Verification that the generic case has one solution
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(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) ];

(D1) [- X3 - X2 + 2 U1, 2 V1 - Y3, 2 U2 - X3, 2 V2 - Y3, 2 U3 - X2, 2 V3, 

			      2			     2	   2   2	    2
			 X2 Y3  - 3 X2 Y Y3, X2 X3 Y3  + X2  Y3  - 3 X X2 Y3 ]
(C2) solve(%,[x,y,u1,v1,u2,v2,u3,v3]);

	   X3 + X2      Y3	 X3 + X2       Y3       X3	 Y3	  X2
(D2) [[X = -------, Y = --, U1 = -------, V1 = --, U2 = --, V2 = --, U3 = --, 
	      3	        3	    2	       2        2	 2	  2

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>(load "midpoints")
Loading midpoints.lisp
Condition:
  Green list: [  ]
  Red list: [ X2 * Y3^2 ]
 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) ]
Condition:
  Green list: [ X2 ]
  Red list: [ Y3 ]
 Basis: [ (2) * U1 + ( - X3), (2) * V1 + ( - Y3), (2) * U2 + ( - X3), (2) * V2 + ( - Y3), (2) * U3, (2) * V3, ( - Y3) * X + (X3) * Y ]
Condition:
  Green list: [ Y3 ]
  Red list: [ X2 + X3 ]
 Basis: [ (2) * U1 + ( - X2 - X3), (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + ( - X2), (2) * V3, (X2 + X3) * Y ]
Condition:
  Green list: [ Y3, X2 + X3 ]
  Red list: [ X3 ]
 Basis: [ (2) * U1, (2) * V1, (2) * U2 + ( - X3), (2) * V2, (2) * U3 + (X3), (2) * V3, (3 * X3) * Y ]
Condition:
  Green list: [ X2, Y3, X3 ]
  Red list: [  ]
 Basis: [ (2) * U1, (2) * V1, (2) * U2, (2) * V2, (2) * U3, (2) * V3 ]
Finished loading midpoints.lisp
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