[1] | 1 | Verification that the generic case has one solution
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| 2 | ----------------------------------------------------------------
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| 3 | (C1) eqns:[ (2) * U1 + ( - X2 - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3 + ( - X2), (2) * V3, ( - 3 * X2 * Y3) * Y + (X2 * Y3^2), ( - 3 * X2 * Y3^2) * X + (X2^2 * Y3^2 + X2 * X3 * Y3^2) ];
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| 4 |
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| 5 | (D1) [- X3 - X2 + 2 U1, 2 V1 - Y3, 2 U2 - X3, 2 V2 - Y3, 2 U3 - X2, 2 V3,
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| 6 |
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| 7 | 2 2 2 2 2
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| 8 | X2 Y3 - 3 X2 Y Y3, X2 X3 Y3 + X2 Y3 - 3 X X2 Y3 ]
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| 9 | (C2) solve(%,[x,y,u1,v1,u2,v2,u3,v3]);
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| 10 |
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| 11 | X3 + X2 Y3 X3 + X2 Y3 X3 Y3 X2
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| 12 | (D2) [[X = -------, Y = --, U1 = -------, V1 = --, U2 = --, V2 = --, U3 = --,
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| 13 | 3 3 2 2 2 2 2
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| 14 |
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| 15 | ----------------------------------------------------------------
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| 16 | >(load "midpoints")
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| 17 | Loading midpoints.lisp
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| 18 | Condition:
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| 19 | Green list: [ ]
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| 20 | Red list: [ X2 * Y3^2 ]
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| 21 | Basis: [ (2) * U1 + ( - X2 - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3 + ( - X2), (2) * V3, ( - 3 * X2 * Y3) * Y + (X2 * Y3^2), ( - 3 * X2 * Y3^2) * X + (X2^2 * Y3^2 + X2 * X3 * Y3^2) ]
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| 22 | Condition:
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| 23 | Green list: [ X2 ]
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| 24 | Red list: [ Y3 ]
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| 25 | Basis: [ (2) * U1 + ( - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3, (2) * V3, ( - Y3) * X + (X3) * Y ]
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| 26 | Condition:
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| 27 | Green list: [ Y3 ]
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| 28 | Red list: [ X2 + X3 ]
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| 29 | Basis: [ (2) * U1 + ( - X2 - X3), (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + ( - X2), (2) * V3, (X2 + X3) * Y ]
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| 30 | Condition:
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| 31 | Green list: [ Y3, X2 + X3 ]
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| 32 | Red list: [ X3 ]
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| 33 | Basis: [ (2) * U1, (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + (X3), (2) * V3, (3 * X3) * Y ]
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| 34 | Condition:
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| 35 | Green list: [ X2, Y3, X3 ]
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| 36 | Red list: [ ]
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| 37 | Basis: [ (2) * U1, (2) * V1, (2) * U2, (2) * V2, (2) * U3, (2) * V3 ]
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| 38 | Finished loading midpoints.lisp
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| 39 | T
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| 40 |
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