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D.15.21.1 MPGS
Procedure from library stdmodule.lib (see stdmodule_lib).
- Usage:
- G free module over subalgebra A, A subalgebra(which is finite sagbi basis).
- Return:
- a list W: generating set for syzygies of G over subalgebra A."
Example:
| | LIB "stdmodule.lib";
// Example 1:
ring r=QQ,(x,y),Dp;
ideal A=x2,y2;
module G=[x4+2x2y2-1,y4],[-x2y2,x2y2],[2x2y4-y2,x4y2+y6],[-x2y2,x2y6+x6y2+2x4y4];
MPGS(G,A);
==> [1]:
==> _[1]=x2*gen(2)-x2*gen(1)+y2*gen(1)-gen(3)+gen(2)
==> _[2]=2y4*gen(1)-x2*gen(3)+x2*gen(1)-2y2*gen(3)+2y2*gen(2)-y2*gen(1)+ge\
n(4)-gen(2)
// Example 2:
ring r2=QQ,(x,y),Dp;
ideal A=x2-xy+y, y2+x;
module G=x2y2-xy3+x3-x2y+y3+x2+y, y4+2xy2+x2-y2-x, 2xy-2x2+2xy-2y;
MPGS(G,A);
==> [1]:
==> _[1]=gen(3)-gen(2)
==> _[2]=x2*gen(2)-x2*gen(1)-xy*gen(2)+xy*gen(1)-y2*gen(1)-x*gen(1)+y*gen(\
2)-y*gen(1)
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