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5.1.75 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.

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