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D.13.6.38 initial

Procedure from library tropical.lib (see tropical_lib).

Usage:
initial(f,w); f poly, w intvec or bigintmat
initial(I,w); I ideal, w intvec or bigintmat

Assume:
I reduced Groebner basis,
w in the maximal Groebner cone of I with respect to the current ordering

Return:
poly or ideal, the initial form of f or the initial ideal of I with respect to w

Example:
 
LIB "tropical.lib";
ring r = 0,(x,y,z),dp;
ideal I = cyclic(3);
intvec w = 1,1,1;
option(redSB);
ideal stdI = std(I);
stdI;
==> stdI[1]=x+y+z
==> stdI[2]=y2+yz+z2
==> stdI[3]=z3-1
ideal inI = initial(stdI,w);
inI;
==> inI[1]=x+y+z
==> inI[2]=y2+yz+z2
==> inI[3]=z3