1 | This output is correct; it says that if u1#0,u2#0,u1^2+u2^2#0 then
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2 | there is exactly one solution. In fact, we plug the Basis of second case
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3 | into macsyma and get the unique solution for this case:
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4 | ----------------------------------------------------------------
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5 | (C12) solve([ ( - 4 * U1) * X7 + (U1^2), ( - 4 * U2) * X8 + (U2^2), ( - U1^2 - U2^2) * X6 + (U1^2 * U2), (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), ( - U1^2 * U2 - U2^3) * X5 + (U1 * U2^3) ],[x1,x2,x3,x4,x5,x6,x7,x8]);
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6 |
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7 | 2 2
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8 | U1 U2 U1 U2 U1 U2 U1 U2
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9 | (D12) [[X1 = --, X2 = --, X3 = --, X4 = --, X5 = ---------, X6 = ---------,
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10 | 2 2 2 2 2 2 2 2
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11 | U2 + U1 U2 + U1
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12 |
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13 | U1 U2
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14 | X7 = --, X8 = --]]
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15 | 4 4
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16 | (C13)
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17 | ----------------------------------------------------------------
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18 |
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19 | >(load "apollonius2.lisp")
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20 | Loading apollonius2.lisp
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21 | Condition:
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22 | Green list: [ ]
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23 | Red list: [ - U1^2 - U2^2, U1, U2 ]
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24 | Basis: [ ( - 4 * U1) * X7 + (U1^2), ( - 4 * U2) * X8 + (U2^2), ( - U1^2 - U2^2) * X6 + (U1^2 * U2), (2) * X1 + ( - U1), (2) * X2 + ( - U2), (2) * X3 + ( - U1), (2) * X4 + ( - U2), ( - U1^2 * U2 - U2^3) * X5 + (U1 * U2^3) ]
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25 | Condition:
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26 | Green list: [ - U1^2 - U2^2 ]
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27 | Red list: [ U1, U2 ]
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28 | Basis: [ (U2^3) ]
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29 | Finished loading apollonius2.lisp
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30 | T
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