#Author := Ayoola Jinadu
# If you find a bug in the code please email me at ajinadu@sfu.ca


Sys := [

aa * t2^2 * t1^2 * b2^2 * b1^2 + 2 * l1 * t1^2 * b2^2 * b1^2 + aa *
t1^2 * b2^2 * b1^2 - 2 * l1 * t2^2 * b2^2 * b1^2 + aa * t2^2 * b2^2
* b1^2 + aa * b2^2 * b1^2
 + 2 * l2 * t2^2 * t1^2 * b1^2 + aa * t2^2 * t1^2 * b1^2 + 2 * l2 *
t1^2 * b1^2 + 2 * l1 * t1^2 * b1^2 + aa * t1^2 * b1^2 + 2 * l2 *
t2^2 * b1^2 - 2 * l1 * t2^2 * b1^2
 + aa * t2^2 * b1^2 + 2 * l2 * b1^2 + aa * b1^2 - 2 * l2 * t2^2 *
t1^2 * b2^2 + aa * t2^2 * t1^2 * b2^2 - 2 * l2 * t1^2 * b2^2 + 2 *
l1 * t1^2 * b2^2 + aa * t1^2 * b2^2
 - 2 * l2 * t2^2 * b2^2 - 2 * l1 * t2^2 * b2^2 + aa * t2^2 * b2^2 -
2 * l2 * b2^2 + aa * b2^2 + aa * t2^2 * t1^2 + 2 * l1 * t1^2 + aa *
t1^2 - 2 * l1 * t2^2 + aa * t2^2 + aa,


2 * l1 * t2 * t1^2 * b2^2 * b1^2 - 2 * l1 * t2^2 * t1 * b2^2 * b1^
2 - 2 * l1 * t1 * b2^2 * b1^2 + 2 * l1 * t2 * b2^2 * b1^2 + 2 * l2
* t2^2 * t1^2 * b2 * b1^2
 + 2 * l2 * t1^2 * b2 * b1^2 + 2 * l2 * t2^2 * b2 * b1^2 + 2 * l2
* b2 * b1^2 + 2 * l1 * t2 * t1^2 * b1^2 - 2 * l1 * t2^2 * t1 * b1^
2 - 2 * l1 * t1 * b1^2 + 2 * l1 * t2 * b1^2
 - 2 * l2 * t2^2 * t1^2 * b2^2 * b1 - 2 * l2 * t1^2 * b2^2 * b1 - 2
* l2 * t2^2 * b2^2 * b1 - 2 * l2 * b2^2 * b1 - 2 * l2 * t2^2 * t1^
2 * b1 - 2 * l2 * t1^2 * b1 - 2 * l2 * t2^2 *
b1 - 2 * l2 * b1 + 2 * l1 * t2 * t1^2 * b2^2 - 2 * l1 * t2^2 * t1
* b2^2 - 2 * l1 * t1 * b2^2 + 2 * l1 * t2 * b2^2 + 2 * l2 * t2^2 *
t1^2 * b2 + 2 * l2 * t1^2 * b2
 + 2 * l2 * t2^2 * b2 + 2 * l2 * b2 + 2 * l1 * t2 * t1^2 - 2 * l1
* t2^2 * t1 - 2 * l1 * t1 + 2 * l1 * t2,


 - al^2 * x * t1^2 * b1^2 - x * t1^2 * b1^2 - l3 * al^2 * t1^2 * b1^2
- l2 * al^2 * t1^2 * b1^2 - l1 * al^2 * t1^2 * b1^2 + l3 * t1^2 *
b1^2 - l2 * t1^2 * b1^2
 - l1 * t1^2 * b1^2 - al^2 * x * b1^2 - x * b1^2 - l3 * al^2 * b1^2
- l2 * al^2 * b1^2 + l1 * al^2 * b1^2 + l3 * b1^2 - l2 * b1^2 + l1
* b1^2 - 4 * l3 * al * t1^2 *
b1 - 4 * l3 * al * b1 - al^2 * x * t1^2 - x * t1^2 + l3 * al^2 * t1^2
+ l2 * al^2 * t1^2 - l1 * al^2 * t1^2 - l3 * t1^2 + l2 * t1^2 - l1
* t1^2 - al^2 * x - x
 + l3 * al^2 + l2 * al^2 + l1 * al^2 - l3 + l2 + l1,

 - al^2 * y * t1^2 * b1^2 - y * t1^2 * b1^2 - 2 * l3 * al * t1^2 *
b1^2 + 2 * l1 * al^2 * t1 * b1^2 + 2 * l1 * t1 * b1^2 - al^2 * y *
b1^2 - y * b1^2 - 2 * l3 * al * b1^2  + 2 * l3 * al^2 * t1^2 * b1 + 2
* l2 * al^2 * t1^2 * b1 - 2 * l3 * t1^2 * b1 + 2 * l2 * t1^2 * b1
+ 2 * l3 * al^2 * b1 + 2 * l2 * al^2 * b1 - 2 * l3 * b1 + 2 * l2 *
b1 - al^2 * y * t1^2 - y * t1^2 + 2 * l3 * al * t1^2 + 2 * l1 * al^2 *
t1 + 2 * l1 * t1 - al^2 * y - y + 2 * l3 * al]:

elim := [t2,b1,b2];
 read det; read newdeg;
 read dixon;read minor; read dixres; read nextprime; read Bmbot;
 with(LinearAlgebra):

    M := dixonmatrix( Sys, elim ):
    rank,rows,cols := minor(M):
    B := M[rows,cols]: # extract minor
    L := StronglyConnectedBlocks(B):
    BlockStructure = map(RowDimension,L);


    X := [t1, aa, al, l1, l2, l3, x, y];
    R := convert(L[1],listlist): 
    n := RowDimension(R); LL := R:
    deg_M := [seq( max(seq(seq(degree(LL[i][j],var),i=1..n),j=1..n)), var in X )];
    rt := [R,X,n ]:
    GlobalCArray := Array(0..n-1,0..n-1,order=C_order,datatype=integer[8]):
    E :=  DixonRes(BB,X);
    nops( expand(E) );