Top
Back: sagbiRreduction
Forward: sagbiNF
FastBack: reszeta_lib
FastForward: sheafcoh_lib
Up: sagbi_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.4.22.2 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 the ideal of algebraic
        relations is defined.

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


Top Back: sagbiRreduction Forward: sagbiNF FastBack: reszeta_lib FastForward: sheafcoh_lib Up: sagbi_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-1, Feb 2010, generated by texi2html.