Counterexample
The collection of points
> | restart: |
> | A:=[0,0];B:=[1,0];C:=[0,alpha];DD:=[infinity , 0] ; EE:=[-3*alpha+1,-1];F:=[-2*alpha,alpha]; G:=[2,-1]; H:=[0,1]; |
![]() |
|
![]() |
|
![]() |
|
![]() |
|
![]() |
|
![]() |
|
![]() |
|
![]() |
(4.3.1.1) |
> | alpha:=I/sqrt(3); |
![]() |
(4.3.1.2) |
> | with(linalg):matrix(3,3,[1,F[1],F[2],1,H[1],H[2],1,EE[1],EE[2]]); |
![]() |
(4.3.1.3) |
> | L1:=det(%); |
![]() |
(4.3.1.4) |
> | matrix(3,3,[1,B[1],B[2],1,C[1],C[2],1,EE[1],EE[2]]); |
![]() |
(4.3.1.5) |
> | L2:=det(%); |
![]() |
(4.3.1.6) |
> | matrix(3,3,[1,F[1],F[2],1,G[1],G[2],1,A[1],A[2]]); |
![]() |
(4.3.1.7) |
> | L3:=det(%); |
![]() |
(4.3.1.8) |
> |
> |
verify the hypothesis but not the conclusion of Maclane's theorem.