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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

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