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7.3.15 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).
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
==>
// print the resolution componentwise:
print(matrix(F[1]));
==> h,f,e
print(matrix(F[2]));
==> f, e, -1,
==> -h-2,0, e,
==> 0, -h+2,-f
// see the exactness at this point:
std(ideal(transpose(F[2])*transpose(F[1])));
==> _[1]=0
print(matrix(F[3]));
==> e,
==> -f,
==> h
// see the exactness at this point:
std(ideal(transpose(F[3])*transpose(F[2])));
==> _[1]=0
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See
ideal (plural);
minres (plural);
module (plural);
mres (plural).
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