Singular Manual: initial

  | #### D.16.1.1 initial `Syntax:` `initial(` poly f, intvec v `)` `initial(` poly f, bigintmat v `)` `initial(` ideal I, intvec v `)` `initial(` ideal I, bigintmat v `)` `Assume:` v has as many entries as there are variables in the basering. `Type:` poly or ideal `Purpose:` computes the initial form of the polynomial f or the initial forms of the generators of I with respect to weight vector v `Note:` for the initial forms of the generators to generate the initial ideal, I must be a reduced standard basis and v has to lie in the maximal Groebner cone of the current ordering. `Example:`
      LIB "gfanlib.so";
      ring r = 0,(x,y),dp;
      poly g = x+y+1;
      initial(g,intvec(1,1));
      ==> x+y
      initial(g,intvec(-1,0));
      ==> y+1
      initial(g,intvec(0,-1));
      ==> x+1

      ideal I = x2-y3,x3-y2-x;
      I = std(I);
      initial(I,intvec(1,1));
      ==> _[1]=y3
      ==> _[2]=x3

User manual for Singular version 4-0-3p3, 2016, generated by texi2html.