Use R ::= Q[t,x,y,z];
Define Det_SubAlgebra(N)
L := [];
For C1 := 1 To N-1 Do
For C2 := C1+1 To N Do
P := y[C1,C2]-(x[1,C1] x[2,C2] - x[2,C1] x[1,C2]);
Append(L,P)
EndFor
Endfor;
Return Ideal(L)
EndDefine;
Define Det_SubAlgebra_Print(N) -- calculate and print relations
J := Det_SubAlgebra(N);
PrintLn NewLine,'N = ',N;
PrintLn 'Sub-algebra equations:';
PrintLn Gens(Elim(x,J))
EndDefine;
Set Indentation;
For N := 3 To 5 Do
S ::= Z/(32003)[y[1..(N-1),2..N],x[1..2,1..N]];
Using S Do
Det_SubAlgebra_Print(N);
EndUsing
EndFor;
N = 3
Sub-algebra equations:
[
0]
N = 4
Sub-algebra equations:
[
2y[1,4]y[2,3] - 2y[1,3]y[2,4] + 2y[1,2]y[3,4]]
N = 5
Sub-algebra equations:
[
2y[2,5]y[3,4] - 2y[2,4]y[3,5] + 2y[2,3]y[4,5],
2y[1,5]y[3,4] - 2y[1,4]y[3,5] + 2y[1,3]y[4,5],
2y[1,5]y[2,4] - 2y[1,4]y[2,5] + 2y[1,2]y[4,5],
2y[1,5]y[2,3] - 2y[1,3]y[2,5] + 2y[1,2]y[3,5],
2y[1,4]y[2,3] - 2y[1,3]y[2,4] + 2y[1,2]y[3,4]]
-------------------------------
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