Top
Back: ncalgebra
Forward: oppose
FastBack: Functions
FastForward: Mathematical background
Up: Functions
Top: Plural Manual
Contents: Table of Contents
Index: Index
About: About this document

3.16 nres

Syntax:
nres ( ideal_expression, int_expression )
nres ( module_expression, int_expression )
Type:
resolution
Purpose:
computes a free resolution of an ideal or module M which is minimized from the second module on (by the Groebner basis method).

 
LIB "poly.lib";
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);
// now we print the resolution componentwise
// and check that F is indeed exact
F;
==>  1      3      3      1      
==> A <--  A <--  A <--  A
==> 
==> 0      1      2      3      
==> resolution not minimized yet
==> 
for (int a=1;a<=size(list(F));a++)
{ 
  printf("Module: %s",a);
  print(matrix(F[a]));
  if (a>1)
  {
    printf("Obstruction of exactness at: (%s,%s)",a-1,a);
    std(flatten(transpose(F[a])*transpose(F[a-1])));
  }
}
==> Module: 1
==> z,y,x
==> Module: 2
==> y,   x,   -1,
==> -z-2,0,   x, 
==> 0,   -z+2,-y 
==> Obstruction of exactness at: (1,2)
==> _[1]=0
==> Module: 3
==> x, 
==> -y,
==> z  
==> Obstruction of exactness at: (2,3)
==> _[1]=0

See ideal; minres; module; mres.


Top Back: ncalgebra Forward: oppose FastBack: Functions FastForward: Mathematical background Up: Functions Top: Plural Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 2-1-99, August 2004, generated by texi2html.