# (c) copyright 1997, 1998, Leroy J. Dickey
print ( `Beginning of the validations.` ) ;

assume ( 't', real ) ;
assume ( 'u', real ) ;
interface (showassumed=0 ) ;

print ( `Re Pappus line`,  Pappus ( A, B, C,  D, E, F ) ) ;

print ( `Re Steiner points, Steiner conics ` ) ;
	print ( `Is S0 on QS0 ?`, point_on_conic ( S0,  QS0 ) ) ;
	print ( `Is S1 on QS1 ?`, point_on_conic ( S1, QS1 ) ) ;

print ( `Re: six conics:` ) ;
	print ( `six cross points on new_conic QF` ) ;
print ( `Is AD.BE on QF ?`, point_on_conic ( cross_point (A,D, B,E), QF) ) ;
print ( `Is BE.CD on QF ?`, point_on_conic ( cross_point (B,E, C,D), QF) ) ;
print ( `Is CD.AE on QF ?`, point_on_conic ( cross_point (C,D, A,E), QF) ) ;
print ( `Is AE.BD on QF ?`, point_on_conic ( cross_point (A,E, B,D), QF) ) ;
print ( `Is BD.CE on QF ?`, point_on_conic ( cross_point (B,D, C,E), QF) ) ;
print ( `Is CE.AD on QF ?`, point_on_conic ( cross_point (C,E, A,D), QF) ) ;

	print ( `six cross points on new_conic QD` ) ;
print ( `Is AE.BF on QD ?`, point_on_conic ( cross_point (A,E, B,F), QD) ) ;
print ( `Is BF.CE on QD ?`, point_on_conic ( cross_point (B,F, C,E), QD) ) ;
print ( `Is CE.AF on QD ?`, point_on_conic ( cross_point (C,E, A,F), QD) ) ;
print ( `Is AF.BE on QD ?`, point_on_conic ( cross_point (A,F, B,E), QD) ) ;
print ( `Is BE.CF on QD ?`, point_on_conic ( cross_point (B,E, C,F), QD) ) ;
print ( `Is CF.AE on QD ?`, point_on_conic ( cross_point (C,F, A,E), QD) ) ;

	print ( `six cross points on new_conic QE` ) ;
print ( `Is AF.BD on QE ?`, point_on_conic ( cross_point (A,F, B,D), QE) ) ;
print ( `Is BD.CF on QE ?`, point_on_conic ( cross_point (B,D, C,F), QE) ) ;
print ( `Is CF.AD on QE ?`, point_on_conic ( cross_point (C,F, A,D), QE) ) ;
print ( `Is AD.BF on QE ?`, point_on_conic ( cross_point (A,D, B,F), QE) ) ;
print ( `Is BF.CD on QE ?`, point_on_conic ( cross_point (B,F, C,D), QE) ) ;
print ( `Is CD.AF on QE ?`, point_on_conic ( cross_point (C,D, A,F), QE) ) ;

	print ( `six cross points on new_conic QC` ) ;
print ( `Is DA.EB on QC ?`, point_on_conic ( cross_point (D,A, E,B), QC) ) ;
print ( `Is EB.FA on QC ?`, point_on_conic ( cross_point (E,B, F,A), QC) ) ;
print ( `Is FA.DB on QC ?`, point_on_conic ( cross_point (F,A, D,B), QC) ) ;
print ( `Is DB.EA on QC ?`, point_on_conic ( cross_point (D,B, E,A), QC) ) ;
print ( `Is EA.FB on QC ?`, point_on_conic ( cross_point (E,A, F,B), QC) ) ;
print ( `Is FB.DA on QC ?`, point_on_conic ( cross_point (F,B, D,A), QC) ) ;

	print ( `six cross points on new_conic QA` ) ;
print ( `Is DB.EC on QA ?`, point_on_conic ( cross_point (D,B, E,C), QA) ) ;
print ( `Is EC.FB on QA ?`, point_on_conic ( cross_point (E,C, F,B), QA) ) ;
print ( `Is FB.DC on QA ?`, point_on_conic ( cross_point (F,B, D,C), QA) ) ;
print ( `Is DC.EB on QA ?`, point_on_conic ( cross_point (D,C, E,B), QA) ) ;
print ( `Is EB.FC on QA ?`, point_on_conic ( cross_point (E,B, F,C), QA) ) ;
print ( `Is FC.DB on QA ?`, point_on_conic ( cross_point (F,C, D,B), QA) ) ;

	print ( `six cross points on new_conic QB` ) ;
print ( `Is DC.EA on QB ?`, point_on_conic ( cross_point (D,C, E,A), QB) ) ;
print ( `Is EA.FC on QB ?`, point_on_conic ( cross_point (E,A, F,C), QB) ) ;
print ( `Is FC.DA on QB ?`, point_on_conic ( cross_point (F,C, D,A), QB) ) ;
print ( `Is DA.EC on QB ?`, point_on_conic ( cross_point (D,A, E,C), QB) ) ;
print ( `Is EC.FA on QB ?`, point_on_conic ( cross_point (E,C, F,A), QB) ) ;
print ( `Is FA.DC on QB ?`, point_on_conic ( cross_point (F,A, D,C), QB) ) ;




assume ( t, real );
assume ( u, real );
interface ( showassumed=0 ) ;

print ( `Re T1 on  QD, QE, and QF` );
	print ( `Is point T1 on conic QD ?`, point_on_conic ( T1, QD ) ) ;
	print ( `Is point T1 on conic QE ?`, point_on_conic ( T1, QE ) ) ;
	print ( `Is point T1 on conic QF ?`, point_on_conic ( T1, QF ) ) ;

print ( `Re T2 on  QD, QE, and QF` );
	print ( `Is point T2 on conic QD ?`, point_on_conic ( T2, QD ) ) ;
	print ( `Is point T2 on conic QE ?`, point_on_conic ( T2, QE ) ) ;
	print ( `Is point T2 on conic QF ?`, point_on_conic ( T2, QF ) ) ;

print ( `Re U1 on  QA, QB, and QC` );
	print ( `Is point U1 on conic QA ?`, point_on_conic ( U1, QA ) ) ;
	print ( `Is point U1 on conic QB ?`, point_on_conic ( U1, QB ) ) ;
	print ( `Is point U1 on conic QC ?`, point_on_conic ( U1, QC ) ) ;

print ( `Re U2 on  QA, QB, and QC` );
	print ( `Is point U2 on conic QA ?`, point_on_conic ( U2, QA ) ) ;
	print ( `Is point U2 on conic QB ?`, point_on_conic ( U2, QB ) ) ;
	print ( `Is point U2 on conic QC ?`, point_on_conic ( U2, QC ) ) ;

print ( `Re V1 on  QA, QB, QC, QD, QE, and QF` );
	print ( `Is point V1 on conic QA ?`, point_on_conic ( V1, QA ) ) ;
	print ( `Is point V1 on conic QB ?`, point_on_conic ( V1, QB ) ) ;
	print ( `Is point V1 on conic QC ?`, point_on_conic ( V1, QC ) ) ;
	print ( `Is point V1 on conic QD ?`, point_on_conic ( V1, QD ) ) ;
	print ( `Is point V1 on conic QE ?`, point_on_conic ( V1, QE ) ) ;
	print ( `Is point V1 on conic QF ?`, point_on_conic ( V1, QF ) ) ;

print ( `Re V2 on  QA, QB, QC, QD, QE, and QF` );
	print ( `Is point V2 on conic QA ?`, point_on_conic ( V2, QA ) ) ;
	print ( `Is point V2 on conic QB ?`, point_on_conic ( V2, QB ) ) ;
	print ( `Is point V2 on conic QC ?`, point_on_conic ( V2, QC ) ) ;
	print ( `Is point V2 on conic QD ?`, point_on_conic ( V2, QD ) ) ;
	print ( `Is point V2 on conic QE ?`, point_on_conic ( V2, QE ) ) ;
	print ( `Is point V2 on conic QF ?`, point_on_conic ( V2, QF ) ) ;

print ( `This is the end of the validations.` ) ;