5.1.74 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 → resolution not minimized yet → list(rs); → [1]: → _[1]=x3+x2y+xy2+y3 → _[2]=xy4 → _[3]=y7 → [2]: → _[1]=-y4*gen(1)+x2*gen(2)+xy*gen(2)+y2*gen(2)+gen(3) → _[2]=-y3*gen(2)+x*gen(3) 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)

See mres; res; sres.