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7.3.11 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
==> 
print(matrix(F[1])); // print F's compactly
==> h,f,e
print(matrix(F[2]));
==> f,   e,   -1,
==> -h-2,0,   e, 
==> 0,   -h+2,-f 
print(matrix(F[3]));
==> e, 
==> -f,
==> h  
resolution MF=minres(F);  MF;
==>  1      3      3      1      
==> A <--  A <--  A <--  A
==> 
==> 0      1      2      3      
==> 
print(matrix(MF[1]));
==> f,e
print(matrix(MF[2]));
==> -ef+2h+2,-e2,  
==> f2,      ef+h-2
print(matrix(MF[3]));
==> e,
==> -f

See mres (plural); nres (plural).


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