Singular Manual: Ssyz

| #### D.15.22.3 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]=y*gen(2)-z*gen(3)
    ==>    _[2]=x*gen(2)-z*gen(4)
    ==>    _[3]=x*gen(3)-y*gen(4)
    MRES; // Note gen(i)
    ==> MRES[1]=0
    ==> MRES[2]=z*gen(1)
    ==> MRES[3]=y*gen(1)
    ==> MRES[4]=x*gen(1)
    ==> MRES[5]=y*gen(2)-z*gen(3)
    ==> MRES[6]=x*gen(2)-z*gen(4)
    ==> MRES[7]=x*gen(3)-y*gen(4)
    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)
See also: Sres.

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