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D.4.20.2 sagbiSPoly
Procedure from library sagbi.lib (see sagbi_lib).
- Usage:
- sagbiSPoly(id [,n]); id ideal, n positive integer.
- Return:
- an ideal
| - If (n=0 or default) an ideal, whose generators are the S-polynomials.
- If (n=1) a list of size 2:
the first element of this list is the ideal of S-polynomials.
the second element of this list is the ring in which is defined
the ideal of algebraic relations.
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Example:
| LIB "sagbi.lib";
ring r=0, (x,y),dp;
poly f1,f2,f3,f4=x2,y2,xy+y,2xy2;
ideal I=f1,f2,f3,f4;
sagbiSPoly(I);
==> _[1]=xy2+1/2y2
==> _[2]=xy4+1/2y4
==> _[3]=x3y4+3/2x2y4+xy4+1/4y4
list L=sagbiSPoly(I,1);
==>
==> // 'sagbiSPoly' created a ring as 2nd element of the list.
==> // The ring contains the ideal 'kern' of algebraic relations between the
==> //leading terms of the generators of I.
==> // To access to this ring and see 'kern' you should give the ring a name,
==> // e.g.:
==> def S = L[2]; setring S; kern;
==>
L[1];
==> _[1]=xy2+1/2y2
==> _[2]=xy4+1/2y4
==> _[3]=x3y4+3/2x2y4+xy4+1/4y4
def S= L[2]; setring S; kern;
==> kern[1]=@y(1)*@y(2)-@y(3)^2
==> kern[2]=4*@y(2)*@y(3)^2-@y(4)^2
==> kern[3]=4*@y(3)^4-@y(1)*@y(4)^2
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