|
|
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).
|
Online Manual
