7.3.13 minres (plural)

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:

LIB "ncalg.lib"; def A = makeUsl2(); setring A; // this algebra is U(sl_2) ideal i=e,f,h; i=std(i); resolution F=nres(i,0); F; ==> 1 3 3 1 ==> A <-- A <-- A <-- A ==> ==> 0 1 2 3 ==> resolution not minimized yet ==> list lF = F; lF; ==> [1]: ==> _[1]=h ==> _[2]=f ==> _[3]=e ==> [2]: ==> _[1]=f*gen(1)-h*gen(2)-2*gen(2) ==> _[2]=e*gen(1)-h*gen(3)+2*gen(3) ==> _[3]=e*gen(2)-f*gen(3)-gen(1) ==> [3]: ==> _[1]=e*gen(1)-f*gen(2)+h*gen(3) print(betti(lF), "betti"); ==> 0 1 2 3 ==> ------------------------------ ==> 0: 1 - 3 1 ==> ------------------------------ ==> total: 1 0 3 1 ==> resolution MF=minres(F); MF; ==> 1 2 2 1 ==> A <-- A <-- A <-- A ==> ==> 0 1 2 3 ==> list lMF = F; lMF; ==> [1]: ==> _[1]=f ==> _[2]=e ==> [2]: ==> _[1]=-ef*gen(1)+f2*gen(2)+2h*gen(1)+2*gen(1) ==> _[2]=-e2*gen(1)+ef*gen(2)+h*gen(2)-2*gen(2) ==> [3]: ==> _[1]=e*gen(1)-f*gen(2) print(betti(lMF), "betti"); ==> 0 1 2 3 ==> ------------------------------ ==> 0: 1 - - - ==> 1: - - 2 1 ==> ------------------------------ ==> total: 1 0 2 1 ==>

See mres (plural); nres (plural).