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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      3      3      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).