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3.12 minres

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:

 
ring A=0,(x,y,z),Dp;
matrix d[3][3];
d[1,2]=-z;
d[1,3]=2x;
d[2,3]=-2y;
ncalgebra(1,d);
ideal i=x,y,z;
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
==> 
int a;
for (a=1;a<=size(list(F));a++)
{
printf("Module: %s",a);
print(matrix(F[a]));
}
==> Module: 1
==> z,y,x
==> Module: 2
==> y,   x,   -1,
==> -z-2,0,   x, 
==> 0,   -z+2,-y 
==> Module: 3
==> x, 
==> -y,
==> z  
resolution MF=minres(F);
MF;
==>  1      3      3      1      
==> A <--  A <--  A <--  A
==> 
==> 0      1      2      3      
==> 
for (a=1;a<=size(list(MF));a++)
{
printf("Module: %s",a);
print(matrix(MF[a]));
}
==> Module: 1
==> y,x
==> Module: 2
==> -xy+2z+2,-x2,  
==> y2,      xy+z-2
==> Module: 3
==> x,
==> -y

See mres; nres.


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