|
7.3.18 nres (plural)
Syntax:
nres ( ideal_expression, int_expression )
nres ( module_expression, int_expression )
Type:
- resolution
Purpose:
- computes a free resolution of an ideal or module which is minimized
from the second module on (by the Groebner basis method).
Note: Assigning a resolution to a list is the best choice of usage. The resolution may be minimized by using the
- command
minres . Use the command betti to compute Betti numbers.
Example:
| LIB "ncalg.lib";
def A = makeUsl2();
setring A; // this algebra is U(sl_2)
option(redSB);
option(redTail);
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 l = F; l;
==> [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)
// see the exactness at this point:
size(ideal(transpose(matrix(l[2]))*transpose(matrix(l[1]))));
==> 0
// see the exactness at this point:
size(ideal(transpose(matrix(l[3]))*transpose(matrix(l[2]))));
==> 0
print(betti(l), "betti");
==> 0 1 2 3
==> ------------------------------
==> 0: 1 - 3 1
==> ------------------------------
==> total: 1 0 3 1
==>
print(betti(minres(l)), "betti");
==> 0 1 2 3
==> ------------------------------
==> 0: 1 - - -
==> 1: - - 2 1
==> ------------------------------
==> total: 1 0 2 1
==>
|
See
ideal (plural);
minres (plural);
module (plural);
mres (plural).
|