Singular Manual: Ssyz

D.2.12.3 Ssyz

Procedure from library schreyer.lib (see schreyer_lib).

Usage:: Ssyz(module M)
Return:: ring, containing a Schreyer resolution
Purpose:: computes a Schreyer resolution of M of length 1 (see the library overview)

Example:

LIB "schreyer.lib";
ring r;
module M = maxideal(1); M;
==> M[1]=x*gen(1)
==> M[2]=y*gen(1)
==> M[3]=z*gen(1)
def S = Ssyz(M); setring S; S;
==> //   characteristic : 32003
==> //   number of vars : 3
==> //        block   1 : ordering IS(0)
==> //        block   2 : ordering dp
==> //                  : names    x y z
==> //        block   3 : ordering C
==> //        block   4 : ordering IS(1)
"Only the first syzygy: ";
==> Only the first syzygy: 
RES;
==> [1]:
==>    _[1]=0
==> [2]:
==>    _[1]=z*gen(1)
==>    _[2]=y*gen(1)
==>    _[3]=x*gen(1)
==> [3]:
==>    _[1]=z*gen(3)-y*gen(2)
==>    _[2]=z*gen(4)-x*gen(2)
==>    _[3]=y*gen(4)-x*gen(3)
MRES; // Note gen(i)
==> MRES[1]=0
==> MRES[2]=z*gen(1)
==> MRES[3]=y*gen(1)
==> MRES[4]=x*gen(1)
==> MRES[5]=z*gen(3)-y*gen(2)
==> MRES[6]=z*gen(4)-x*gen(2)
==> MRES[7]=y*gen(4)-x*gen(3)
kill S;
setring r; kill M;
module M = 0;
def S = Ssyz(M); setring S; S;
==> //   characteristic : 32003
==> //   number of vars : 3
==> //        block   1 : ordering IS(0)
==> //        block   2 : ordering dp
==> //                  : names    x y z
==> //        block   3 : ordering C
==> //        block   4 : ordering IS(1)
"Only the first syzygy: ";
==> Only the first syzygy: 
RES;
==> [1]:
==>    _[1]=0
==> [2]:
==>    _[1]=0
==> [3]:
==>    _[1]=gen(2)
MRES;
==> MRES[1]=0
==> MRES[2]=0
==> MRES[3]=gen(2)