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D.15.17.4 SGB
Procedure from library sagbigrob.lib (see sagbigrob_lib).
- Usage:
- SGB(I,A); I ideal of subalgebra A, A subalgebra (which is a finite sagbi basis).
- Return:
- an ideal SB.
Example:
| | LIB "sagbigrob.lib";
// Example 1:
ring r=ZZ,(x,y),Dp;
ideal A=2x2+xy,2y2,3xy;
ideal I=4x2y2+2xy3,18x2y4;
SGB(I,A);
==> 18xy5
==> 0
==> 0
==> -2x2y6+8xy7
==> 0
==> 0
==> 0
==> _[1]=4x2y2+2xy3
==> _[2]=18x2y4
==> _[3]=18xy5
==> _[4]=-2x2y6+8xy7
// Example 2:
ring r2=QQ,(w,x,y,z),lp;
ideal A=wxy+2z2, y2-4z, x+3y;
ideal I= wxy-y2+2z2+4z, x+y2+3y-4z, x2+6xy+9y2;
SGB(I,A);
==> 0
==> -y6+12y4z-48y2z2+64z3
==> 0
==> _[1]=wxy-y2+2z2+4z
==> _[2]=x+y2+3y-4z
==> _[3]=x2+6xy+9y2
==> _[4]=-y6+12y4z-48y2z2+64z3
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