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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
See ideal (plural); minres (plural); module (plural); mres (plural).


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