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