Singular Manual: modSyz

D.4.18.3 modSyz

Procedure from library modstd.lib (see modstd_lib).

Usage:: modSyz(I); I ideal/module
Return:: a generating set of syzygies of I
Note:: The procedure computes a the syzygy module of I (over the rational numbers) by using modular methods with high probability. The property of being a syzygy is tested.

Example:

LIB "modstd.lib";
ring R1 = 0, (x,y,z,t), dp;
ideal I = 3x3+x2+1, 11y5+y3+2, 5z4+z2+4;
modSyz(I);
==> _[1]=z4*gen(1)-3/5x3*gen(3)-1/5x2*gen(3)+1/5z2*gen(1)-1/5*gen(3)+4/5*gen(\
   1)
==> _[2]=y5*gen(1)-3/11x3*gen(2)+1/11y3*gen(1)-1/11x2*gen(2)-1/11*gen(2)+2/11\
   *gen(1)
==> _[3]=y5*gen(3)-5/11z4*gen(2)+1/11y3*gen(3)-1/11z2*gen(2)+2/11*gen(3)-4/11\
   *gen(2)
simplify(syz(I),1);
==> _[1]=z4*gen(1)-3/5x3*gen(3)-1/5x2*gen(3)+1/5z2*gen(1)-1/5*gen(3)+4/5*gen(\
   1)
==> _[2]=y5*gen(1)-3/11x3*gen(2)+1/11y3*gen(1)-1/11x2*gen(2)-1/11*gen(2)+2/11\
   *gen(1)
==> _[3]=y5*gen(3)-5/11z4*gen(2)+1/11y3*gen(3)-1/11z2*gen(2)+2/11*gen(3)-4/11\
   *gen(2)