Singular

5.1.91 minres

Syntax:

minres ( list_expression )

Type:

list

Syntax:

minres ( resolution_expression )

Type:

resolution

Purpose:

minimizes a free resolution of an ideal or module given by the list_expression, resp. resolution_expression.

Example:

ring r1=32003,(x,y),dp; ideal i=x5+xy4,x3+x2y+xy2+y3; resolution rs=lres(i,0); rs; ==> 1 2 1 ==> r1 <-- r1 <-- r1 ==> ==> 0 1 2 ==> list(rs); ==> [1]: ==> _[1]=x3+x2y+xy2+y3 ==> _[2]=xy4 ==> [2]: ==> _[1]=xy4*gen(1)-x3*gen(2)-x2y*gen(2)-xy2*gen(2)-y3*gen(2) minres(rs); ==> 1 2 1 ==> r1 <-- r1 <-- r1 ==> ==> 0 1 2 ==> list(rs); ==> [1]: ==> _[1]=x3+x2y+xy2+y3 ==> _[2]=xy4 ==> [2]: ==> _[1]=xy4*gen(1)-x3*gen(2)-x2y*gen(2)-xy2*gen(2)-y3*gen(2)