Singular Manual: schreyerSyzExt

D.15.24.1 schreyerSyzExt

Procedure from library sresext.lib (see sresext_lib).

Usage:: schreyerSyzExt(m); m a module over the exterior algebra.
Return:: module
Purpose:: computes the syzygy module of a m over the exterior algebra.
Theory:

Example:

LIB "sresext.lib";
ring r = (0,q),(x,y,z),dp;
def e = Exterior(); setring e;
vector f1 = [x,y,0,z,0,0];
vector f2 = [0,x,y,0,z,0];
vector f3 = [0,0,0,x,y,z];
module m = f1,f2,f3;
m = std(m);
schreyerSyzExt(m);
==> _[1]=-x*gen(1)-y*gen(2)-z*gen(3)
==> _[2]=-x*gen(2)+gen(4)
==> _[3]=-x*gen(4)
==> _[4]=-x*gen(3)+gen(5)
==> _[5]=-x*gen(5)
==> _[6]=-x*gen(6)
==> _[7]=y*gen(4)+z*gen(5)
==> _[8]=y*gen(5)+gen(6)
==> _[9]=y*gen(6)
==> _[10]=-z*gen(6)