Singular

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