V^2 * Z - 9 * V * Y + Z^2 - 9 * Z, 243 * V^2 * X^2 - 243 * V^2 * Y^2 - 1296 * V^2 * Z - 108 * V * Y * Z^2 + 324 * V * Y * Z + 108 * X^2 * Z + 648 * X^2 + 135 * Y^2 * Z - 648 * Y^2 - 4 * Z^4 + 48 * Z^3 + 108 * Z^2 - 1944 * Z, 2 * V^3 + V * Z + 3 * V - Y, 6 * U * V^2 - U * Z + 9 * U - 3 * X, 3 * U^2 - 3 * V^2 - Z, 4 * U * V * Z - 3 * U * Y + 3 * V * X, 9 * U * V * Y - 2 * U * Z^2 + 18 * U * Z - 9 * V^2 * X - 6 * X * Z, 27 * U * Y^2 - 8 * U * Z^3 + 72 * U * Z^2 - 36 * V^2 * X * Z - 27 * V * X * Y - 24 * X * Z^2, 27 * V * X^2 * Z + 81 * V * X^2 + 135 * V * Y^2 * Z - 81 * V * Y^2 + 8 * V * Z^4 + 96 * V * Z^3 + 216 * V * Z^2 + 81 * X^2 * Y - 81 * Y^3 - 12 * Y * Z^3 - 324 * Y * Z, 18 * V^2 * Z^2 + 54 * V^2 * Z - 54 * V * Y * Z - 27 * X^2 + 27 * Y^2 + Z^3 - 18 * Z^2 + 81 * Z, 4374 * V * X^2 * Y + 8748 * V * Y^3 * Z - 4374 * V * Y^3 + 648 * V * Y * Z^4 + 5184 * V * Y * Z^3 + 17496 * V * Y * Z^2 - 729 * X^4 + 5832 * X^2 * Y^2 - 189 * X^2 * Z^3 - 2430 * X^2 * Z^2 + 2187 * X^2 * Z - 5103 * Y^4 - 945 * Y^2 * Z^3 + 972 * Y^2 * Z^2 - 19683 * Y^2 * Z + 8 * Z^6 - 72 * Z^5 - 648 * Z^4 + 5832 * Z^3, 8748 * V * Y^3 * Z^2 + 648 * V * Y * Z^5 + 5832 * V * Y * Z^4 + 17496 * V * Y * Z^3 + 17496 * V * Y * Z^2 - 729 * X^4 * Z - 2187 * X^4 + 5832 * X^2 * Y^2 * Z + 4374 * X^2 * Y^2 - 189 * X^2 * Z^4 - 2997 * X^2 * Z^3 - 5103 * X^2 * Z^2 + 6561 * X^2 * Z - 5103 * Y^4 * Z - 2187 * Y^4 - 945 * Y^2 * Z^4 + 81 * Y^2 * Z^3 - 16767 * Y^2 * Z^2 - 6561 * Y^2 * Z + 8 * Z^7 - 48 * Z^6 - 864 * Z^5 + 3888 * Z^4 + 17496 * Z^3, 19683 * X^6 - 59049 * X^4 * Y^2 + 10935 * X^4 * Z^3 + 118098 * X^4 * Z^2 - 59049 * X^4 * Z + 59049 * X^2 * Y^4 + 56862 * X^2 * Y^2 * Z^3 + 118098 * X^2 * Y^2 * Z + 1296 * X^2 * Z^6 + 34992 * X^2 * Z^5 + 174960 * X^2 * Z^4 - 314928 * X^2 * Z^3 - 19683 * Y^6 + 10935 * Y^4 * Z^3 - 118098 * Y^4 * Z^2 - 59049 * Y^4 * Z - 1296 * Y^2 * Z^6 + 34992 * Y^2 * Z^5 - 174960 * Y^2 * Z^4 - 314928 * Y^2 * Z^3 - 64 * Z^9 + 10368 * Z^7 - 419904 * Z^5 ]
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| 17 | Warning: Test 3 - staple
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| 18 | ------------------- CASE 1 -------------------
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| 19 | Condition:
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| 20 | Green list: [ ]
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| 21 | Red list: [ U - 1 ]
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| 22 | Basis: [ (U - 1) * X, ( - U + 1) * Y ]
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| 23 | ------------------- CASE 2 -------------------
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| 24 | Condition:
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| 25 | Green list: [ U - 1 ]
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| 26 | Red list: [ ]
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| 27 | Basis: [ (1) * X + (1) * Y ]
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| 28 | Warning: Test 4 - staple
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| 29 | ------------------- CASE 1 -------------------
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| 30 | Condition:
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| 31 | Green list: [ U ]
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| 32 | Red list: [ ]
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| 33 | Basis: [ (1) * X, (1) * Y ]
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| 34 | ------------------- CASE 2 -------------------
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| 35 | Condition:
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| 36 | Green list: [ ]
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| 37 | Red list: [ U, U - 1 ]
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| 38 | Basis: [ (U^2 - U) * X, (U - 1) * Y ]
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| 39 | ------------------- CASE 3 -------------------
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| 40 | Condition:
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| 41 | Green list: [ U - 1 ]
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| 42 | Red list: [ U ]
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| 43 | Basis: [ (1) * X + (1) * Y ]
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| 44 | Warning: Test 5 - a small robot example
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| 45 | ------------------- CASE 1 -------------------
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| 46 | Condition:
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| 47 | Green list: [ ]
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| 48 | Red list: [ L3, A^2 + B^2, L2, A ]
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| 49 | Basis: [ ( - 2 * A * L2 * L3) * S2 + ( - 2 * A^2 * L2 - 2 * B^2 * L2) * S1 + (A^2 * B + B^3 + B * L2^2 - B * L3^2), ( - 2 * L2 * L3) * C2 + (A^2 + B^2 - L2^2 - L3^2), ( - 2 * A * L2) * C1 + ( - 2 * B * L2) * S1 + (A^2 + B^2 + L2^2 - L3^2), (4 * A^2 * L2^2 + 4 * B^2 * L2^2) * S1^2 + ( - 4 * A^2 * B * L2 - 4 * B^3 * L2 - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (A^4 + 2 * A^2 * B^2 - 2 * A^2 * L2^2 - 2 * A^2 * L3^2 + B^4 + 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4) ]
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| 50 | ------------------- CASE 2 -------------------
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| 51 | Condition:
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| 52 | Green list: [ A^2 + B^2 ]
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| 53 | Red list: [ L3, A^2 * B + B^3 + B * L2^2 - B * L3^2, L2, A ]
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| 54 | Basis: [ (4 * A * B * L2^3 * L3 - 4 * A * B * L2 * L3^3) * S2 + ( - 2 * B^2 * L2^4 + 4 * B^2 * L2^2 * L3^2 - 2 * B^2 * L3^4), ( - 2 * L2 * L3) * C2 + ( - L2^2 - L3^2), (4 * A * L2^3 - 4 * A * L2 * L3^2) * C1 + (4 * B^2 * L2^2 - L2^4 + 2 * L2^2 * L3^2 - L3^4), ( - 4 * B * L2^3 + 4 * B * L2 * L3^2) * S1 + (4 * B^2 * L2^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4) ]
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| 55 | ------------------- CASE 3 -------------------
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| 56 | Condition:
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| 57 | Green list: [ A^2 + B^2, L2^2 - L3^2 ]
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| 58 | Red list: [ L3, A, L2, A^4 + 2 * A^2 * B^2 - 2 * A^2 * L2^2 - 2 * A^2 * L3^2 + B^4 + 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4 ]
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| 59 | Basis: [ (4 * B^2 * L3^2) ]
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| 60 | ------------------- CASE 4 -------------------
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| 61 | Condition:
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| 62 | Green list: [ A ]
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| 63 | Red list: [ L3, B, L2 ]
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| 64 | Basis: [ (4 * B^2 * L2^2) * C1^2 + (B^4 - 2 * B^2 * L2^2 - 2 * B^2 * L3^2 + L2^4 - 2 * L2^2 * L3^2 + L3^4), (2 * B * L2 * L3) * S2 + ( - 2 * B^2 * L2) * C1, ( - 2 * L2 * L3) * C2 + (B^2 - L2^2 - L3^2), ( - 2 * B * L2) * S1 + (B^2 + L2^2 - L3^2) ]
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| 65 | ------------------- CASE 5 -------------------
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| 66 | Condition:
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| 67 | Green list: [ A, B ]
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| 68 | Red list: [ L3, L2, A^2 + B^2 + L2^2 - L3^2 ]
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| 69 | Basis: [ (L2^2 - L3^2) ]
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| 70 | ------------------- CASE 6 -------------------
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| 71 | Condition:
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| 72 | Green list: [ A, B, L2^2 - L3^2 ]
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| 73 | Red list: [ L3, L2 ]
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| 74 | Basis: [ (1) * C1^2 + (1) * S1^2 + ( - 1), (L3) * S2, (L3) * C2 + (L2) ]
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| 75 | Warning: Test 6 - Circle of Apollonius
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| 76 | ------------------- CASE 1 -------------------
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| 77 | Condition:
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| 78 | Green list: [ U2, U1 ]
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| 79 | Red list: [ ]
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| 80 | Basis: [ (2) * X1, (2) * X2, (2) * X3, (2) * X4, ( - 4) * X6^2 + (8) * X6 * X8, (4) * S * X5^2 + ( - 8) * S * X5 * X7 + ( - 4) ]
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| 81 | ------------------- CASE 2 -------------------
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| 82 | Condition:
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| 83 | Green list: [ U2 ]
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| 84 | Red list: [ U1 ]
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| 85 | Basis: [ ( - 4 * U1^3) ]
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| 86 | ------------------- CASE 3 -------------------
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| 87 | Condition:
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| 88 | Green list: [ U1 ]
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| 89 | Red list: [ U2 ]
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| 90 | Basis: [ (4 * U2^2) ]
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| 91 | ------------------- CASE 4 -------------------
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| 92 | Condition:
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| 93 | Green list: [ ]
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| 94 | Red list: [ U1, U2, U1^2 - U2^2, U1^2 + U2^2 ]
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| 95 | Basis: [ (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), (U1^2 * U2 + U2^3) * X5 + ( - U1 * U2^3), ( - U1^2 - U2^2) * X6 + (U1^2 * U2), ( - 4 * U1^5 + 4 * U1 * U2^4) * X7 + (U1^6 + 2 * U1^4 * U2^2 - 3 * U1^2 * U2^4), ( - 4 * U1^4 * U2 + 4 * U2^5) * X8 + (3 * U1^4 * U2^2 - 2 * U1^2 * U2^4 - U2^6), (2 * U1^6 * U2^2 - 2 * U1^4 * U2^4) * S + (4 * U1^6 - 4 * U1^2 * U2^4) ]
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| 96 | ------------------- CASE 5 -------------------
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| 97 | Condition:
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| 98 | Green list: [ U1^2 - U2^2 ]
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| 99 | Red list: [ U1, U1^2 + U2^2, U2 ]
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| 100 | Basis: [ (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), (2 * U2^3) * X5 + ( - U1 * U2^3), ( - 2 * U2^2) * X6 + (U2^3), (4 * U1) * X7 + ( - 4 * U2) * X8, ( - 8 * U2^5) * S * X8 + (2 * U2^6) * S + ( - 8 * U2^4) ]
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| 101 | ------------------- CASE 6 -------------------
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| 102 | Condition:
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| 103 | Green list: [ U1^2 + U2^2 ]
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| 104 | Red list: [ U1, U2 ]
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| 105 | Basis: [ ( - U2^3) ]
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| 106 | Warning: Test 7
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| 107 | ------------------- CASE 1 -------------------
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| 108 | Condition:
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| 109 | Green list: [ ]
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| 110 | Red list: [ A * C^2 + B * C^2, A^2 + B ]
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| 111 | Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
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| 112 | ------------------- CASE 2 -------------------
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| 113 | Condition:
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| 114 | Green list: [ A^2 + B ]
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| 115 | Red list: [ A * C^2 + B * C^2, A^3 * B + A^3 * C ]
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| 116 | Basis: [ (A^3 * B + A^3 * C) * X * Y, (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
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| 117 | ------------------- CASE 3 -------------------
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| 118 | Condition:
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| 119 | Green list: [ A^2 - C, B + C ]
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| 120 | Red list: [ A * C^2 + B * C^2 ]
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| 121 | Basis: [ (A * C^2 + B * C^2) * X^2 + (B) * Y + (4) ]
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| 122 | ------------------- CASE 4 -------------------
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| 123 | Condition:
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| 124 | Green list: [ A * C^2 + B * C^2 ]
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| 125 | Red list: [ B, A^2 + B ]
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| 126 | Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (B) * Y + (4) ]
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| 127 | ------------------- CASE 5 -------------------
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| 128 | Condition:
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| 129 | Green list: [ A * C^2 - C^2, A^2 + B, B * C^2 + C^2 ]
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| 130 | Red list: [ B, A^3 * B + A^3 * C ]
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| 131 | Basis: [ (A^3 * B + A^3 * C) * X * Y, (B) * Y + (4) ]
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| 132 | ------------------- CASE 6 -------------------
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| 133 | Condition:
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| 134 | Green list: [ B + 1, C - 1, A - 1 ]
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| 135 | Red list: [ B ]
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| 136 | Basis: [ (B) * Y + (4) ]
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| 137 | ------------------- CASE 7 -------------------
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| 138 | Condition:
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| 139 | Green list: [ B, C^2 ]
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| 140 | Red list: [ 4, A^2 + B ]
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| 141 | Basis: [ (A^2 + B) * X^2 * Y + (A^3 * B + A^3 * C) * X * Y, (4) ]
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| 142 | ------------------- CASE 8 -------------------
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| 143 | Condition:
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| 144 | Green list: [ A^2, A * C^2, B ]
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| 145 | Red list: [ 4 ]
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| 146 | Basis: [ (4) ]
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| 147 | Warning: Test 8
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| 148 | ------------------- CASE 1 -------------------
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| 149 | Condition:
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| 150 | Green list: [ ]
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| 151 | Red list: [ A^2 ]
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| 152 | Basis: [ (A^2) * X + (5 * A) ]
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| 153 | ------------------- CASE 2 -------------------
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| 154 | Condition:
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| 155 | Green list: [ A^2 ]
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| 156 | Red list: [ ]
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| 157 | Basis: [ ]
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| 158 | Warning: Test 9 - the discriminant of a quadratic polynomial
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| 159 | ------------------- CASE 1 -------------------
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| 160 | Condition:
|
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| 161 | Green list: [ ]
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| 162 | Red list: [ A, 4 * A * C - B^2 ]
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| 163 | Basis: [ (4 * A * C - B^2) ]
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| 164 | ------------------- CASE 2 -------------------
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| 165 | Condition:
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| 166 | Green list: [ 4 * A * C - B^2 ]
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| 167 | Red list: [ A ]
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| 168 | Basis: [ (2 * A) * X + (B) ]
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| 169 | Warning: Test 10 - the discriminant of a cubic polynomial
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| 170 | ------------------- CASE 1 -------------------
|
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| 171 | Condition:
|
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| 172 | Green list: [ ]
|
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| 173 | Red list: [ P, 4 * P^3 + 27 * Q^2 ]
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| 174 | Basis: [ ( - 4 * P^3 - 27 * Q^2) ]
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| 175 | ------------------- CASE 2 -------------------
|
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| 176 | Condition:
|
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| 177 | Green list: [ 4 * P^3 + 27 * Q^2 ]
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| 178 | Red list: [ P ]
|
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| 179 | Basis: [ (2 * P) * X + (3 * Q) ]
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| 180 | ------------------- CASE 3 -------------------
|
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| 181 | Condition:
|
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| 182 | Green list: [ P ]
|
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| 183 | Red list: [ Q ]
|
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| 184 | Basis: [ (3 * Q) ]
|
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| 185 | ------------------- CASE 4 -------------------
|
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| 186 | Condition:
|
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| 187 | Green list: [ P, Q ]
|
|---|
| 188 | Red list: [ ]
|
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| 189 | Basis: [ (3) * X^2 ]
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| 190 | Warning: Test 11 - the discriminant of a quartic polynomial
|
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| 191 | ------------------- CASE 1 -------------------
|
|---|
| 192 | Condition:
|
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| 193 | Green list: [ ]
|
|---|
| 194 | Red list: [ 16 * P^4 * R - 4 * P^3 * Q^2 - 128 * P^2 * R^2 + 144 * P * Q^2 * R - 27 * Q^4 + 256 * R^3, P, 2 * P^3 - 8 * P * R + 9 * Q^2 ]
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| 195 | Basis: [ (16 * P^6 * R - 4 * P^5 * Q^2 - 128 * P^4 * R^2 + 144 * P^3 * Q^2 * R - 27 * P^2 * Q^4 + 256 * P^2 * R^3) ]
|
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| 196 | ------------------- CASE 2 -------------------
|
|---|
| 197 | Condition:
|
|---|
| 198 | Green list: [ 16 * P^4 * R - 4 * P^3 * Q^2 - 128 * P^2 * R^2 + 144 * P * Q^2 * R - 27 * Q^4 + 256 * R^3 ]
|
|---|
| 199 | Red list: [ P, 2 * P^3 - 8 * P * R + 9 * Q^2 ]
|
|---|
| 200 | Basis: [ ( - 2 * P^3 + 8 * P * R - 9 * Q^2) * X + ( - P^2 * Q - 12 * Q * R) ]
|
|---|
| 201 | ------------------- CASE 3 -------------------
|
|---|
| 202 | Condition:
|
|---|
| 203 | Green list: [ 2 * P^3 - 8 * P * R + 9 * Q^2 ]
|
|---|
| 204 | Red list: [ P, P^2 * Q + 12 * Q * R ]
|
|---|
| 205 | Basis: [ ( - P^2 * Q - 12 * Q * R) ]
|
|---|
| 206 | ------------------- CASE 4 -------------------
|
|---|
| 207 | Condition:
|
|---|
| 208 | Green list: [ 2 * P^3 - 8 * P * R + 9 * Q^2, P^2 * Q + 12 * Q * R, 32 * P * Q * R - 9 * Q^3, 3 * P * Q^3 + 128 * Q * R^2, 27 * Q^5 + 4096 * Q * R^3, 8 * P^2 * R - 3 * P * Q^2 - 32 * R^2 ]
|
|---|
| 209 | Red list: [ P ]
|
|---|
| 210 | Basis: [ (2 * P) * X^2 + (3 * Q) * X + (4 * R) ]
|
|---|
| 211 | ------------------- CASE 5 -------------------
|
|---|
| 212 | Condition:
|
|---|
| 213 | Green list: [ P ]
|
|---|
| 214 | Red list: [ Q, 72 * P * Q^2 * R - 27 * Q^4 + 256 * R^3 ]
|
|---|
| 215 | Basis: [ (27 * Q^4 - 256 * R^3) ]
|
|---|
| 216 | ------------------- CASE 6 -------------------
|
|---|
| 217 | Condition:
|
|---|
| 218 | Green list: [ P, 27 * Q^4 - 256 * R^3 ]
|
|---|
| 219 | Red list: [ Q ]
|
|---|
| 220 | Basis: [ (3 * Q) * X + (4 * R) ]
|
|---|
| 221 | ------------------- CASE 7 -------------------
|
|---|
| 222 | Condition:
|
|---|
| 223 | Green list: [ P, Q ]
|
|---|
| 224 | Red list: [ R ]
|
|---|
| 225 | Basis: [ (4 * R) ]
|
|---|
| 226 | ------------------- CASE 8 -------------------
|
|---|
| 227 | Condition:
|
|---|
| 228 | Green list: [ P, Q, R ]
|
|---|
| 229 | Red list: [ ]
|
|---|
| 230 | Basis: [ (4) * X^3 ]
|
|---|
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