|\^/| Maple V Release 4 (WMI Campus Wide License) ._|\| |/|_. Copyright (c) 1981-1996 by Waterloo Maple Inc. All rights \ MAPLE / reserved. Maple and Maple V are registered trademarks of <____ ____> Waterloo Maple Inc. | Type ? for help. Warning, new definition for norm Warning, new definition for trace This is the beginning of the verbs. This is the end of the verbs. A := [1, 0, 0] B := [0, 1, 0] C := [1, -t, 0] D := [0, 0, 1] E := [1, 1, 1] F := [1, 1, u + 1] Begin the calculuations. Pappus line, [t u, -1, 1] [ 2 ] S0 := [-u + t, t (u + 1 + t u), t (1 + u + u)] [ 2 ] [ -2 t -t t (1 + t)] QS0 := [ ] [ -t -2 1 ] [ ] [t (1 + t) 1 0 ] Is S0 on QS0 ?, TRUE [ 2 ] S1 := [t u + t + u, -t (-1 + t u), t (1 + u + u)] [ 2 2 ] [2 t t -t ] [ ] QS1 := [ t 2 -1 - t] [ ] [ 2 ] [-t -1 - t 0 ] Is S1 on QS1 ?, TRUE Six conics: six points on QF AD.BE on QF , [-1, 0, -1] BE.CD on QF , [1, -t, 1] CD.AE on QF , [1, -t, -t] AE.BD on QF , [0, -1, -1] BD.CE on QF , [0, 1 + t, 1] CE.AD on QF , [-1 - t, 0, -t] [ -2 t -2 - 2 t 2 t + 1 ] [ ] QF := [-2 - 2 t -2 2 + t ] [ ] [2 t + 1 2 + t -2 - 2 t] six cross points on new_conic QE AF.BD on QE , [0, -1, -1 - u] BD.CF on QE , [0, 1 + t, u + 1] CF.AD on QE , [-1 - t, 0, -t (u + 1)] AD.BF on QE , [-1, 0, -1 - u] BF.CD on QE , [1, -t, u + 1] CD.AF on QE , [1, -t, -t (u + 1)] [ 2 2 ] [ 2 (u + 1) t 2 (1 + t) (u + 1) -(u + 1) (2 t + 1)] [ ] QE := [ 2 2 ] [2 (1 + t) (u + 1) 2 (u + 1) -(u + 1) (2 + t) ] [ ] [-(u + 1) (2 t + 1) -(u + 1) (2 + t) 2 + 2 t ] six cross points on QD AE.BF on QD , [-1, -1 - u, -1 - u] BF.CE on QD , [1, u + 1 + t u, u + 1] CE.AF on QD , [-u - t u - t, -t, -t (u + 1)] AF.BE on QD , [-1 - u, -1, -1 - u] BE.CF on QD , [u + 1, 1 - t u, u + 1] CF.AE on QD , [-t + u, -t (u + 1), -t (u + 1)] QD := [ 2 2 ] [2 (u + 1) t , 2 (1 + t) (u + 1) , -(u + 1) (u + 2) (2 t + 1)] [ 2 2 ] [2 (1 + t) (u + 1) , 2 (u + 1) , -(u + 1) (u + 2) (2 + t)] [ [-(u + 1) (u + 2) (2 t + 1) , -(u + 1) (u + 2) (2 + t) , 2 ] 2 (3 + u + 3 u) (1 + t)] six cross points on new_conic QC DA.EB on QC , [-1, 0, -1] EB.FA on QC , [u + 1, 1, u + 1] FA.DB on QC , [0, -1, -1 - u] DB.EA on QC , [0, 1, 1] EA.FB on QC , [-1, -1 - u, -1 - u] FB.DA on QC , [1, 0, u + 1] [-2 u - 2 -1 - u u + 2] [ ] QC := [ -1 - u -2 u - 2 u + 2] [ ] [ u + 2 u + 2 -2 ] six cross points on new_conic QB DC.EA on QB , [1, -t, -t] EA.FC on QB , [-u + t, t (u + 1), t (u + 1)] FC.DA on QB , [-1 - t, 0, -t (u + 1)] DA.EC on QB , [1 + t, 0, t] EC.FA on QB , [-u - t u - t, -t, -t (u + 1)] FA.DC on QB , [-1, t, t (u + 1)] QB := [ 2 ] [2 (u + 1) t , (u + 1) t (t + 3) , -(u + 2) (1 + t) t] [ 2 ] [(u + 1) t (t + 3) , 2 (u + 1) (t + 3 t + 3) , -(2 + t) (1 + t) (u + 2)] [ 2] [-(u + 2) (1 + t) t , -(2 + t) (1 + t) (u + 2) , 2 (1 + t) ] six cross points on new_conic QA DB.EC on QA , [0, 1 + t, 1] EC.FB on QA , [-1, -u - t u - 1, -1 - u] FB.DC on QA , [1, -t, u + 1] DC.EB on QA , [-1, t, -1] EB.FC on QA , [u + 1, 1 - t u, u + 1] FC.DB on QA , [0, -1 - t, -1 - u] QA := [ 2 [2 (u + 1) (3 t + 3 t + 1) , (u + 1) (3 t + 1) , ] -(1 + t) (2 t + 1) (u + 2)] [(u + 1) (3 t + 1) , 2 u + 2 , -(u + 2) (1 + t)] [ 2] [-(1 + t) (2 t + 1) (u + 2) , -(u + 2) (1 + t) , 2 (1 + t) ] # Let { T1, T2 } = L1 meet QF 2 1/2 T1 := [-1 - t + (1 + t + t ) , t, 0] 2 1/2 T2 := [-1 - t - (1 + t + t ) , t, 0] # Let { U1, U2 } = L2 meet QC 2 1/2 U1 := [1, 1, u + 2 + (1 + u + u) ] 2 1/2 U2 := [1, 1, u + 2 - (1 + u + u) ] # Two more cross points [ 2 1/2 2 1/2 2 1/2 V1 := [-2 (1 + u + u) - t (1 + u + u) + 2 (1 + t + t ) 2 1/2 2 1/2 2 1/2 + (1 + t + t ) u, (1 + u + u) + 2 t (1 + u + u) 2 1/2 2 1/2 2 1/2 ] + (1 + t + t ) u + 2 (1 + t + t ) , 3 (1 + t + t ) (u + 1)] [ 2 1/2 2 1/2 2 1/2 V2 := [(1 + t + t ) u + 2 (1 + t + t ) + t (1 + u + u) 2 1/2 2 1/2 2 1/2 + 2 (1 + u + u) , -(1 + u + u) - 2 t (1 + u + u) 2 1/2 2 1/2 2 1/2 ] + (1 + t + t ) u + 2 (1 + t + t ) , 3 (1 + t + t ) (u + 1)] This is the end of the calculuations.