5.1.73 minor

Syntax:

minor ( matrix_expression, int_expression )
minor ( matrix_expression, int_expression, ideal_expression )

Type:

ideal

Purpose:

returns the set of all minors (=subdeterminants) of the given size of a matrix. The optional third argument must be a standard basis. If a third argument is given, the computations will be performed modulo that ideal.

Example:

ring r=0,(x(1..5)),ds; matrix m[2][4]=x(1..4),x(2..5); print(m); → x(1),x(2),x(3),x(4), → x(2),x(3),x(4),x(5) ideal j=minor(m,2); j; → j[1]=-x(4)^2+x(3)*x(5) → j[2]=-x(3)*x(4)+x(2)*x(5) → j[3]=-x(2)*x(4)+x(1)*x(5) → j[4]=x(3)^2-x(2)*x(4) → j[5]=x(2)*x(3)-x(1)*x(4) → j[6]=-x(2)^2+x(1)*x(3) minor(m,2,std(ideal(x(1)))); → _[1]=-x(4)^2+x(3)*x(5) → _[2]=-x(3)*x(4)+x(2)*x(5) → _[3]=-x(2)*x(4) → _[4]=x(3)^2-x(2)*x(4) → _[5]=x(2)*x(3) → _[6]=-x(2)^2

See det.